#### Transcript Q 1 - Wiley

Presentation Slides Microeconomics David Besanko & Ronald R. Braeutigam 3rd Edition Start 1 About This Presentation • Use the menu buttons on the left of each slide to navigate the presentation. You may also just click anywhere in the presentation to advance one slide or hit the “escape” button to exit the slide show; • The “Information” icon at the bottom right of some of the slides is an Internet link to relevant information. Click on it and you will be taken to an appropriate Internet site for reference. Once you close or minimize the Internet site you will return to the last slide you were viewing; • The Internet links work only when in “Slide Show” mode; • Here are the commands for the following icons: Navigation Key Home- Presentation Beginning Index - Last Slide Take me to Wiley Publishing Chapters - Chapter Overview Back One Slide Forward One Slide Back to the Last Slide Viewed 2 About Chapter Directory Take me to the Text: 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: Analyzing Economic Problems Demand and Supply Analysis Consumer Preferences and the Concept of Utility Consumer Choice The Theory of Demand Inputs and Production Functions Costs and Cost Minimization Cost Curves Perfectly Competitive Markets Competitive Markets: Applications Monopoly and Monopsony Capturing Surplus Market Structure and Competition Game Theory and Strategic Behavior Risk and Information General Equilibrium Theory Externalities and Public Goods 3 Chapter Directory Chapter One Analyzing Economic Problems 4 Chapter One Chapter One Overview 1. Defining Microeconomics 2. Who Should Study Microeconomics? 3. Microeconomic Modeling • Elements of Models • Solving the Models 4. The Types of Microeconomic Analysis 5 Chapter One Microeconomics Defined Microeconomics is the study of the economic behavior of individual economic decisionmakers such as consumers, workers, firms or managers. This study involves both the behavior of these economic agents on their own and the way their behavior interacts to form larger units, such as markets. 6 Chapter One Who Should Study Microeconomics? Example: The Railroad Industry in the US 74.9% of all freight, 1929 39.8% of all freight, 1970 1970’s: • Poor profits, bankruptcies, and an inability to invest 1980’s: • Loosened regulation and union rules improved profitability 7 Chapter One Who Should Study Microeconomics? Analysis of these issues requires Microeconomic tools and the key players below need to know something about Microeconomics. Policy Makers Managers Union Leaders Lenders Business Owners 8 Chapter One Microeconomics and Global Warming Analysis of the impact of Global Warming on: World Economic Stability National Economic Policies Consumer Spending Economic Partnerships Trade Agreements 9 Chapter One Key Societal Questions Societies must answer these questions that relate to microeconomics: 1. What goods and services will be produced and in what quantities 2. Who will produces these services and how will they produce them 3. Who will receive these goods and services and how will they get them 10 Chapter One Microeconomic Modeling Choice vs. Alternatives Models are like maps – using visual methods, they simply the process and facilitate understanding of complex concepts. Microeconomic models need to: Resemble Reality Be Understandable Be an Appropriate Scale 11 Chapter One Microeconomic Modeling Choice vs. Alternatives Price Per Pound Supply (P,W) Example: World-wide market for unprocessed coffee beans, December, 1997 Quantity in Pounds 12 Chapter One Microeconomic Modeling Choice vs. Alternatives Price Per Pound Supply (P,W) Example: World-wide market for unprocessed coffee beans, December, 1997 Demand (P,I) Quantity in Pounds 13 Chapter One Opportunity Cost Dependent on How One Specifies Alternatives Defined: The Opportunity Cost of a resource is the value of that resource in its best alternative use. • $100 in facilities yields $800 Revenue • $100 in R&D yields $1000 revenue • Opportunity cost of investing in facilities = $1000 • Opportunity cost if investing in R&D = $800 14 Chapter One The Objective Function Dependent on How the Objective Function is Specified Defined: The Objective Function specifies what the agent cares about. • Does manager care more about raising profits or increasing “power”? 15 Chapter One The Constraints Defined: Constrains are whatever limits is placed on the resources available to the agent. Time Budget Other Resources Technical Capabilities The Marketplace Rules, Regulations, and Laws 16 Chapter One The Constraint Optimization Behavior can be modeled as optimizing the objective function, subject to various constraints. Manager’s Investment Choice • Facilities ( F ): • R&D ( R ): N = budget / $30 N = budget / $100 Cost Per Unit of Time • Max N • (F,R) • Subject to: expenditure < $100 • Where: N is the number of workers • Facilities workers cost $30 • R&D workers cost $100 17 Chapter One The Constraint Optimization Consumer purchases Food (F), Clothing ( C ), Income (I) Price of food (pf), price of clothing (pc) Satisfaction from purchases: S = (FC)1/2 Max S(F,C) - subject to: pfF + pcC < I Note: "as if modeling" 18 Chapter One The Constraint Optimization Example – Consumer Purchases F PFF + PCC = I 0 C Chapter One 19 The Constraint Optimization Example – Consumer Purchases F PFF + PCC = I (FC)1/2 = S0 0 C Chapter One 20 The Constraint Optimization Example – Consumer Purchases F PFF + PCC = I (FC)1/2 = S1 (FC)1/2 = S0 0 C Chapter One 21 The Constraint Optimization Example – Consumer Purchases F PFF + PCC = I S2 > S1 > S0 (FC)1/2 = S2 (FC)1/2 = S1 (FC)1/2 = S0 0 C Chapter One 22 Exogenous & Endogenous Variables Defined: Variables that have values taken as given in the analysis are exogenous variables. Variables that have values determined as a result of the model’s workings are endogenous variables. “How would a manager hire the most possible workers on a budget of $100?” vs. “How would a manager minimize the cost of hiring three workers?” OR “How much food and clothing should the consumer purchase in order to maximize satisfaction on a budget of I?” vs. “What is the minimum level of expenditure that the consumer must receive in order to reach a subsistence level of satisfaction?” 23 Chapter One Equilibrium Defined: Equilibrium is defined as the point where demand just equals supply in this market (i.e., the point where the demand and supply curves cross). Equilibrium analysis is an analysis of a system in a state that will continue indefinitely as long as the exogenous factors remain unchanged. 24 Chapter One Equilibrium Example – Sale of Coffee Beans 25 Chapter One Equilibrium Example – Sale of Coffee Beans • Demand (P,I) 26 Chapter One Equilibrium Example – Sale of Coffee Beans P* • Demand (P,I) Q* 27 Chapter One Comparative Statics Analysis Defined: A Comparative Statics Analysis compares the equilibrium state of a system before a change in the exogenous variables to the equilibrium state after the change. 28 Chapter One Equilibrium 29 Chapter One Equilibrium • Demand (P,I) 30 Chapter One Equilibrium • • New Supply (P,W) Demand (P,I) 31 Chapter One Equilibrium P * P** • • New Supply (P,W) Demand (P,I) Q* Q** Chapter One 32 Consumer Choice Revisited 33 Chapter One Consumer Choice Revisited (FC)1/2 = S0 • 34 Chapter One Consumer Choice Revisited (FC)1/2 = S0 • PFF + PCC = I1 35 Chapter One Consumer Choice Revisited (FC)1/2 = S0 • • (FC)1/2 = S1 PFF + PCC = I1 36 Chapter One Consumer Choice Revisited S0 > S1 I0 > I 1 (FC)1/2 = S0 F* F** • • (FC)1/2 = S1 PFF + PCC = I1 C** C* 37 Chapter One Marginal Impact Defined: The Marginal Impact of a change in the exogenous variable is the incremental impact of the last unit of the exogenous variable on the endogenous variable. 38 Chapter One Marginal Impact Advertising Example Budget = $1M to allocate between TV ( T ) and radio ( R ) Problem: Max B(T,R) (T,R) Subject to: pTT + pRR < $1m where: B is "barrels“ and pT, pR are the prices of TV and radio advertising, respectively. 39 Chapter One Marginal Impact Advertising Example 40 Chapter One Microeconomic Analysis Some Types Positive Analysis: • Can explain what has happened due to an economic policy or it can predict what might happen due to an economic policy. Normative Analysis: • Is an analysis of what should be done 41 Chapter One Microeconomic Analysis Some Examples Example: “Should we increase income equality rather than focus on economic efficiency?” Example: “Should we impose a progressive income tax or a sales tax to increase income equality?” Example: “Will a progressive income tax reduce aggregate hours worked?” 42 Chapter One Chapter Two Demand and Supply Analysis 43 Chapter Two Chapter Two Overview 1. Motivation – U.S. dot coms 2. Competitive Markets Defined 3. The Market Demand Curve 4. The Market Supply Curve 5. Equilibrium 6. Characterizing Demand and Supply – Elasticity 7. Back of the Envelope Techniques 44 Chapter Two Motivations Example: 1995 U.S. Corn Market Historical price: $2.00 per bushel Prices rose to $2.70 per bushel • Long term contracts based on this price Prices rise to $5.00 per bushel • Litigation to annul contracts Why? • Weather • Asian economic boom 45 Chapter Two Motivations Example: 1995 U.S. Corn Market Historical price: $2.00 per bushel Prices return to $2.00 per bushel Why? • Increased acreage • Asian economic cool-down 46 Chapter Two Competitive Markets Defined: Competitive Markets are those with sellers and buyers that are small and numerous enough that they take the market price as given when they decide how much to buy and sell. 47 Chapter Two The Market Demand Function Defined: The Market Demand Function tells us how the quantity of a good demanded by the sum of all consumers in the market depends on various factors. 48 Chapter Two Demand Curves Defined: The Demand Curve plots the aggregate quantity of a good that consumers are willing to buy at different prices, holding constant other demand drivers such as prices of other goods, consumer income, quality. 49 Chapter Two The Demand for Cars 50 Chapter Two The Demand for Cars We always graph P on vertical axis and Q on horizontal axis, but we write demand as Q as a function of P… If P is written as function of Q, it is called the inverse demand. Markets defined by commodity, geography, time. 51 Chapter Two The Law of Demand Defined: The Law of Demand states that the quantity of a good demanded decreases when the price of this good increases. The Demand Curve shifts when factors other than own price change such as: If the change increases the willingness of consumers to acquire the good, the demand curve shifts right If the change decreases the willingness of consumers to acquire the good, the demand curve shifts left 52 Chapter Two Demand Curve Rule Defined: A move along the demand curve for a good can only be triggered by a change in the price of that good. Any change in another factor that affects the consumers’ willingness to pay for the good results in a shift in the demand curve for the good. 53 Chapter Two Market Supply vs. Demand Tells us how the quantity of a good supplied by the sum of all producers in the market depends on various factors Plots the aggregate quantity of a good that will be offered for sale at different prices. 54 Chapter Two Supply Curve for Wheat 55 Chapter Two The Law of Supply Defined: The Law of Supply states that the quantity of a good offered increases when the price of this good increases. The Supply Curve shifts when factors other than own price change such as: If the change increases the willingness of producers to offer the good at the same price, the supply curve shifts right If the change decreases the willingness of producers to offer the good at the same price, the supply curve shifts left 56 Chapter Two Supply Curve Rule Defined: A move along the supply curve for a good can only be triggered by a change in the price of that good. Any change in another factor that affects the producers’ willingness to offer for the good results in a shift in the supply curve for the good. 57 Chapter Two Example: Canadian Wheat Supply Curve Rule Example QS = p + .05r QS = quantity of wheat (billions of bushels) p = price of wheat (dollars per bushel) r = average rainfall in western Canada, May – August (inches per month) 58 Chapter Two Example: Canadian Wheat Supply Curve Rule Example a. Quantity of wheat supplied at price of $2 and rainfall of 3 inches per month = 2.15 b. Supply curve when rainfall is 3 inches per month: QS = p + 0.15 c. Law of supply holds d. As rainfall increases, supply curve shifts right (e.g., r = 4 => Q = p + 0.2) 59 Chapter Two Example: Canadian Wheat 60 Chapter Two Example: Canadian Wheat .15 61 Chapter Two Market Equilibrium Defined: A Market Equilibrium is a price such that, at this price, the quantities demanded and supplied are the same. Demand and supply curves intersect at equilibrium 62 Chapter Two Market Equilibrium for Cranberries Qd = 500 – 4p QS = -100 + 2p p = price of cranberries (dollars per barrel) Q = demand or supply in millions of barrels per year The equilibrium price of cranberries is calculated by equating demand to supply: Qd = QS … or… 500 – 4p = -100 + 2p …solving p* = $100 Plug equilibrium price into either demand or supply to get equilibrium quantity: 63 Chapter Two Market Equilibrium for Cranberries Q* = 100 64 Chapter Two Excess Supply Defined: If sellers cannot sell as much as they would like at the current price, there is Excess Supply. If there is no excess supply or excess demand, there is no pressure for prices to change and thus there is equilibrium. When a change in an exogenous variable causes the demand curve or the supply curve to shift, the equilibrium shifts as well. 65 Chapter Two Excess Supply 66 Chapter Two Price Elasticity Defined: The Price Elasticity of Demand is the percentage change in quantity demanded brought about by a one-percent change in the price of the good. Q,P= (Q/Q) = (Q/p)(p/Q) (p/p) 67 Chapter Two Price Elasticity • Slope is the ratio of absolute changes in quantity and price. (= Q/P). • Elasticity is the ratio of relative (or percentage) changes in quantity and price. 68 Chapter Two Grocery Products Elasticity 69 Chapter Two Price Elasticity • When a one percent change in price leads to a greater than one-percent change in quantity demanded, the demand curve is elastic. (Q,P < -1) • When a one-percent change in price leads to a less than one-percent change in quantity demanded, the demand curve is inelastic. (0 > Q,P > -1) • When a one-percent change in price leads to an exactly one-percent change in quantity demanded, the demand curve is unit elastic. (Q,P = -1) 70 Chapter Two Elasticity – Linear Demand Curve Qd = a – bp Where: • a and b are positive constants • p is price • b is the slope • a/b is the choke price Elasticity is: 71 Chapter Two Elasticity – Linear Demand Curve P a/b Q,P = - Elastic region a/2b • Q,P = -1 Inelastic region Q,P = 0 0 a a/2 Q 72 Chapter Two Elasticity – Linear Demand Curve 73 Chapter Two Constant Elasticity vs. Linear Demand Curve Price • P Observed price and quantity Constant elasticity demand curve Linear demand curve 0 Q Quantity 74 Chapter Two Price Elasticity and Cars Berry, Levinsohn and Pakes, "Automobile Price in Market Equilibrium," Econometrica 63 (July 1995), 841-890 75 Chapter Two Price Elasticity and Cars Berry, Levinsohn and Pakes, "Automobile Price in Market Equilibrium," Econometrica 63 (July 1995), 841-890 76 Chapter Two Durable Goods Defined: The Durable Good is a good that provides valuable services over a long time (usually many years). Demand for non-durables is less elastic in the short run when consumers can only partially adapt their behavior. Demand for durables is more elastic in the short run because consumers can delay purchase. 77 Chapter Two Durable Goods 78 Chapter Two Other Elasticities 79 Chapter Two Elasticities & the Cola Wars Source: Gasmi, Laffont and Vuong, "Econometric Analysis of Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311. 80 Chapter Two Estimating Demand & Supply 81 Chapter Two Estimating Demand & Supply 82 Chapter Two Estimating Demand & Supply 83 Chapter Two Estimating Demand & Supply From Past Shifts 84 Chapter Two Identifying Demand By a Shift in Supply 85 Chapter Two Identifying Demand By a Shift in Supply This technique only works if one or the other of the curves stays constant. Identifying demand when both curves shift 86 Chapter Two Chapter Three Consumer Preferences and the Concept of Utility 87 Chapter Three Chapter Three Overview 1. Motivation 2. Consumer Preferences and the Concept of Utility 3. Indifference Curves 4. The Marginal Rate of Substitution 5. The Utility Function • Marginal Utility and Diminishing Marginal Utility 6. Some Special Functional Forms • Marginal Utility and the Marginal Rate of Substitution 88 Chapter Three Motivation • Equilibrium/comparative statics studies may predict the direction of change but: • Over what price range? • How much? • Elasticity good descriptive measure of demand and supply but it not predictive • Back of the envelope techniques miss nonlinearities 89 Chapter Three Consumer Preferences Consumer Preferences tell us how the consumer would rank (that is, compare the desirability of) any two combinations or allotments of goods, assuming these allotments were available to the consumer at no cost. These allotments of goods are referred to as baskets or bundles. These baskets are assumed to be available for consumption at a particular time, place and under particular physical circumstances. 90 Chapter Three Consumer Preferences Preferences are complete if the consumer can rank any two baskets of goods (A preferred to B; B preferred to A; or indifferent between A and B) Preferences are transitive if a consumer who prefers basket A to basket B, and basket B to basket C also prefers basket A to basket C A B; B C = > A C 91 Chapter Three Consumer Preferences Preferences are monotonic if a basket with more of at least one good and no less of any good is preferred to the original basket. 92 Chapter Three Intransitivity and Age Age 4 5 6 7 8 9 10 11 12 13 Adults Number of Subjects Intransitive (%) 39 33 23 35 40 52 45 65 81 81 99 83 82 82 78 68 57 52 37 23 41 13 Source: See Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth Edition. Prentice Hall: Upper Saddle River, New Jersey. 1998. 93 Chapter Three Indifference Curves An Indifference Curve or Indifference Set: is the set of all baskets for which the consumer is indifferent An Indifference Map : Illustrates a set of indifference curves for a consumer Averages preferred to extremes => indifference curves are bowed toward the origin (convex to the origin). 94 Chapter Three Indifference Curves 1). Monotonicity => indifference curves have negative slope – and indifference curves are not “thick” 2). Transitivity => indifference curves do not cross 3). Completeness => each basket lies on only one indifference curve 95 Chapter Three Indifference Curves Number of Children Number of Boys Number of Families 2 2 1 0 3 2 1 0 4 3 2 1 0 35,674 64,585 31,607 10,431 26,497 24,897 8,948 2,619 8,260 11,489 7,527 2,241 3 4 Families that had another Child 56 51 56 47 44 45 48 40 40 38 40 41 Source: See Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth Edition. Prentice Hall: Upper Saddle River, New Jersey. 1998. 96 Chapter Three Indifference Curves boys Preference direction (locally) 2 1 • 0 1 Indifference curves 2 girls 97 Chapter Three Indifference Curves 98 Chapter Three Indifference Curves 99 Chapter Three Indifference Curves Suppose that B preferred to A. but..by definition of IC, B indifferent to C A indifferent to C => B indifferent to C by transitivity. And thus a contradiction. 100 Chapter Three Indifference Curves 101 Chapter Three Indifference Curves Non-monotonic preferences with a bliss point. 102 Chapter Three Indifference Curves Are these: Compete, Transitive, Monotonic – are averages preferred to extremes? 103 Chapter Three Marginal Rate of Substitution The marginal rate of substitution: is the maximum rate at which the consumer would be willing to substitute a little more of good x for a little less of good y; It is the increase in good x that the consumer would require in exchange for a small decrease in good y in order to leave the consumer just indifferent between consuming the old basket or the new basket; It is the rate of exchange between goods x and y that does not affect the consumer’s welfare; It is the negative of the slope of the indifference curve: MRSx,y = -y/x (for a constant level of preference) 104 Chapter Three Indifference Curves If the more of good x you have, the more you are willing to give up to get a little of good y or the indifference curves get flatter as we move out along the horizontal axis and steeper as we move up along the vertical axis 105 Chapter Three Indifference Curves Example: For the following indifference curves, the marginal rate of substitution between x and y is: 1, .5, 2, 5 diminishing? 106 Chapter Three Indifference Curves Example: For the following indifference curves, the marginal rate of substitution between x and y is: 0? Infinite? undefined ? Diminishing? all of the above? 107 Chapter Three The Utility Function The utility function assigns a number to each basket so that more preferred baskets get a higher number than less preferred baskets. Utility is an ordinal concept: the precise magnitude of the number that the function assigns has no significance. 108 Chapter Three The Utility Function Students take an exam. After the exam, the students are ranked according to their performance. An ordinal ranking lists the students in order of their performance (i.e., Harry did best, Joe did second best, Betty did third best, and so on). A cardinal ranking gives the mark of the exam, based on an absolute marking standard (i.e., Harry got 80, Joe got 75, Betty got 74 and so on). Alternatively, if the exam were graded on a curve, the marks would be an ordinal ranking. 109 Chapter Three The Utility Function Difference in magnitudes of utility have no interpretation per se utility not comparable across individuals any transformation of a utility function that preserves the original ranking of bundles is an equally good representation of preferences. e.g. U = xy vs. U = xy + 2 represent the same preferences. Example: U = xy Check that underlying preferences are complete, transitive, monotonic and averages are preferred to extremes. 110 Chapter Three The Utility Function Example: Utility and the single indifference curve. 111 Chapter Three Marginal Utility The marginal utility of a good, x, is the additional utility that the consumer gets from consuming a little more of x when the consumption of all the other goods in the consumer’s basket remain constant. • U/x (y held constant) = MUx • U/y (x held constant) = MUy The marginal utility of x is the slope of the utility function with respect to x. The principle of diminishing marginal utility states that the marginal utility falls as the consumer consumes more of a good. 112 Chapter Three Marginal Utility Relative Income and Life Satisfaction Within Nations Relative Income Percent > "Satisfied" Lowest quartile 70 Second quartile 78 Third quartile 82 Highest quartile 85 Source: Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth Edition. Prentice Hall: Upper Saddle River, New Jersey. 1998. 113 Chapter Three Marginal Utility Relative Income and Life Satisfaction Across Nations Source: Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth Edition. Prentice Hall: Upper Saddle River, New Jersey. 1998. Chapter Three 114 Marginal Utility MUx(x) + MUy(y) = 0 …along an IC… MUx/MUy = -y/x = MRSx,y Positive marginal utility implies the indifference curve has a negative slope (implies monotonicity) Diminishing marginal utility implies the indifference curves are convex to the origin (implies averages preferred to extremes) 115 Chapter Three Marginal Utility Example: U = Ax2+By2; MUx=2Ax; MUy=2By (where: A and B positive) MRSx,y = MUx/MUy = 2Ax/2By = Ax/By Marginal utilities are positive (for positive x and y) Marginal utility of x increases in x; marginal utility of y increases in y 116 Chapter Three Marginal Utility Implications of this substitution: • Indifference curves are negatively-sloped, bowed out from the origin, preference direction is up and right • Indifference curves intersect the axes 117 Chapter Three Indifference Curves y Example: Graphing Indifference Curves Preference direction IC1 IC2 0 x Chapter Three 118 Indifference Curves Example: U= (xy).5;MUx=y.5/2x.5; MUy=x.5/2y.5 A. Is more better for both goods? Yes, since marginal utilities are positive for both. B. Are the marginal utility for x and y diminishing? Yes. (For example, as x increases, for y constant, MUx falls.) C. What is the marginal rate of substitution of x for y? MRSx,y = MUx/MUy = y/x 119 Chapter Three Indifference Curves Do the indifference intersect the axes? curves A value of x = 0 or y = 0 is inconsistent with any positive level of utility. 120 Chapter Three Indifference Curves y Example: Graphing Indifference Curves Preference direction IC2 IC1 x Chapter Three 121 Special Functional Forms Cobb-Douglas: U = Axy where: + = 1; A, , positive constants MUX = Ax-1y Axy-1 MUY = MRSx,y = (y)/(x) “Standard” case 122 Chapter Three Special Functional Forms y Example: Cobb-Douglas (speed vs. maneuverability) Preference Direction IC2 IC1 x Chapter Three 123 Special Functional Forms Perfect Substitutes: U = Ax + By Where: A, B positive constants MUx = A MUy = B MRSx,y = A/B so that 1 unit of x is equal to B/A units of y everywhere (constant MRS). 124 Chapter Three Special Functional Forms y Example: Perfect Substitutes • (Tylenol, Extra-Strength Tylenol) Slope = -A/B IC1 IC2 0 IC3 x Chapter Three 125 Special Functional Forms Perfect Complements: U = Amin(x,y) where: A is a positive constant. MUx = 0 or A MUy = 0 or A MRSx,y is 0 or infinite or undefined (corner) 126 Chapter Three Special Functional Forms y Example: Perfect Complements • (nuts and bolts) IC2 IC1 0 x Chapter Three 127 Special Functional Forms U = v(x) + Ay Where: A is a positive constant. MUx = v’(x) = V(x)/x, where small MUy = A "The only thing that determines your personal trade-off between x and y is how much x you already have." *can be used to "add up" utilities across individuals* 128 Chapter Three Special Functional Forms y Example: Quasi-linear Preferences • (consumption of beverages) IC2 IC’s have same slopes on any vertical line IC1 • • 0 x Chapter Three 129 Chapter Four Consumer Choice 130 Chapter Four Chapter Four Overview 1. Motivation 2. The Budget Constraint 3. Consumer Choice 4. Duality 5. Some Applications 6. Revealed Preference 131 Chapter Four Motivation Consumer Expenditures, US, 2001 Yearly After Tax Income: $42,362 Yearly Total Expenditures: $40,900 Allocation of Spending Food $5,904 Housing $12,248 Transportation $8,672 Health care $2,239 Entertainment $1,958 132 Chapter Four The Budget Constraint Assume only two goods available: X and Y • Price of x: Px ; Price of y: Py • Income: I Total expenditure on basket (X,Y): PxX + PyY The Basket is Affordable if total expenditure does not exceed total Income: PXX + PYY ≤ I 133 Chapter Four Key Definitions Budget Set: • The set of baskets that are affordable Budget Constraint: • The set of baskets that the consumer may purchase given the limits of the available income. Budget Line: • The set of baskets that one can purchase when spending all available income. PxX + PyY = I Y = I/Py – (Px/Py)X 134 Chapter Four A Budget Constraint Example Two goods available: X and Y I = $10 Px = $1 Py = $2 Budget Line 1: 1X + 2Y = 10 Or Y = 5 – X/2 135 Chapter Four A Budget Constraint Example Y If the price of X rises, the budget line gets steeper and the horizontal intercept shifts in If the price of X falls, the budget line gets flatter and the horizontal intercept shifts out Budget line = BL1 I/PY= 5 A • -PX/PY = -1/2 B •C • I/PX = 10 Chapter Four X 136 A Budget Constraint Example Y I = $12 PX = $1 PY = $2 Shift of a budget line If the price of X rises, the budget line gets steeper and the horizontal intercept shifts in 6 Y = 6 - X/2 …. BL2 5 If the price of X falls, the budget line gets flatter and the horizontal intercept shifts out BL2 BL1 10 12 X 137 Chapter Four A Budget Constraint Example Y Rotation of a budget line If the price of X rises, the budget line gets steeper and the horizontal intercept shifts in I = $10 PX = $1 BL1 PY = $3 6 5 If the price of X falls, the budget line gets flatter and the horizontal intercept shifts out Y = 3.33 - X/3 …. BL2 3.33 BL2 10 Chapter Four X 138 Consumer Choice Assume: Only non-negative quantities "Rational” choice: The consumer chooses the basket that maximizes his satisfaction given the constraint that his budget imposes. Consumer’s Problem: Max U(X,Y) (X,Y) Subject to: PxX + PyY < I 139 Chapter Four Interior Optimum Interior Optimum: The optimal consumption basket is at a point where the indifference curve is just tangent to the budget line. A tangent: to a function is a straight line that has the same slope as the function…therefore…. MRSx,y = Px/Py “The rate at which the consumer would be willing to exchange X for Y is the same as the rate at which they are exchanged in the marketplace.” 140 Chapter Four Interior Consumer Optimum Y • B Preference Direction • •C Optimal Choice (interior solution) IC BL X 0 Chapter Four 141 Interior Consumer Optimum • U (X,Y) = XY and MUX =Y while MUY = X • I = $1,000 • PX = $50 and PY = $200 • Basket A contains (X=4, Y=4) • Basket B contains (X=10, Y=2.5) • Question: • Is either basket the optimal choice for the consumer? Basket A: MRSx,y = MUx/MUy = Y/X = 4/4 = 1 Slope of budget line = -Px/Py = -1/4 Basket B: MRSx,y = MUx/MUy = Y/X = 1/4 142 Chapter Four Interior Consumer Optimum Y 50X + 200Y = E 25 = XY (constraint) Y/X = 1/4 (tangency condition) 2.5 • 0 10 U = 25 Chapter Four X 143 Equal Slope Condition “At the optimal basket, each good gives equal bang for the buck” Now, we have two equations to solve for two unknowns (quantities of X and Y in the optimal basket): 1. MUx/Px = MUY/PY 2. PxX + PyY = I 144 Chapter Four Contained Optimization What are the equations that the optimal consumption basket must fulfill if we want to represent the consumer’s choice among three goods? • MUX / PX = MUY / PY is an example of “marginal reasoning” to maximize • PX X + PY Y = “I” reflects the constraint 145 Chapter Four Corner Solution A corner solution occurs when the optimal bundle contains none of one of the goods. The tangency condition may not hold at a corner solution. How do you know whether the optimal bundle is interior or at a corner? Graph the indifference curves Check to see whether tangency condition ever holds at positive quantities of X and Y 146 Chapter Four Corner Solution Example: Let U(X,Y) = X + Y. I = $1000, Px = $50 and PY = $200. What is the optimal consumption basket? Budget line: Y = $5 - X/4 147 Chapter Four Corner Consumer Optimum What would be the optimal consumption bundle if PX = PY = $50? What if PX = $200, PY = $50? 148 Chapter Four Corner Consumer Optimum Example: Let U(X,Y) = min(X,Y). Let I = $1000, Px = $50 and PY = $200. What is the optimal consumption basket? Budget line: Y = $5 - X/4 149 Chapter Four Duality The mirror image of the original (primal) constrained optimization problem is called the dual problem. Min PxX + PyY (X,Y) subject to: U(X,Y) = U* where: U* is a target level of utility. If U* is the level of utility that solves the primal problem, then an interior optimum, if it exists, of the dual problem also solves the primal problem. 150 Chapter Four Optimal Choice Y Example: Expenditure Minimization • Optimal Choice (interior solution) U = U* Decreases in expenditure level PXX + PYY = E* 0 X 151 Chapter Four Optimal Choice Y Example: A consumer purchases X and Y and has utility U(X,Y) = XY, with marginal utilities MUx = Y and MUY = X. Let PX = $50 and PY = $200. What is the basket that minimizes the expenditure necessary to attain a utility level of U = 25? 50X + 200Y = E 25 = XY (constraint) Y/X = 1/4 (tangency condition) 2.5 0 X 10 152 Chapter Four Optimal Choice Y Example: Expenditure Minimization 50X + 200Y = E 25 = XY (constraint) Y/X = 1/4 (tangency condition) 2.5 • 0 10 U = 25 X 153 Chapter Four Optimal Choice Composite Good, Units I+V Example: Housing Vouchers and Income Subsidies • I Which is a better way to increase the amount of housing chosen by the consumer? B A hA hF I/Ph (I+V)/Ph Housing (units) 154 Chapter Four Optimal Choice I+S I+V Composite Good, Units Preference Direction C • I B • A hA hF I/Ph (I+V)/Ph (I+S)/Ph Housing (units) 155 Chapter Four Optimal Choice I+S I+V Composite Good, Units Preference Direction I • B • •D A hA hF C hB I/Ph (I+V)/Ph (I+S)/Ph Housing (units) 156 Chapter Four Optimal Choice I2 + I1(1+r) I2 C2, spending next year ($) •A Example: Borrowing and Lending •B C2B Preference Direction IC2 IC1 I1 C1B I1+I2/(1+r) Chapter Four C1, spending this year ($)157 Optimal Choice 300 Composite Good Preference Direction 200 Example: Discount Clubs IC1 • • Should the A consumer join the IC2 club or not? • B CDs (number) 0 10 15 Chapter Four 20 158 Revealed Preference Suppose that preferences are not known. Can we infer them from purchasing behavior? If A purchased, it must be preferred to all other affordable bundles 159 Chapter Four Revealed Preference Suppose that preferences are “standard” – then: All baskets to the Northeast of A must be preferred to A. This gives us a narrower range over which indifference curve must lie This type of analysis is called revealed preference analysis. 160 Chapter Four Revealed Preference Can we test whether a consumer is maximizing utility by using revealed preference analysis? Suppose that preferences do not change over the period of observation. 1. Let basket A be purchased in period 1. Let basket B be affordable at period 1 prices. 2. A B 3. Let basket B be purchased in period 2. 161 Chapter Four Revealed Preference 4. Let basket A be purchased in period 1. Let basket B be affordable at period 1 prices. AB 5. Let basket B be purchased in period 2. 6. In fact, if both are affordable and B is bought, the consumer cannot be behaving according to utility maximization. 162 Chapter Four Revealed Preference Alternatively: If: PxXA+PyYA > PxXB+PyYB … and A chosen, then it must NOT be the case that: P’xXB+P’yYB > P’xXA+P’yYA … and B chosen (“Weak Axiom of Revealed Preference”) 163 Chapter Four Revealed Preference Example: Consumer Choice that Fails to Maximize Utility Two goods, X and Y: I = $24 (PX,PY) = (4,2) (P’x,P’Y) = (3,3) (XA,YA) = (5,2) A chosen when BL is BL1 (XB,YB) = (2,6) B chosen when BL is BL2 164 Chapter Four Revealed Preference 12 Composite Good BL1 C 8 • • BL1 Y = 12 - 2X BL2 Y = 8 - X B • A D • BL2 X 6 8 Chapter Four 165 Revealed Preference IF PxXA + PyYA > PxXB + PyYB 4(5)+2(2) > 4(2)+2(6) (i.e., if A is chosen when budget is BL1 but B is affordable) Then it must NOT be the case that: P’xXB + P’yYB > P’xXA + P’yYA 3(2)+3(6) > 3(5)+3(2)? (i.e. at the new prices for BL2, B is chosen when A is affordable) So utility maximization condition fails 166 Chapter Four Chapter Five The Theory Of Demand 167 Chapter Five Chapter Five Overview 1. Individual Demand Curves 2. Income and Substitution Effects & the Slope of Demand • Applications: The Work-Leisure Trade-off Consumer Surplus 3. Constructing Aggregate Demand 168 Chapter Five Individual Demand Curves The Price Consumption Curve of Good X: Is the set of optimal baskets for every possible price of good x, holding all other prices and income constant. 169 Chapter Five Price Consumption Curves Y (units) The price consumption curve for good x can be written as the quantity consumed of good x for any price of x. This is the individual’s demand curve for good x. PY = $4 I = $40 10 • 0 XA=2 Price Consumption Curve • PX = 4 XB=10 • PX = 1 PX = 2 XC=16 Chapter Five 20 X (units) 170 Individual Demand Curve PX Individual Demand Curve For X PX = 4 • PX = 2 PX = 1 XA • XB • XC Chapter Five U increasing X 171 Individual Demand Curve The consumer is maximizing utility at every point along the demand curve The marginal rate of substitution falls along the demand curve as the price of x falls (if there was an interior solution). As the price of x falls, utility increases along the demand curve. 172 Chapter Five Price Consumption Curve Y (units) Example: Suppose U = x + y. Income, I, is spent only on x and y. Prices are px and py. Y*=I/PY When px < py, the price consumption curve is I/px= x. When px > py, the price consumption curve is I/py = y*. Between, it is x + y = I PX>PY X (units) 0 173 Chapter Five Price Consumption Curve Y (units) Y*=I/PY PX<PY PX=PY PX>PY X (units) 0 174 Chapter Five Price Consumption Curve Y (units) IC1 IC2 IC3 Y*=I/PY PX<PY PX=PY PX>PY X (units) 0 175 Chapter Five Demand Curve for “X” PX PY I/PX The corresponding demand for x is: py py 0 I/PY -Y X = I/px when px < I – y when px = when px > py X 176 Chapter Five Demand Curve for “X” Algebraically, we can solve for the individual’s demand using the following equations: 1. pxx + pyy = I 2. MUx/px = MUy/py – at a tangency. (If this never holds, a corner point may be substituted where x = 0 or y = 0) 177 Chapter Five Demand Curve with an Interior Solution Suppose that U(x,y) = xy. MUx = y and MUy = x. The prices of x and y are px and py, respectively and income = I. We Have: 1. pxx + pyy = I 2. x/py = y/px Substituting the second condition into the budget constraint, we then have: 3. pxx + py(px/py)x = I or…x = I/2px 178 Chapter Five Demand Curve with a Corner Point Suppose U = xy + 10x. MUx=y + 10 and MUy = x. All the other notation is as in the last example. Recall that indifference curves such as these are convex and intersect the x axis. We Have: 1. pxx + pyy = I 2. (y+10)/x = px/py Substituting the second equation into the budget line, we have the demand curve for y: 3. y = (I-10py)/(2py) 4. If I > 10py, demand for y is positive. 179 Chapter Five Demand Curve with a Corner Point What if I < 10py? We have a corner point because: At y = 0, it is the case that: MUx/px = (y+10)/pX = 10/pX MUy/py = x/py = (I/px)/py y=0 will be the optimal choice only if: MUx/px > MUy/py …or… 10/px >(I/px)/py …or… I – 10py < 0 180 Chapter Five Change in Income & Demand The income consumption curve of good x is the set of optimal baskets for every possible level of income. We can graph the points on the income consumption curve as points on a shifting demand curve. 181 Chapter Five Income Consumption Curve 182 Chapter Five Engel Curves The income consumption curve for good x also can be written as the quantity consumed of good x for any income level. This is the individual’s Engel Curve for good x. When the income consumption curve is positively sloped, the slope of the Engel Curve is positive. 183 Chapter Five Engel Curves I ($) “X is a normal good” 40 0 X (units) 10 184 Chapter Five Engel Curves I ($) “X is a normal good” 68 40 0 10 X (units) 18 185 Chapter Five Engel Curves I ($) “X is a normal good” 92 68 40 0 10 18 X (units) 24 186 Chapter Five Engel Curves I ($) Engel Curve “X is a normal good” 92 68 40 0 10 18 X (units) 24 187 Chapter Five Definitions of Goods • If the income consumption curve shows that the consumer purchases more of good x as her income rises, good x is a normal good. • Equivalently, if the slope of the Engel curve is positive, the good is a normal good. • If the income consumption curve shows that the consumer purchases less of good x as her income rises, good x is an inferior good. • Equivalently, if the slope of the Engel curve is negative, the good is an inferior good. 188 Chapter Five Definitions of Goods Example: Backward Bending Engel Curve – a good can be normal over some ranges and inferior over others 189 Chapter Five Price & Demand – What’s the Connection? Definition: As the price of x falls, all else constant, purchasing power rises. This is called the income effect of a change in price. The income effect may be positive (normal good) or negative (inferior good). 190 Chapter Five The Substitution Effect • As the price of x falls, all else constant, good x becomes cheaper relative to good y. This change in relative prices alone causes the consumer to adjust his/ her consumption basket. This effect is called the substitution effect. • The substitution effect always is negative. • Usually, a move along a demand curve will be composed of both effects. The Substitution Effect Can be Depicted Graphically 191 Chapter Five The Substitution Effect 192 Chapter Five The Substitution Effect 193 Chapter Five Giffen Goods If a good is so inferior that the net effect of a price decrease of good x, all else constant, is a decrease in consumption of good x, good x is a Giffen good. For Giffen goods, demand does not slope down. When might an income effect be large enough to offset the substitution effect? The good would have to represent a very large proportion of the budget. 194 Chapter Five Giffen Goods – Income and Substitution Effects 195 Chapter Five Giffen Goods – Income and Substitution Effects Example: Suppose U(x,y) = 2x1/2 + y. MUx = 1/x1/2 MUy = 1. Py = $1 and I = $10. Suppose that px = $0.50. What is the (initial) optimal consumption basket? Tangency Condition: MUx/MUy = px/py px = 1/x1/2 196 Chapter Five Giffen Goods – Income and Substitution Effects Solving for x as a function of its price, x = 1/(px2) Substituting, xA = 4 at the initial price. Budget Constraint: pxx + pyy = 10 yA = 8 at the initial price. (UA = 2xA1/2 +yA=2(41/2)+8=12) 197 Chapter Five Giffen Goods – Income and Substitution Effects Suppose that px = $0.20. What is the (final) optimal consumption basket? Using the demand derived in (a), xC = 25 and yC =5 (UC=2xC1/2+yC=2(251/2)+5=15) 198 Chapter Five Giffen Goods – Income and Substitution Effects What are the substitution and income effects that result from the decline in px? Decomposition Basket: Constraint: U = 2x1/2 + y = 12 Tangency: MUx/MUy = px/py 1/x1/2 = .2 So that xB = 25 and yB = 2 Substitution Effect: xB-xA = 25 - 4 = 21 Income Effect: xC-xB = 25 - 25 = 0 199 Chapter Five Quasi-Linear Utility For this type of utility, the income effect due to a price change for good x is zero. In other words, all the income effect is concentrated in y. Let U(x,y) = v(x) + Ay (where A is a constant). Then MUx = v’(x) and MUy = A. At an interior optimum, MUx/MUy = px/py => MUx/A = px/py 200 Chapter Five Quasi-Linear Utility As income changes, MUx must remain the same at the new consumption bundle. But if x changes, MUx will change, in general. Therefore, x must stay the same. In other words, (x/I) = 0. Similarly, the income effect due to a price change must also be zero 201 Chapter Five Income & Substitution Effects “ Pay rises may have worsened the nursing shortage in Massachusetts by enabling nurses to work fewer hours, the American Hospital Association says.” “Labor” includes all work hours when the consumer is earning income. (L hours per day at wage rate w per hour. Let w = $5) “Leisure” includes all nonwork activities (so hours of leisure, l = 24 – L) U= U(y,l) The consumer likes the "good", leisure. 202 Chapter Five Income & Substitution Effects The composite good, y, has price py = $1 Daily income = wL The budget line gives all the combinations of y and l that the consumer can afford. If l = 24, y = 0 If l = 0, y = 120 Slope of budget line is -$5 As the wage rate rises, y is less expensive in terms of hours of work needed to purchase a unit of y. The budget line rotates. The optimal choice shifts. Why? 203 Chapter Five Income & Substitution Effects • The substitution effect leads to less leisure and more labor as w increases. • As w increases, the consumer feels as though he has more income because less work is needed to buy a unit of y. This creates an income effect. • If leisure is a normal good, the income effect on leisure is positive • Therefore, the income effect on labor is negative 204 Chapter Five Income & Substitution Effects This information can be used to construct the consumer’s labor supply function, L(w). If the income effect of a wage increase outweighs the substitution effect, the labor supply curve bends backwards. This information can be used to construct the consumer’s labor supply function, L(w). If the income effect of a wage increase outweighs the substitution effect, the labor supply curve bends backwards. 205 Chapter Five Income & Substitution Effects Wage ($/hour) Example: Leisure Trade-Off Supply of Labor 25 • 20 15 10 5 • • • • Work (hours/day) 9 10 11 206 Chapter Five Income & Substitution Effects Daily Income in units of composite good, Y 207 Chapter Five Consumer Surplus • The individual’s demand curve can be seen as the individual’s willingness to pay curve. • On the other hand, the individual must only actually pay the market price for (all) the units consumed. 208 Chapter Five Consumer Surplus PX G = .5(10-3)(28) = 98 H+I= 28 +2 = 30 CS2 = .5(10-2)(32) = 128 CSP = (10-P)(40-4P) 10 X = 40 - 4PX • Demand G 3 2 H I 28 Chapter Five 32 40 X 209 Consumer Surplus Definition: The net economic benefit to the consumer due to a purchase (i.e. the willingness to pay of the consumer net of the actual expenditure on the good) is called consumer surplus. The area under an ordinary demand curve and above the market price provides a measure of consumer surplus 210 Chapter Five Aggregate Demand The market, or aggregate, demand function is the horizontal sum of the individual (or segment) demands. In other words, market demand is obtained by adding the quantities demanded by the individuals (or segments) at each price and plotting this total quantity for all possible prices. 211 Chapter Five Aggregate Demand P 10 P Q = 10 - p P Q = 20 - 5p 4 Segment 1 Q Segment 2 Q Aggregate demand Q 212 Chapter Five Network Externalities If one consumer's demand for a good changes with the number of other consumers who buy the good, there are network externalities. If one person's demand decreases with the number of other consumers, then the externality is positive. If one person's demand decreases with the number of other consumers, then the externality is negative. Examples: • Telephone (physical network) • Software (virtual network) 213 Chapter Five Network Externalities D60 PX Bandwagon Effect: • (increased quantity demanded D30 when more consumers purchase) 20 10 • A • B Pure Price Effect 30 38 • C Market Demand Bandwagon Effect 60 Chapter Five X (units) 214 Network Externalities PX Market Demand 1200 900 Snob Effect: • (decreased quantity demanded when more consumers purchase) • A • • C B D1000 D1300 Snob Effect X (units) Pure Price Effect 1000 1300 1800 Chapter Five 215 Chapter Six Inputs and Production Functions 216 Chapter Six Chapter Six Overview 1. Motivation 2. The Production Function Marginal and Average Products Isoquants The Marginal Rate of Technical Substitution 3. Technical Progress 4. Returns to Scale 5. Some Special Functional Forms 217 Chapter Six Production of Semiconductor Chips “Fabs” cost $1 to $2 billion to construct and obsolete in 3 to 5 years Must get fab design “right” Choice: Robots or Humans? Up-front investment in robotics vs. better chip yields and lower labor costs? Capital-intensive or labor-intensive production process? 218 Chapter Six Key Concepts Productive resources, such as labor and capital equipment, that firms use to manufacture goods and services are called inputs or factors of production. The amount of goods and services produces by the firm is the firm’s output. Production transforms a set of inputs into a set of outputs Technology determines the quantity of output that is feasible to attain for a given set of inputs. 219 Chapter Six Key Concepts The production function tells us the maximum possible output that can be attained by the firm for any given quantity of inputs. Example: Q = f(L,K,M) Example: Q = f(P,F,L,A) Example: Chips = f1(L,K,M) = f2(L,K,M) A technically efficient is attaining the maximum possible output from its inputs (using whatever technology is appropriate) 220 Chapter Six The Production Function & Technical Efficiency Q Production Function Q = f(L) D C • •A • •B Production Set L 221 Chapter Six The Production Function & Technical Efficiency Definition: The feasible but inefficient points below the production function make up the firm’s production set. Are firms technically efficient? • Shirking, “perquisites” • Strategic reasons for technical inefficiency • Imperfect information on “best practices” • “63% efficient” 222 Chapter Six The Production Function & Technical Efficiency • The variables in the production function are flows (the amount of the input used per unit of time), not stocks (the absolute quantity of the input). • Example: stock of capital is the total factory installation; flow of capital is the machine hours used per unit of time in production (including depreciation). • Capital refers to physical capital (definition: goods that are themselves produced goods) and not financial capital (definition: the money required to start or maintain production). 223 Chapter Six The Production Function & Technical Efficiency Q = (1/192)[K2-(1/36)K3][L2 – (1/36)L3] Q = K1/2L1/2 224 Chapter Six The Production Function & Technical Efficiency Production Function Q = K1/2L1/2 in Table Form K: 0 10 20 30 40 50 L: 0 0 0 0 0 0 0 10 0 10 14 17 20 22 20 0 14 20 24 28 32 30 0 17 24 30 35 39 40 0 20 28 35 40 45 50 0 22 32 39 45 50 225 Chapter Six The Production & Utility Functions Production Function Utility Function Output from inputs Preference level from purchases Derived from technologies Derived from preferences Cardinal(Defn: given Ordinal amount of inputs yields a unique and specific amount of output) Marginal Product Marginal Utility 226 Chapter Six The Production & Utility Functions Production Function Utility Function Isoquant(Defn: all Indifference Curve possible combinations of inputs that just suffice to produce a given amount of output) Marginal Rate of Marginal Rate of Technical Substitution Substitution 227 Chapter Six The Marginal Product Definition: The marginal product of an input is the change in output that results from a small change in an input holding the levels of all other inputs constant. MPL = Q/L • (holding constant all other inputs) MPK = Q/K • (holding constant all other inputs) Example: MPL = (1/2)L-1/2K1/2 MPK = (1/2)K-1/2L1/2 228 Chapter Six The Average Product & Diminishing Returns Definition: The average product of an input is equal to the total output that is to be produced divided by the quantity of the input that is used in its production: APL = Q/L APK = Q/K Example: APL = [K1/2L1/2]/L = K1/2L-1/2 APK = [K1/2L1/2]/K = L1/2K-1/2 Definition: The law of diminishing marginal returns states that marginal products (eventually) decline as the quantity used of a single input increases. 229 Chapter Six Total, Average, and Marginal Magnitudes Student Height (CM) Arrival Height Total Average Marginal 1 2 3 4 5 160 180 190 150 150 160 340 530 680 830 160 170 176.67 170 166 "TP" "AP" 160 180 190 150 150 "MP" 230 Chapter Six Total, Average, and Marginal Magnitudes • When a total magnitude is rising, corresponding marginal magnitude is positive. the • When an average magnitude is falling, the corresponding marginal magnitude must be smaller than the average magnitude. 231 Chapter Six Total, Average, and Marginal Magnitudes TPL maximized where MPL is zero. TPL falls where MPL is negative; TPL rises where MPL is positive. 232 Chapter Six Isoquants Definition: An isoquant traces out all the combinations of inputs (labor and capital) that allow that firm to produce the same quantity of output Example: Q = K1/2L1/2 What is the equation of the isoquant for Q = 20? 20 = K1/2L1/2 => 400 = KL => K = 400/L And… 233 Chapter Six Isoquants …and the isoquant for Q = Q*? 1/2 1/2 Q* = K L Q*2 = KL K = Q*2/L 234 Chapter Six Isoquants K All combinations of (L,K) along the isoquant produce 20 units of output. Q = 20 Slope=K/L Q = 10 L 0 235 Chapter Six Marginal Rate of Technical Substitution Definition: The marginal rate of technical substitution measures the amount of an input, L, the firm would require in exchange for using a little less of another input, K, in order to just be able to produce the same output as before. MRTSL,K = -K/L (for a constant level of output) Marginal products and the MRTS are related: MPL(L) + MPK(K) = 0 => MPL/MPK = -K/L = MRTSL,K Therefore 236 Chapter Six Marginal Rate of Technical Substitution • If both marginal products are positive, the slope of the isoquant is negative. • If we have diminishing marginal returns, we also have a diminishing marginal rate of technical substitution • For many production functions, marginal products eventually become negative. Why don't most graphs of Isoquants include the upwards-sloping portion? 237 Chapter Six Isoquants Isoquants K MPK < 0 Example: The Economic and the Uneconomic Regions of Production Q = 20 MPL < 0 Q = 10 L 0 238 Chapter Six Elasticity of Substitution Definition: The elasticity of substitution, , measures how the capital-labor ratio, K/L, changes relative to the change in the MRTSL,K. = [(K/L)/MRTSL,K]x[MRTSL,K/(K/L)] Example: Suppose that: • MRTSAL,K = 4, KA/LA = 4 • MRTSBL,K = 1, KB/LB = 1 MRTSL,K = MRTSBL,K - MRTSAL,K = -3 = [(K/L)/MRTSL,K]x[MRTSL,K/(K/L)] = (-3/-3)(4/4) = 1 239 Chapter Six Elasticity of Substitution K "The shape of the isoquant indicates the degree of substitutability of the inputs…" =0 =1 = 5 = L 0 240 Chapter Six Technological Progress Definition: Technological progress (or invention) shifts the production function by allowing the firm to achieve more output from a given combination of inputs (or the same output with fewer inputs). Neutral technological progress shifts the isoquant corresponding to a given level of output inwards, but leaves the MRTSL,K unchanged along any ray from the origin 241 Chapter Six Technological Progress Labor saving technological progress results in a fall in the MRTSL,K along any ray from the origin Capital saving technological progress results in a rise in the MRTSL,K along any ray from the origin. 242 Chapter Six Neutral Technological Progress K Q = 100 ante Q = 100 post MRTS remains same K/L L Chapter Six 243 Labor Saving Technological Progress K Q = 100 ante Q = 100 post MRTS gets smaller K/L L Chapter Six 244 Capital Saving Technological Progress K Q = 100 ante Q = 100 post MRTS gets larger K/L L Chapter Six 245 Production Function Q = 500[L+3K] its production function becomes: Q = 1000[.5L + 10K] MPL1= 500 MPL2 = 500 MPK1= 1500 MPK2 = 10,000 So MRTSL,K has decreased (“labor saving technological progress has occurred”) 246 Chapter Six Chemicals in the UK • Evidence of materials-saving and capital using technological progress; • In other words, evidence that MPM DECREASED relative to the MP0; • MPK INCREASED relative to MP0; • Further, 30% growth of input attributable to technological progress. productivity 247 Chapter Six Returns to Sale • How much will output increase when ALL inputs increase by a particular amount? • RTS = [%Q]/[% (all inputs)] • If a 1% increase in all inputs results in a greater than 1% increase in output, then the production function exhibits increasing returns to scale. • If a 1% increase in all inputs results in exactly a 1% increase in output, then the production function exhibits constant returns to scale. • If a 1% increase in all inputs results in a less than 1% increase in output, then the production function exhibits decreasing returns to scale. 248 Chapter Six Returns to Sale K 2K Q = Q1 K Q = Q0 0 L L 2L 249 Chapter Six Returns to Sale • The marginal product of a single factor may diminish while the returns to scale do not • Returns to scale need not be the same at different levels of production • Many production processes obey the cube-square rule, resulting in increasing returns to scale. 250 Chapter Six Returns to Sale Example: Q1 = AL1K1 Q2 = A(L1)(K1) = + AL1K1 = +Q1 So returns to scale will depend on the value of +. + = 1 … CRS + <1 … DRS + >1 … IRS What are the returns to scale of: Q1 = 500L1+400K1? 251 Chapter Six Returns to Sale Example: Electric Power Generation 1950s, estimate Q = ALKF . Find ++>1 • More recently, find this sum equals 1 Example: Returns to scale in oil pipelines Q = AH.37D1.73 • Increasing returns to scale in horsepower and diameter 252 Chapter Six Special Production Functions Linear Production Function: Q = aL + bK MRTS constant - constant returns to scale = Example 253 Chapter Six Linear Production Function 254 Chapter Six Fixed Proportions Function 2. Fixed Proportions Production Function (Leontief Production Function) Q = min(aL, bK) L-shaped isoquants MRTS varies (0, infinity, undefined) =0 255 Chapter Six Fixed Proportions Function O 2 Q = 2 (molecules) Q = 1 (molecule) 1 0 2 H 4 256 Chapter Six Cobb-Douglas Production Function • Q = aLK • if + > 1 then IRTS • if + = 1 then CRTS • if + < 1 then DRTS • smooth isoquants • MRTS varies along isoquants •=1 257 Chapter Six Cobb-Douglas Production Function K Q = Q1 Q = Q0 0 L 258 Chapter Six Constant Elasticity Production Function • Q = [aL+bK]1/ Where = (-1)/ • if = 0, we get Leontief case • if = , we get linear case • if = 1, we get the Cobb-Douglas case 259 Chapter Six Chapter Seven Costs and Cost Minimization 260 Chapter Seven Chapter Seven Overview 1. Introduction: Burke Mills 2. What are Costs? 3. Long Run Cost Minimization • The constraint minimization problem • Comparative statics • Input demands 4. Short Run Cost Minimization 261 Chapter Seven Opportunity Cost The relevant concept of cost is opportunity cost: the value of a resource in its best alternative use. The only alternative we consider is the best alternative 262 Chapter Seven Opportunity Cost Example: Investing $50M - $50M to invest with four alternatives: 1.) If invest now in CD-ROM factory, expected revenues are $100M 2.) If wait a year, expected revenues from CD-ROM investment are 75M 3.) If build new technology plant now, 50% chance that revenues are $0, 50% chance yields $150M. 4.) If wait a year, will know whether revenues are $0 or $150M. 263 Chapter Seven Opportunity Cost What is the opportunity cost of investing in CDROM plant now? Hence, (4) is the best alternative and the opportunity cost is $112.5M Costs depend on the decision being made Example: Opportunity Cost of Steel Purchase steel for $1M. Since then, price has gone up so that it is worth $1.2M (3) yields .5($0) + .5($150M) = $75M (4) yields .5($75M) + .5($150M)=$112.5M 264 Chapter Seven Opportunity Cost 1) Manufacture 2000 automobiles 2) Resell the steel What is the opportunity cost of manufacturing the cars? $1.2M Costs depend on the perspective we take • Opportunity costs often are implicit 265 Chapter Seven Opportunity Cost – DRAM Chips Both a long term and a spot market for DRAM chips exist Opportunity cost equals the current spot price, not the historical contract price Backflush if opportunity cost of holding chips rises Accounting costs may be lower or higher than economic costs 266 Chapter Seven Sunk Costs Sunk Costs are costs that must be incurred no matter what the decision. These costs are not part of opportunity costs. • It costs $5M to build and has no alternative uses • $5M is not sunk cost for the decision of whether or not to build the factory • $5M is sunk cost for the decision of whether to operate or shut down the factory 267 Chapter Seven Long-Run Cost Minimization Suppose that a firm’s owners wish to minimize costs Let the desired output be Q0 Technology: Q = f(L,K) Owner’s problem: min TC = rK + wL • K,L • Subject to Q0 = f(L,K) TC0 = rK + wL …or… K = TC0/r – (w/r)L Is the isocost line A Graphical Solution 268 Chapter Seven Isocost Lines K Direction of increase in total cost TC2/r TC1/r TC0/r Slope = -w/r TC0/w TC1/w TC2/w Chapter Seven L 269 Isocost Lines • Cost minimization subject to satisfaction of the isoquant equation: Q0 = f(L,K) • Note: analogous to expenditure minimization for the consumer Tangency Condition: • MRTSL,K = -MPL/MPK = -w/r •Constraint: Q0 = f(K,L) 270 Chapter Seven Cost Minimization TC2/r K Direction of increase in total cost TC1/r TC0/r • Isoquant Q = Q0 TC0/w TC1/w TC2/w Chapter Seven L 271 Interior Solution Q = 50L1/2K1/2 MPL = 25L-1/2K1/2 MPK = 25L1/2K-1/2 w = $5 r = $20 Q0 = 1000 MPL/MPK = K/L => K/L = 5/20…or…L=4K 1000 = 50L1/2K1/2 K = 10; L = 40 272 Chapter Seven Corner Solution Q = 10L + 2K MPL = 10 MPK = 2 w = $5 r = $2 Q0 = 200 MPL/MPK = 10/2 > w/r = 5/2 But… the “bang for the buck” in labor larger than the “bang for the buck” in capital… MPL/w = 10/5 > MPK/r = 2/2 K = 0; L = 20 What is the effect on the optimal input combination if w = $9? 273 Chapter Seven Costs Minimization Corner Solution K Direction of increase in total cost Isoquant Q = Q0 Isocost Lines • L Cost-minimizing input combination Chapter Seven 274 Comparative Statics A change in the relative price of inputs changes the slope of the isocost line. All else equal, an increase in w must decrease the cost minimizing quantity of labor and increase the cost minimizing quantity of capital with diminishing MRTSL,K. All else equal, an increase in r must decrease the cost minimizing quantity of capital and increase the cost minimizing quantity of labor. 275 Chapter Seven Change in Relative Prices of Inputs K Cost minimizing input combination w=2, r=1 • Cost minimizing input combination, w=1 r=1 • Isoquant Q = Q0 0 L 276 Chapter Seven Some Key Definitions An increase in Q0 moves the isoquant Northeast. • Definition: The cost minimizing input combinations, as Q0 varies, trace out the expansion path. • Definition: If the cost minimizing quantities of labor and capital rise as output rises, labor and capital are normal inputs. • Definition: If the cost minimizing quantity of an input decreases as the firm produces more output, the input is called an inferior input. 277 Chapter Seven An Expansion Path TC2/r K Expansion path TC1/r • TC0/r • Isoquant Q = Q0 • TC0/w TC1/w TC2/w Chapter Seven L 278 An Expansion Path K Substitution & Income Effects Path – Burke Mills • • 0 L Chapter Seven 279 Input Demand Functions Definition: The cost minimizing quantities of labor and capital for various levels of Q, w and r are the input demand functions. L = L*(Q,w,r) K = K*(Q,w,r) 280 Chapter Seven Input Demand Functions 281 Chapter Seven Input Demand Functions Q = 50L1/2K1/2 MPL/MPK = w/r => K/L = w/r … or… K=(w/r)L This is the equation for the expansion path… Q0 = 50L1/2[(w/r)L]1/2 => L*(Q,w,r) = (Q0/50)(r/w)1/2 K*(Q,w,r) = (Q0/50)(w/r)1/2 • Labor and capital are both normal inputs • Labor is a decreasing function of w • Labor is an increasing function of r 282 Chapter Seven Duality “Reverse engineering” – the production functions from the input demands. Example: Cobb-Douglas Revisited Start with the input demands and solve for w: L = (Q0/50)(r/w)1/2 => w = [Q0/(50L)]2r = Plug w into the demand for K K = (Q0/50)[{Q0/(50L)}2r/r]1/2 = Q02/2500L => 283 Chapter Seven Duality Solve for Q0 as a function of K and L: Q0 = 50K1/2L1/2 Why can we do this? Because the tangencies that generate the input demand trace out the isoquants…by keeping Q fixed, we keep “purchasing power” fixed. 284 Chapter Seven Short Run Cost Minimization Suppose that one factor (say, K) is fixed. Definition: The firm’s short run cost minimization problem is to choose quantities of the variable inputs so as to minimize total costs given that the firm wants to produce an output level Q0 – and under the constraint that the quantities of the fixed factors do not change. 285 Chapter Seven Short Run Cost Minimization Min wL + mM + rK* L,M Subject to: Q = f(L,K*,M) Note: L,M are the variable inputs and: • L+mM is the total variable cost • K* is the fixed input and • rK* is the total fixed cost Tangency condition: MPL/w = MPM/m Constraint: Q0 = f(L,K*,M) 286 Chapter Seven Short Run Input Demand Functions The demand functions are the solutions to the short run cost minimization problem: Ls = L(Q,K*,w,m) Ms= M(Q,K*,w,m) So demand for materials and labor depends on plant size (and design) 287 Chapter Seven Short Run Input Demand Functions Suppose that K* is the long run cost minimizing level of capital for output level Q. Then when the firm produces Q, the short run demands for L and M must yield the long run cost minimizing levels of L and M 288 Chapter Seven Key Examples Q = K1/2L1/4M1/4 MPL = (1/4)K1/2L-3/4M1/4 MPK = (1/4)K1/2L1/4M-3/4 w = 16 m=1 r =2 K = K* 289 Chapter Seven Tangency Condition What is the solution to the firm’s short run cost minimization problem? Tangency Condition: MPL/MPM = w/m => (1/4K*1/2L-3/4M1/4)/(1/4K*1/2L1/4M-3/4) = 16/1 M = 16L Constraint: Q0 = K*1/2L1/4(M)1/4 Combining these, we can obtain the short run (conditional) demand functions for labor and materials Ls(Q,K*) = Q2/(4K*) Ms(Q,K*) = (4Q2)/K* 290 Chapter Seven Tangency Condition What is the solution to the firm’s long run cost minimization problem given that the firm wants to produce Q units of output? MPL/MPM = w/m (1/4K1/2L-3/4M1/4)/(1/4K1/2L1/4M-3/4)=16/1 M = 16L MPL/MPK = w/r (1/4K1/2L-3/4M1/4)/(1/4K-1/2L1/4M1/4)=16/1 K = 16L 291 Chapter Seven Tangency Condition Three equations and three unknowns. Combining these, we can obtain the long run demand functions for labor, capital and materials: • L(Q) = Q/8 • M(Q)= 2Q • K(Q) = 2Q Q = K1/2L1/4M1/4 292 Chapter Seven Tangency Condition Suppose that K* = 20. Is it the case that: Ls(10,20) = L(10) Ms(10,20) = M(10)? Ls(10,20) = 100/(4(20) = 1.25 Ms(10,20) = 4(100)/20 = 20 L(10) = 10/8 = 1.25 M(10)= 2(10) = 20 293 Chapter Seven Tangency Condition Suppose that K* = 16 and L* = 256. The firm wishes to produce Q = 48. What is the demand for materials? 48 = (16)1/2(256)1/4M1/4 M = 81 294 Chapter Seven Chapter Eight Costs Curves 295 Chapter Eight Chapter Eight Overview 1. Introduction: HiSense 2. Long Run Cost Functions • • • • Shifts Long run average and marginal cost functions Economies of scale Deadweight loss – "A Perfectly Competitive Market Without Intervention Maximizes Total Surplus" 3. Short Run Cost Functions 4. The Relationship Between Long Run and Short Run Cost Functions 296 Chapter Eight Long Run Cost Functions Definition: The long run total cost function relates minimized total cost to output, Q, to the factor prices (w and r). TC(Q,w,r) = wL*(Q,w,r) + rK*(Q,w,r) Where: L* and K* are the long run input demand functions 297 Chapter Eight Long Run Cost Functions What is the long run total cost function for production function Q = 50L1/2K1/2? L*(Q,w,r) = (Q/50)(r/w)1/2 K*(Q,w,r) = (Q/50)(w/r)1/2 TC(Q,w,r) = w[(Q/50)(r/w)1/2]+r[(Q/50)(w/r)1/2] = (Q/50)(wr)1/2 + (Q/50)(wr)1/2 = (Q/25)(wr)1/2 What is the graph of the total cost curve when w = 25 and r = 100? TC(Q) = 2Q 298 Chapter Eight A Total Cost Curve TC ($ per year) TC(Q) = 2Q $4M. Q (units per year) 299 Chapter Eight A Total Cost Curve TC ($ per year) TC(Q) = 2Q $2M. Q (units per year) 1 M. 300 Chapter Eight A Total Cost Curve TC(Q) = 2Q TC ($ per year) $4M. $2M. Q (units per year) 1 M. 2 M. 301 Chapter Eight Long Run Total Cost Curve Definition: The long run total cost curve shows minimized total cost as output varies, holding input prices constant. Graphically, what does the total cost curve look like if Q varies and w and r are fixed? 302 Chapter Eight Long Run Total Cost Curve 303 Chapter Eight Long Run Total Cost Curve 304 Chapter Eight Long Run Total Cost Curve 305 Chapter Eight Long Run Total Cost Curve K Q1 Q0 K1 K0 TC ($/yr) 0 • • TC = TC0 TC = TC1 L0 L1 L (labor services per year) Q (units per year) 0 306 Chapter Eight Long Run Total Cost Curve K Q1 Q0 K1 K0 TC ($/yr) 0 • • TC = TC0 TC = TC1 L0 L1 L (labor services per year) LR Total Cost Curve TC0 =wL0+rK0 Q (units per year) 0 Q0 307 Chapter Eight Long Run Total Cost Curve K Q1 Q0 K1 K0 TC ($/yr) 0 • • L0 L1 TC = TC0 TC = TC1 L (labor services per year) TC1=wL1+rK1 LR Total Cost Curve TC0 =wL0+rK0 0 Q0 Q1 Q (units per year) Chapter Eight 308 Long Run Total Cost Curve Graphically, how does the total cost curve shift if wages rise but the price of capital remains fixed? 309 Chapter Eight A Change in Input Prices K TC0/r 0 L 310 Chapter Eight A Change in Input Prices K TC1/r TC0/r -w1/r -w0/r 0 L 311 Chapter Eight A Change in Input Prices K TC1/r B TC0/r • • A -w1/r -w0/r 0 L 312 Chapter Eight A Change in Input Prices K TC1/r B TC0/r • • A Q0 -w1/r -w0/r 0 L 313 Chapter Eight A Shift in the Total Cost Curve TC ($/yr) TC(Q) post Q (units/yr) 314 Chapter Eight A Shift in the Total Cost Curve TC ($/yr) TC(Q) post TC(Q) ante Q (units/yr) 315 Chapter Eight A Shift in the Total Cost Curve TC ($/yr) TC(Q) post TC(Q) ante TC0 Q (units/yr) 316 Chapter Eight A Shift in the Total Cost Curve TC ($/yr) TC(Q) post TC(Q) ante TC1 TC0 Q (units/yr) Q0 317 Chapter Eight Input Price Changes How does the total cost curve shift if all input prices rise (the same amount)? For example, suppose that all input prices double: 318 Chapter Eight All Input Price Changes K (capital services/yr) • A L (labor services/yr) 0 319 Chapter Eight All Input Price Changes K (capital services/yr) L (labor -w/r services/yr) 0 320 Chapter Eight All Input Price Changes K (capital services/yr) • A Q0 L (labor -w/r services/yr) 0 321 Chapter Eight All Input Price Changes K (capital services/yr) • 2 A Q0 L (labor -w/r 0 services/yr) 1 322 Chapter Eight All Input Price Changes Example: TC(Q,w,r) = (wr)1/2Q/25 TC(Q, λw, λr) = (λw)1/2(λr)1/2Q/25 = λ(wr)1/2Q/25 = λTC(Q,w,r) 323 Chapter Eight Long Run Average Cost Function Definition: The long run average cost function is the long run total cost function divided by output, Q. That is, the LRAC function tells us the firm’s cost per unit of output… AC(Q,w,r) = TC(Q,w,r)/Q 324 Chapter Eight Long Run Marginal Cost Function Definition: The long run marginal cost function measures the rate of change of total cost as output varies, holding constant input prices. MC(Q,w,r) = {TC(Q+Q,w,r) – TC(Q,w,r)}/Q = TC(Q,w,r)/Q where: w and r are constant 325 Chapter Eight Long Run Marginal Cost Function Recall that, for the production function Q = 50L1/2K1/2, the total cost function was TC(Q,w,r) = (Q/25)(wr)1/2. If w = 25, and r = 100, TC(Q) = 2Q. 326 Chapter Eight Long Run Marginal Cost Function a. What are the long run average and marginal cost functions for this production function? AC(Q,w,r) = (wr)1/2/25 MC(Q,w,r) = (wr)1/2/25 b. What are the long run average and marginal cost curves when w = 25 and r = 100? AC(Q) = 2Q/Q = 2. MC(Q) = (2Q)/Q = 2. 327 Chapter Eight Average & Marginal Cost Curves AC, MC ($ per unit) AC(Q) = MC(Q) = 2 $2 Q (units/yr) 0 328 Chapter Eight Average & Marginal Cost Curves AC, MC ($ per unit) AC(Q) = MC(Q) = 2 $2 Q (units/yr) 0 1M 329 Chapter Eight Average & Marginal Cost Curves AC, MC ($ per unit) AC(Q) = MC(Q) = 2 $2 Q (units/yr) 0 1M 2M Chapter Eight 330 Average & Marginal Cost Curves Suppose that w and r are fixed: When marginal cost is less than average cost, average cost is decreasing in quantity. That is, if MC(Q) < AC(Q), AC(Q) decreases in Q. 331 Chapter Eight Average & Marginal Cost Curves When marginal cost is greater than average cost, average cost is increasing in quantity. That is, if MC(Q) > AC(Q), AC(Q) increases in Q. When marginal cost equals average cost, average cost does not change with quantity. That is, if MC(Q) = AC(Q), AC(Q) is flat with respect to Q. 332 Chapter Eight Average & Marginal Cost Curves AC, MC ($/yr) “typical” shape of AC AC Q (units/yr) 0 333 Chapter Eight Average & Marginal Cost Curves AC, MC ($/yr) “typical” shape of AC MC AC • Q (units/yr) 0 334 Chapter Eight Average & Marginal Cost Curves AC, MC ($/yr) “typical” shape of AC MC AC • AC at minimum when AC(Q)=MC(Q) Q (units/yr) 0 335 Chapter Eight Economies & Diseconomies of Scale Definition: If average cost decreases as output rises, all else equal, the cost function exhibits economies of scale. Similarly, if the average cost increases as output rises, all else equal, the cost function exhibits diseconomies of scale. Definition: The smallest quantity at which the long run average cost curve attains its minimum point is called the minimum efficient scale. 336 Chapter Eight Minimum Efficiency Scale (MES) AC ($/yr) AC(Q) Q (units/yr) 0 Q* = MES 337 Chapter Eight MES – Selected Food & Beverages Industry MES as % of US market output: Beet Sugar (processed) Cane Sugar (processed) Flour Breakfast Cereal Baby food 1.87 12.01 .68 9.47 2.59 338 Chapter Eight Returns to Scale & Economies of Scale When the production function exhibits increasing returns to scale, the long run average cost function exhibits economies of scale so that AC(Q) decreases with Q, all else equal. 339 Chapter Eight Returns to Scale & Economies of Scale • When the production function exhibits decreasing returns to scale, the long run average cost function exhibits diseconomies of scale so that AC(Q) increases with Q, all else equal. • When the production function exhibits constant returns to scale, the long run average cost function is flat: it neither increases nor decreases with output. 340 Chapter Eight Returns to Scale & Economies of Scale CRS IRS DRS Production Function Q = L Q = L2 Q = L1/2 Labor Demand L*=Q L*=Q1/2 L*=Q2 Total Cost Function TC=wQ wQ1/2 wQ2 Average Cost Function AC=w w/Q1/2 wQ Economies of Scale none EOS DOS 341 Chapter Eight Output Elasticity of Total Cost Definition: The percentage change in total cost per one percent change in output is the output elasticity of total cost, TC,Q. TC,Q = (TC/Q)(Q/TC) = = MC/AC • If TC,Q < 1, MC < AC, so AC must be decreasing in Q. Therefore, we have economies of scale. • If TC,Q > 1, MC > AC, so AC must be increasing in Q. Therefore, we have diseconomies of scale. • If TC,Q = 1, MC = AC, so AC is just flat with respect to Q. 342 Chapter Eight Output Elasticity of Total Cost Example: For Selected Manufacturing Industries in India Industry TC,Q Iron and Steel Cotton Textiles Cement Electricity and Gas 0.553 1.211 1.162 0.3823 343 Chapter Eight Short Run & Total Variable Cost Functions Definition: The short run total cost function tells us the minimized total cost of producing Q units of output, when (at least) one input is fixed at a particular level. Definition: The total variable cost function is the minimized sum of expenditures on variable inputs at the short run cost minimizing input combinations. 344 Chapter Eight Total Fixed Cost Function Definition: The total fixed cost function is a constant equal to the cost of the fixed input (s). STC(Q,K0) = TVC(Q,K0) + TFC(Q,K0) Where: K0 is the fixed input and w and r are fixed (and suppressed as arguments) 345 Chapter Eight Key Cost Functions Interactions TC ($/yr) Example: Short Run Total Cost, Total Variable Cost and Total Fixed Cost TFC Q (units/yr) 346 Chapter Eight Key Cost Functions Interactions TC ($/yr) Example: Short Run Total Cost, Total Variable Cost and Total Fixed Cost TVC(Q, K0) TFC Q (units/yr) 347 Chapter Eight Key Cost Functions Interactions TC ($/yr) Example: Short Run Total Cost, Total Variable Cost and Total Fixed Cost STC(Q, K0) TVC(Q, K0) TFC Q (units/yr) 348 Chapter Eight Key Cost Functions Interactions TC ($/yr) Example: Short Run Total Cost, Total Variable Cost and Total Fixed Cost STC(Q, K0) rK0 TVC(Q, K0) TFC rK0 Q (units/yr) 349 Chapter Eight Key Cost Functions Interactions Suppose that the production function is Q = K1/2L1/4M1/4. Let w = 16, m = 1 and r = 2. What is the short run total cost curve when capital is fixed at level K0? What is the (short run) total variable cost curve? What is the (short run) total fixed cost curve? 350 Chapter Eight Key Cost Functions Interactions Recall that the short run input demand functions for labor and materials are: Ls (Q,K0) = Q2/(4K0) & Ms(Q,K0) = (4Q2)/K0 STC(Q,K0) = 16(Q2/(4K0))+ (4Q2)/K0 + 2K0 = (8Q2/K0) + 2K0 TVC(Q,K0) = (8Q2)/K0 TFC(K0) = 2K0 NB: for constant Q, TVC decreases in K0 351 Chapter Eight Long and Short Run Total Cost Functions The firm can minimize costs at least as well in the long run as in the short run because it is “less constrained”. Hence, the short run total cost curve lies everywhere above the long run total cost curve. 352 Chapter Eight Long and Short Run Total Cost Functions However, when the quantity is such that the amount of the fixed inputs just equals the optimal long run quantities of the inputs, the short run total cost curve and the long run total cost curve coincide. 353 Chapter Eight Long and Short Run Total Cost Functions K TC0/r 0 TC0/w Chapter Eight L 354 Long and Short Run Total Cost Functions K TC1/r TC0/r K0 0 •B TC0/w TC1/w Chapter Eight L 355 Long and Short Run Total Cost Functions TC2/r TC1/r K Q1 • TC0/r K0 0 C • A •B TC0/w TC1/w TC2/w Chapter Eight L 356 Long and Short Run Total Cost Functions TC2/r TC1/r K Q1 Expansion Path • TC0/r C Q0 K0 0 • A Q0 B • TC0/w TC1/w TC2/w Chapter Eight L 357 Long and Short Run Total Cost Functions Total Cost ($/yr) STC(Q,K0) TC(Q) K0 is the LR cost-minimising quantity of K for Q0 0 Q0 Q1 Q (units/yr) 358 Chapter Eight Long and Short Run Total Cost Functions STC(Q,K0) Total Cost ($/yr) TC(Q) TC0 • A K0 is the LR cost-minimising quantity of K for Q0 0 Q0 Q1 Q (units/yr) 359 Chapter Eight Long and Short Run Total Cost Functions STC(Q,K0) Total Cost ($/yr) TC(Q) •C TC1 TC0 • A K0 is the LR cost-minimising quantity of K for Q0 0 Q0 Q1 Q (units/yr) 360 Chapter Eight Long and Short Run Total Cost Functions STC(Q,K0) Total Cost ($/yr) • •C TC2 B TC1 TC0 TC(Q) • A K0 is the LR cost-minimising quantity of K for Q0 0 Q0 Q1 Q (units/yr) 361 Chapter Eight Short Run Average Cost Function Definition: The Short run average cost function is the short run total cost function divided by output, Q. That is, the SAC function tells us the firm’s short run cost per unit of output. SAC(Q,K0) = STC(Q,K0)/Q Where: w and r are held fixed 362 Chapter Eight Short Run Marginal Cost Function Definition: The short run marginal cost function measures the rate of change of short run total cost as output varies, holding constant input prices and fixed inputs. SMC(Q,K0)={STC(Q+Q,K0)– STC(Q,K0)}/Q = STC(Q,K0)/Q where: w,r, and K0 are constant 363 Chapter Eight Summary Cost Functions Note: When STC = TC, SMC = MC STC = TVC + TFC SAC = AVC + AFC Where: SAC = STC/Q AVC = TVC/Q (“average variable cost”) AFC = TFC/Q (“average fixed cost”) The SAC function is the VERTICAL sum of the AVC and AFC functions 364 Chapter Eight Summary Cost Functions $ Per Unit Example: Short Run Average Cost, Average Variable Cost and Average Fixed Cost AFC 0 Q (units per year) 365 Chapter Eight Summary Cost Functions $ Per Unit AVC Example: Short Run Average Cost, Average Variable Cost and Average Fixed Cost AFC 0 Q (units per year) 366 Chapter Eight Summary Cost Functions SAC $ Per Unit AVC Example: Short Run Average Cost, Average Variable Cost and Average Fixed Cost AFC 0 Q (units per year) 367 Chapter Eight Summary Cost Functions $ Per Unit SMC SAC AVC Example: Short Run Average Cost, Average Variable Cost and Average Fixed Cost AFC 0 Q (units per year) 368 Chapter Eight Long Run Average Cost Function $ per unit SAC(Q,K3) AC(Q) • 0 • • Q1 Q2 Q3 Q (units per year) 369 Chapter Eight Long Run Average Cost Function $ per unit SAC(Q,K1) AC(Q) • 0 • • Q1 Q2 Q3 Q (units per year) 370 Chapter Eight Long Run Average Cost Function $ per unit SAC(Q,K1) SAC(Q,K2) AC(Q) • 0 • • Q1 Q2 Q3 Q (units per year) 371 Chapter Eight Long Run Average Cost Function $ per unit SAC(Q,K3) SAC(Q,K1) SAC(Q,K2) AC(Q) • 0 • • Q1 Q2 Q3 Q (units per year) 372 Chapter Eight Long Run Average Cost Function Example: Let Q = K1/2L1/4M1/4 and let w = 16, m = 1 and r = 2. For this production function and these input prices, the long run input demand curves are: Therefore, the long run total cost curve is: TC(Q) = 16(Q/8) + 1(2Q) + 2(2Q) = 8Q The long run average cost curve is: AC(Q) = TC(Q)/Q = 8Q/Q = 8 Chapter Eight L* (Q )= Q/ 8 M *( Q) = 2 Q K *( Q) = 2 373 Short Run Average Cost Function Recall, too, that the short run total cost curve for fixed level of capital K0 is: STC(Q,K0) = (8Q2)/K0 + 2K0 If the level of capital is fixed at K0 what is the short run average cost curve? SAC(Q,K0) = 8Q/K0 + 2K0/Q 374 Chapter Eight Cost Function Summary $ per unit MC(Q) Q (units per year) 0 375 Chapter Eight Cost Function Summary $ per unit MC(Q) AC(Q) Q (units per year) 0 376 Chapter Eight Cost Function Summary $ per unit MC(Q) AC(Q) SAC(Q,K2) • • SMC(Q,K ) 1 Q (units per 0 Q1 Q2 year) Q3 377 Chapter Eight Cost Function Summary $ per unit MC(Q) MC(Q) SAC(Q,K3) SAC(Q,K1) AC(Q) SAC(Q,K2) • • SMC(Q,K ) 1 • Q (units per 0 Q1 Q2 year) Q3 378 Chapter Eight Cost Function Summary $ per unit MC(Q) MC(Q) SAC(Q,K3) SAC(Q,K1) AC(Q) SAC(Q,K2) • • SMC(Q,K ) 1 • Q (units per 0 Q1 Q2 year) Q3 379 Chapter Eight Chapter Nine Perfectly Competitive Markets 380 Chapter Nine Chapter Nine Overview 1. Introduction: Nakao Growers 2. Perfect Competition Defined 3. The Profit Maximization Hypothesis 4. The Profit Maximization Condition 5. Short Run Equilibrium • Short Run Supply Curve for the Firm • Short Run Market Supply Curve • Short Run Perfectly Competitive Equilibrium • Producer Surplus 6. Long Run Equilibrium • • Long Run Equilibrium Conditions Long Run Supply Curve 381 Chapter Nine Perfectly Competitive Markets A perfectly competitive market consists of firms that produce identical products that sell at the same price. Each firm’s volume of output is so small in comparison to the overall market demand that no single firm has an impact on the market price. 382 Chapter Nine Perfectly Competitive Markets A. Firms produce undifferentiated products in the sense that consumers perceive them to be identical B. Consumers have perfect information about the prices all sellers in the market charge 383 Chapter Nine Perfectly Competitive Markets C. Each buyer’s purchases are so small that he/she has an imperceptible effect on market price. D. Each seller’s sales are so small that he/she has an imperceptible effect on market price. Each seller’s input purchases are so small that he/she perceives no effect on input prices E. All firms (industry participants and new entrants) have equal access to resources (technology, inputs). 384 Chapter Nine Implications of Conditions The Law of One Price: Conditions (a) and (b) imply that there is a single price at which transactions occur. Price Takers: Conditions (c) and (d) imply that buyers and sellers take the price of the product as given when making their purchase and output decisions. Free Entry: Condition (e) implies that all firms have identical long run cost functions 385 Chapter Nine The Profit Maximization Hypothesis Definition: Economic Profit Sales Revenue-Economic (opportunity) Cost Example: • Revenues: $1M • Costs of supplies and labor: $850,000 • Owner’s best outside offer: $200,000 386 Chapter Nine The Profit Maximization Hypothesis “Accounting Profit”: $1M - $850,000 = $150,000 “Economic Profit”: $1M - $850,000 - $200,000 = -$50,000 • Business “destroys” $50,000 of wealth of owner 387 Chapter Nine The Profit Maximization Condition Max (q) = Pq – TC(q) q Definition: A firm’s marginal revenue is the rate at which total revenue changes with respect to output: MR(q) = {TR(q + q)-TR(q)}/q = (Pq)/q = P…the firm's "marginal benefit" from a sale 388 Chapter Nine The Profit Maximization Condition If P > MC then profit rises if output is increased If P < MC then profit falls if output is increased. Therefore, the profit maximization condition for a price-taking firm is P = MC 389 Chapter Nine The Profit Maximization Condition 390 Chapter Nine The Profit Maximization Condition Where these have been drawn for: TC(q) = 242q - .9q2 + (.05/3)q3 MC(q) = 24 - 1.8q + .05q2 P = 15 At profit maximizing point: 1. P = MC 2. MC rising “firm demand" = P (sells as much as likes at P) “firm supply" defined by MC curve? Not quite: 391 Chapter Nine Short Run Equilibrium For the following, the short run is the period of time in which the firm’s plant size is fixed and the number of firms in the industry is fixed. STC(Q) = SFC + NSFC + TVC(q) for q > 0 SFC for q = 0 392 Chapter Nine Short Run Equilibrium SFC is the cost of the firm’s fixed input that are unavoidable at q = 0 Output insensitive for q > 0 = Sunk NSFC is the cost of the firm’s inputs that are avoidable if the firm produces zero (salaries of some employees, for example) Output insensitive for q > 0 = Non-sunk TFC = SFC + NSFC TVC(q) are the output sensitive costs (and are non-sunk) 393 Chapter Nine Short Run Supply Curve (SRSC) Definition: The firm’s Short run supply curve tells us how the profit maximizing output changes as the market price changes. Case 1: Short Run Supply Curve: NSFC=0 If the firm chooses to produce a positive output, P = SMC defines the short run supply curve of the firm. But… 394 Chapter Nine Shut Down Price The firm will choose to produce a positive output only if: (q) > (0) …or… Pq – TVC(q) – TFC > -TFC Pq – TVC(q) > 0 P > AVC(q) Definition: The price below which the firm would opt to produce zero is called the shut down price, Ps. In this case, Ps is the minimum point on the AVC curve. 395 Chapter Nine Short Run Supply Function Therefore, the firm’s short run supply function is defined by: 1. P=SMC, where SMC slopes upward as long as P > Ps 2. 0 where P < Ps This means that a perfectly competitive firm may choose to operate in the short run even if economic profit is negative. 396 Chapter Nine Short Run Supply Curve $/yr NSFC = 0 SMC SAC AVC Ps Quantity (units/yr) 397 Chapter Nine Cost Considerations At prices below SAC but above AVC, profits are negative if the firm produces…but the firm loses less by producing than by shutting down because of sunk costs. Example: STC(q) = 100 + 20q + q2 TFC = 100 (nb: this is sunk) TVC(q) = 20q + q2 AVC(q) = 20 + q SMC(q) = 20 + 2q 398 Chapter Nine Cost Considerations The minimum level of AVC is the point where AVC = SMC or: 20+q = 20+2q q=0 AVC minimized at 20 The firm’s short run supply curve is, then: P < Ps = 20: qs = 0 P > Ps = 20: P = SMC P = 20+2q qs = 10 + ½P 399 Chapter Nine SRSC When All Costs are Non-Sunk If the firm chooses to produce a positive output, P = SMC defines the short run supply curve of the firm. But the firm will choose to produce a positive output only if: (q) > (0) …or… Pq – TVC(q) - TFC > 0 P > AVC(q) + AFC(q) = SAC(q) Now, the shut down price, Ps is the minimum of the SAC curve 400 Chapter Nine SRSC When All Costs are Non-Sunk $/yr SMC SAC Ps AVC Quantity (units/yr) 401 Chapter Nine SRSC When All Costs are Non-Sunk STC(q) = F + 20q + q2 F = 100, all of which is sunk: AVC(q) = 20 + q SMC(q) = 20 + 2q SAC(q) = 100/q + 20 + q SAC = SMC at q = 10 At any P > 40, the firm earns positive economic profit At any P < 40, the firm earns negative economic profit. 402 Chapter Nine Market Supply and Equilibrium Definition: The market supply at any price is the sum of the quantities each firm supplies at that price. The short run market supply curve is the horizontal sum of the individual firm supply curves. 403 Chapter Nine Short Run market & Supply Curves 404 Chapter Nine Short Run Perfectly Completive Equilibrium Definition: A short run perfectly competitive equilibrium occurs when the market quantity demanded equals the market quantity supplied. ni=1 qs(P) = Qd(P) and qs(P) is determined by the firm's individual profit maximization condition. 405 Chapter Nine Short Run Perfectly Completive Equilibrium 406 Chapter Nine Deriving a Short Run Market Equilibrium 300 Identical Firms Qd(P) = 60 – P STC(q) = 0.1 + 150q2 SMC(q) = 300q NSFC = 0 AVC(q) = 150q 407 Chapter Nine Deriving a Short Run Market Equilibrium Short Run Equilibrium Profit maximization condition: P = 300q qs(P) = P/300 Qs(P) = Qd(P) P = 60 – P P*= 30 q* = 30/300=.1 Q* = 30 408 Chapter Nine Deriving a Short Run Market Equilibrium Do firms make positive profits at the market equilibrium? SAC = STC/q = .1/q + 150q When each firm produces .1, SAC per firm is: .1/.1 + 150(.1) = 16 Therefore, P* > SAC so profits are positive 409 Chapter Nine Producer Surplus Definition: Producer Surplus is the area above the market supply curve and below the market price. It is a monetary measure of the benefit that producers derive from producing a good at a particular price. …that the producer earns the price for every unit sold, but only incurs the SMC for each unit. This is why the difference between the P and SMC curve measures the total benefit derived from production. 410 Chapter Nine Producer Surplus Further, since the market supply curve is simply the sum of the individual supply curves…which equal the marginal cost curves the difference between price and the market supply curve measures the surplus of all producers in the market. …that producer’s surplus does not deduct fixed costs, so it does not equal profit. 411 Chapter Nine Producer Surplus P Market Supply Curve P* Producer Surplus Chapter Nine Q 412 Long Run Market Equilibrium For the following, the long run is the period of time in which all the firm’s inputs can be adjusted. The number of firms in the industry can change as well. The firm should use long run cost functions for evaluating the cost of outputs it might produce in this longer term period…i.e., decisions to modify plant size, enter or exit, change production process and so on would all be based on long term analysis 413 Chapter Nine Long Run Market Equilibrium MC $/unit P AC SMC0 SAC0 SAC1 Example: Incentive to Change Plant Size SMC1 For example, at P, this firm has an incentive to change plant size to level K1 from K0: 1.8 q 6 (000 units/yr) 414 Chapter Nine Long Run Market Equilibrium The firm’s long run supply curve: P = MC for P > min(AC) = Ps 0 (exit) for P < min(AC) = Ps A long run perfectly competitive equilibrium occurs at a market price, P*, a number of firms, n*, and an output per firm, q* that satisfies: 415 Chapter Nine Long Run Market Equilibrium Long run profit maximization with respect to output and plant size: P* = MC(q*) Zero economic profit P* = AC(q*) Demand equals supply Qd(P*) = n*q* …or… n* = Qd(P*)/q* 416 Chapter Nine Long Run Perfectly Competitive $/unit $/unit n* = 10,000,000/50,000=200 MC SAC Market demand AC P* SMC q*=50,000 q Q*=10M. 417 Chapter Nine Q Calculating Long Run Equilibrium TC(q) = 40q - q2 + .01q3 AC(q) = 40 – q + .01q2 MC(q) = 40 – 2q + .03q2 Qd(P) = 25000-1000P The long run equilibrium satisfies the following: a. P* = 40 – 2q* - .03q*2 b. P* = 40 – q* + .01q*2 c. 25000-1000P* = q*n* 418 Chapter Nine Calculating Long Run Equilibrium Using (a) and (b), we have: 40 – 2q* + .03q*2 = 40-q*+.01q*2 q* = 50 P* = 15 Qd(P*) = 10000 Using (c ) we have: n* = 10000/50 = 200 419 Chapter Nine Calculating Long Run Equilibrium Summarizing long run equilibrium – “If anyone can do it, you can’t make money at it” Or if the firm’s strategy is based on skills that can be easily imitated or resources that can be easily acquired, in the long run your economic profit will be competed away. 420 Chapter Nine Long Run Market Supply Curve We have calculated a point at which the market will be in long run equilibrium. This is a point on the long run market supply curve. This curve can be derived explicitly, however. Definition: The Long Run Market Supply Curve tells us the total quantity of output that will be supplied at various market prices, assuming that all long run adjustments (plant, entry) take place. 421 Chapter Nine Long Run Market Supply Curve Since new entry can occur in the long run, we cannot obtain the long run market supply curve by summing the long run supplies of current market participants Instead, we must construct the long run market supply curve. We reason that, in the long run, output expansion or contraction in the industry occurs along a horizontal line corresponding to the minimum level of long run average cost. If P > min(AC), entry would occur, driving price back to min(AC) If P < min(AC), firms would earn negative profits and would supply nothing 422 Chapter Nine Long Run Market Supply Curve $/unit $/unit n** = 18M/52,000 = 360 SS0 SS1 D1 MC 23 15 SAC D0 AC LS SMC q (000s) 50 52 10 Chapter Nine 18 423 Q (M.) Chapter Ten Competitive Markets: Applications 424 Chapter Ten Chapter Ten Overview 1. Motivation: Agricultural Price Supports 2. Deadweight Loss • A Perfectly Competitive Market Without Intervention Maximizes Total Surplus" 3. Government Intervention – Who Wins and Who Loses? 4. Examples of Various Government Polices • • • • Excise Taxes Price Ceilings Production Quotas Import Tariffs 5. Conclusions 425 Chapter Ten Deadweight Loss At the Perfectly Competitive Equilibrium, (Q*,P*), Total Surplus is maximized. Consumer's Surplus at (Q*,P*): ABC Producer's Surplus at (Q*,P*) : DBC Total Surplus at (Q*,P*): ADC 426 Chapter Ten Deadweight Loss Definition: A deadweight loss is a reduction in net economic benefits resulting from an inefficient allocation of resources. 427 Chapter Ten Surplus Maximization in Competitive Equilibrium P Supply A Pd C P* B Ps D Demand Q1 Q Q* 428 Chapter Ten Surplus Maximization in Competitive Equilibrium P Supply A Ps P* B Pd C D Demand Q* Q2 Chapter Ten Q 429 Economic Efficiency Definition: Economic Efficiency means that the total surplus is maximized. "Every consumer who is willing to pay more than the opportunity cost of the resources needed to produce extra output is able to buy; every consumer who is not willing to pay the opportunity cost of the extra output does not buy.“ "All gains from trade (between buyers and suppliers) are exhausted at the efficient point." The perfectly competitive economic efficiency. equilibrium attains 430 Chapter Ten Government Intervention: Winners & Losers Intervention Type: Effect on Effect on Effect on Effect on (domestic) (domestic) (domestic) (domestic) Is a (domestic) Quantity Consumer Producer Government Deadweight Traded Surplus Surplus Budget Loss created? Excise Tax Falls Falls Falls Positive Yes Subsidies to Producers Rises Rises Rises Negative Yes Maximum Price Ceilings for Producers Falls; Excess Demand Rise or Fall Falls Zero Yes Minimum Price Floors for Producers Falls; Excess Supply Falls Rise or Fall Zero Yes Production Quotas Falls; Excess Supply Falls Rise or Fall Zero Yes Import Tariffs Falls Falls Rises Positive Yes Import Quotas Falls Falls Rises Zero Yes 431 Chapter Ten Policy: Excise Tax Definition: An excise tax (or a specific tax) is an amount paid by either the consumer or the producer per unit of the good at the point of sale. (The amount paid by the demanders exceeds the total amount received by the sellers by amount T) 432 Chapter Ten Policy: Excise Tax S’ P S T Pd P* Ps Demand Q Q1 Q* 433 Chapter Ten Key Definitions Definition: The amount by which the price paid by buyers, PD, rises over the non-tax equilibrium price, P*, is the incidence of the tax on consumers; the amount by which the price received by sellers, PS, falls below P* is called the incidence of the tax on producers. 434 Chapter Ten Incidence of Tax in Two Cases P Pd=P*+T S’ T Ps = P* S P D S Q Pd = P* Ps = P*-T T Q D 435 Chapter Ten Back of the Envelope "Back of the Envelope" method calculate the incidence of a specific tax to Pd/Ps = / where: is the own-price elasticity of supply is the own-price elasticity of demand 436 Chapter Ten Back of the Envelope Why – consider a small tax applied to an economy at point (Q*,P*) =(Q/Q*)/(Pd/P*)… Q/Q*=Pd/P* =(Q/Q*)/(Ps/P*)… Q/Q*=Ps/P* but for market to clear, Q/Q* must be the same for demand and supply, hence Pd/P* = Ps/P* 437 Chapter Ten Tax Affect Example: Let = -.5 and = 2. What is the relative incidence of a specific tax on consumers and producers? Pd/Ps = 2/-.5 = -4 interpretation: "consumers pay four times as much as the decrease in price producers receive. Hence, an excise tax of $1 results in an increase in consumer price of $.8 and a decrease in price received by producers of $.2" Note: Subsidies are negative taxes. 438 Chapter Ten Subsidies P S’ Ps Pd D Q* Q2 Q 439 Chapter Ten Subsidies P S S’ T Ps Pd D Q* Q2 Q 440 Chapter Ten Subsidies P S S’ T Ps Pd D Q* Q2 Q 441 Chapter Ten Policy: Price Ceilings Definition: A price ceiling is a legal maximum on the price per unit that a producer can receive. If the price ceiling is below the pre-control competitive equilibrium price, then the ceiling is called binding. 442 Chapter Ten Policy: Price Ceilings P S D Q 443 Chapter Ten Policy: Price Ceilings P S PMAX D Q 444 Chapter Ten Policy: Price Ceilings P S PMAX Excess Demand D Qs Q* Qd Q 445 Chapter Ten Policy: Price Floor Definition: A price floor is a minimum price that consumers can legally pay for a good. Price floors sometimes are referred to as price supports. If the price floor is above the pre-control competitive equilibrium price, it is said to be binding. 446 Chapter Ten Policy: Price Floor P S D Q 447 Chapter Ten Policy: Price Floor P S Excess Supply PMIN D Qd Q* Qs Q 448 Chapter Ten Policy: Production Quotas Definition: A production quota is a limit on either the number of producers in the market or on the amount that each producer can sell. The quota usually has a goal of placing a limit on the total quantity that producers can supply to the market. 449 Chapter Ten Policy: Production Quotas P Original Supply Demand QMAX Q* Q 450 Chapter Ten Policy: Production Quotas P Supply with quota Original Supply P* Demand QMAX Q* Q 451 Chapter Ten Policy: Import Tariffs & Quotas Definition: Tariffs are taxes levied by a government on goods imported into the government's own country. Tariffs sometimes are called duties. Definition: An import quota is a limit on the total number of units of a good that can be imported into the country. 452 Chapter Ten Import of a Good P A Domestic Supply D Domestic Demand Q 453 Chapter Ten Import of a Good P A Domestic Supply P* D Domestic Demand Q 454 Chapter Ten Import of a Good P Domestic Supply A P* PW D C Q1 B Q4 Foreign Supply Domestic Demand Q 455 Chapter Ten Import of a Good – With Tariff P Domestic Supply Domestic Demand Q 456 Chapter Ten Import of a Good – With Tariff P Domestic Supply PW+T PW T Domestic Demand Q1 Q2 Q Q3 Q4 457 Chapter Ten Import of a Good – With Tariff P Domestic Supply PW+T PW D A C B T Domestic Demand Q1 Q2 Q Q3 Q4 458 Chapter Ten Comparing a Tariff to a Quota Let quota limit imports to Q3-Q2…the equilibrium price would be the same as for the tariff…and the (world) deadweight loss would be the same as well. Is there a difference? The quota generates no government revenue. Hence, while the total supply and total price for the domestic market remains the same under the two policies, domestic deadweight loss is larger under the quota. 459 Chapter Ten Chapter Eleven Monopoly & Monopsony 460 Chapter Eleven Chapter Eleven Overview 1. Introduction: Brush Wellman 2. The Monopolist’s Profit Maximization Problem • • • The Profit Maximization Condition Equilibrium The Inverse Pricing Elasticity Rule 3. Multi-plant Monopoly and Cartel Production 4. The Welfare Economics and Monopoly 461 Chapter Eleven A Monopoly Definition: A Monopoly Market consists of a single seller facing many buyers. The monopolist's profit maximization problem: Max (Q) = TR(Q) - TC(Q) Q where: TR(Q) = QP(Q) and P(Q) is the (inverse) market demand curve. 462 Chapter Eleven A Monopoly – Profit Maximizing Profit maximizing condition for a monopolist: TR(Q)/Q = TC(Q)/Q MR(Q) = MC(Q) The monopolist sets output so that marginal profit of additional production is just zero. Recall: A perfect competitor sets P = MC…in other words, marginal revenue equals price. 463 Chapter Eleven A Monopoly – Profit Maximizing Why is this not so for the monopolist? TR = P1Q + Q0P => TR(Q0)/Q = P1 + Q0P/Q = MR(Q0) and, as we let the change in output get very small, this approaches: • MR(Q0) = P0 + Q0P/Q • MR(Q0) < P0 for any Q0 > 0 • MR may be negative or positive for a perfect competitor, demand was "flat" so MR = P 464 Chapter Eleven Marginal Revenue Price Price Competitive Firm Monopolist Demand facing firm P0 Demand facing firm P0 P1 A B q q+1 C A Firm output B Q0 Q0+1 Firm output 465 Chapter Eleven Marginal Revenue Curve and Demand Price The MR curve lies below the demand curve. P(Q0) P(Q), the (inverse) demand curve MR(Q0) MR(Q), the marginal revenue curve Quantity Q0 Chapter Eleven 466 Market Power Definition: An agent has Market Power if s/he can affect, through his/her own actions, the price that prevails in the market. Sometimes this is thought of as the degree to which a firm can raise price above marginal cost. 467 Chapter Eleven Market Power P(Q) = a - bQ & linear demand TR(Q) = QP(Q) What is the equation of the marginal revenue curve? P/Q = -b MR(Q) = P + QP/Q = a - bQ + Q(-b) = a - 2bQ twice the slope of demand for linear demand 468 Chapter Eleven Market Power What is the equation of the average revenue curve? AR(Q) = TR(Q)/Q = P = a - bQ (you earn more on the average unit than on an additional unit) 469 Chapter Eleven Market Power What is the profit-maximizing output if: TC(Q) = 100 + 20Q + Q2 MC(Q) = 20 + 2Q AVC(Q) = 20 + Q AC(Q) = 100/Q + 20 + Q P(Q) = 100 - Q MR = MC => 100 - 2Q = 20 + 2Q Q* = 20 P* = 80 470 Chapter Eleven Shutdown Condition In the short run, the monopolist shuts down if the most profitable price does not cover AVC (or average non-sunk costs). In the long run, the monopolist shuts down if the most profitable price does not cover AC. Here, P* exceeds both AVC and AC. * = 700 (= Q*P* - 100 - 20(Q*) - Q*2) 471 Chapter Eleven Positive Profits for Monopolist This profit is positive. Why? Because the monopolist takes into account the pricereducing effect of increased output so that the monopolist has less incentive to increase output than the perfect competitor. Profit can remain positive in the long run. Why? Because we are assuming that there is no possible entry in this industry, so profits are not competed away. 472 Chapter Eleven Positive Profits for Monopolist Price MC 100 AVC 80 MR 20 Demand Curve 20 50 Chapter Eleven Quantity 473 Positive Profits for Monopolist Price MC 100 AVC e 80 MR 20 Demand Curve 20 50 Chapter Eleven Quantity 474 Positive Profits for Monopolist Price MC 100 AVC e 80 AC MR 20 Demand Curve 20 50 Chapter Eleven Quantity 475 Equilibrium A monopolist does not have a supply curve (i.e., an optimal output for any exogenouslygiven price) because price is endogenouslydetermined by demand: the monopolist picks a preferred point on the demand curve. One could also think of the monopolist choosing output to maximize profits subject to the constraint that price be determined by the demand curve. 476 Chapter Eleven Inverse Elasticity Pricing Rule We can rewrite the MR curve as follows: MR = P + QP/Q = P(1 + (Q/P)(P/Q)) = P(1 + 1/) where: is the price elasticity of demand, (P/Q)(Q/P) 477 Chapter Eleven Inverse Elasticity Pricing Rule Using this formula: • When demand is elastic ( < -1), MR > 0 • When demand is inelastic ( > -1), MR < 0 • When demand is unit elastic ( = -1), MR= 0 478 Chapter Eleven Elasticity Region of the Demand Curve Price a Elastic region ( < -1), MR > 0 Unit elastic (=-1), MR=0 Inelastic region (0>>-1), MR<0 a/2b a/b Chapter Eleven Quantity 479 Elasticity Region of the Demand Curve Therefore: The monopolist will always operate on the elastic region of the market demand curve As demand becomes more elastic at each point, marginal revenue approaches price Example A: QD = 100P-2 MC = $50 What is the monopolist's optimal price? MR = MC P(1+1/) = MC P(1+1/(-2)) = 50 P* = 100 480 Chapter Eleven Elasticity Region of the Demand Curve Example B: Now, suppose that QD = 100P-b and MC = c (constant). What is the monopolist's optimal price now? P(1+1/-b) = c P* = cb/(b-1) We need the assumption that b > 1 ("demand is everywhere elastic") to get an interior solution. As b -> 1 (demand becomes everywhere less elastic), P* -> infinity and P - MC, the "price-cost margin" also increases to infinity. As b -> , the monopoly price approaches marginal cost. 481 Chapter Eleven The Lerner Index of Market Power Definition: the Lerner Index of market power is the price-cost margin, (P*-MC)/P*. This index ranges between 0 (for the competitive firm) and 1, for a monopolist facing a unit elastic demand. 482 Chapter Eleven The Lerner Index of Market Power Restating the monopolist's profit maximization condition, we have: P*(1 + 1/) = MC(Q*) …or… [P* - MC(Q*)]/P* = -1/ In words, the monopolist's ability to price above marginal cost depends on the elasticity of demand. 483 Chapter Eleven Multi-Plant Monopoly Recall: • In the perfectly competitive model, we could derive firm outputs that varied depending on the cost characteristics of the firms. The analogous problem here is to derive how a monopolist would allocate production across the plants under its management. Assume: • The monopolist has two plants: one plant has marginal cost MC1(Q) and the other has marginal cost MC2(Q). 484 Chapter Eleven Multi-Plant Monopoly – Production Allocation Whenever the marginal costs of the two plants are not equal, the firm can increase profits by reallocating production towards the lower marginal cost plant and away from the higher marginal cost plant. Example: Suppose the monopolist wishes to produce 6 units 3 units per plant => • MC1 = $6 • MC2 = $3 Reducing plant 1's units and increasing plant 2's units raises profits 485 Chapter Eleven Multi-Plant Monopoly – Production Allocation Price MC1 MCT 6 • Example: Multi-Plant Monopolist This is analogous to exit by higher cost firms and an increase in entry by low-cost firms in the perfectly competitive model. 3 3 6 9 Chapter Eleven Quantity 486 Multi-Plant Monopoly – Production Allocation Price MC2 MC1 MCT 6 3 • Example: Multi-Plant Monopolist This is analogous to exit by higher cost firms and an increase in entry by low-cost firms in the perfectly competitive model. • 3 6 9 Chapter Eleven Quantity 487 Multi-Plant Marginal Costs Curve Question: How much should the monopolist produce in total? Definition: The Multi-Plant Marginal Cost Curve traces out the set of points generated when the marginal cost curves of the individual plants are horizontally summed (i.e. this curve shows the total output that can be produced at every level of marginal cost.) Example: For MC1 = $6, Q1 = 3 MC2 = $6, Q2 = 6 Therefore, for MCT = $6, QT = Q1 + Q2 = 9 488 Chapter Eleven Multi-Plant Marginal Costs Curve The profit maximization condition that determines optimal total output is now: • MR = MCT The marginal cost of a change in output for the monopolist is the change after all optimal adjustment has occurred in the distribution of production across plants. 489 Chapter Eleven Multi-Plant Monopolistic Maximization Price MC1 MC2 MCT P* MR Chapter Eleven Quantity 490 Multi-Plant Monopolistic Maximization Price MC1 MC2 MCT P* Demand Q*1 Q*2 Q*T MR Chapter Eleven Quantity 491 Multi-Plant Monopolistic Maximization Example: P = 120 - 3Q …demand… MC1 = 10 + 20Q1 …plant 1… MC2 = 60 + 5Q2 …plant 2… What are the monopolist's optimal total quantity and price? Step 1: Derive MCT as the horizontal sum of MC1 and MC2. Inverting marginal cost (to get Q as a function of MC), we have: Q1 = -1/2 + (1/20)MCT Q2 = -12 + (1/5)MCT 492 Chapter Eleven Multi-Plant Monopolistic Maximization Let MCT equal the common marginal cost level in the two plants. Then: • QT = Q1 + Q2 = -12.5 + .25MCT And, writing this as MCT as a function of QT: • MCT = 50 + 4QT Using the monopolist's profit maximization condition: • MR = MCT => 120 - 6QT = 50 + 4QT • QT* = 7 • P* = 120 - 3(7) = 99 493 Chapter Eleven Multi-Plant Monopolistic Maximization Example: P = 120 - 3Q …demand… MC1 = 10 + 20Q1 …plant 1… MC2 = 60 + 5Q2 …plant 2… What is the optimal division of output across the monopolist's plants? MCT* = 50 + 4(7) = 78 Therefore, Q1* = -1/2 + (1/20)(78) = 3.4 Q2* = -12 + (1/5)(78) = 3.6 494 Chapter Eleven Cartel Definition: A cartel is a group of firms that collusively determine the price and output in a market. In other words, a cartel acts as a single monopoly firm that maximizes total industry profit. 495 Chapter Eleven Cartel The problem of optimally allocating output across cartel members is identical to the monopolist's problem of allocating output across individual plants. Therefore, a cartel does not necessarily divide up market shares equally among members: higher marginal cost firms produce less. This gives us a benchmark against which we can compare actual industry and firm output to see how far the industry is from the collusive equilibrium 496 Chapter Eleven The Welfare Economies of Monopoly Since the monopoly equilibrium output does not, in general, correspond to the perfectly competitive equilibrium it entails a dead-weight loss. Suppose that we compare a monopolist to a competitive market, where the supply curve of the competitors is equal to the marginal cost curve of the monopolist 497 Chapter Eleven The Welfare Economies of Monopoly CS with competition: A+B+C CS with monopoly: A PS with competition: D+E PS with monopoly:B+D A MC PM B PC DWL = C+E C E D Demand QM MR QC Chapter Eleven 498 Natural Monopolies Dead-weight loss in a Natural Monopoly Market Definition: A market is a natural monopoly if the total cost incurred by a single firm producing output is less than the combined total cost of two or more firms producing this same level of output among them. Benchmark: What would be the market outcome if the monopolist produced according to the same rule as a perfect competitor (i.e., P = MC)? 499 Chapter Eleven Natural Monopolies Price Demand Quantity Chapter Eleven 500 Natural Monopolies Price Natural Monopoly falling average costs AC Demand Quantity Chapter Eleven 501 Natural Monopolies P = MC cannot be the appropriate benchmark here to calculate deadweight loss due to monopoly…P = AC may be a better benchmark. For small outputs, this is a natural monopoly – for large outputs, it is not. P = MC is the appropriate benchmark for these types of natural monopolies. 502 Chapter Eleven Natural Monopolies – With Rising Average Cost Price AC 1.2 4.5 12 Chapter Eleven Demand Quantity 503 Natural Monopolies – With Rising Average Cost Price 1.4 1.2 1 4.5 6 9 12 Chapter Eleven Demand Quantity 504 Natural Monopolies – With Rising Average Cost Price 1.4 1.2 1 AC 4.5 6 9 12 Demand Chapter Eleven Quantity 505 Chapter Twelve Capturing Surplus 506 Chapter Twelve Chapter Twelve Overview 1. Introduction: Airline Tickets 2. Price Discrimination • First Degree • Second Degree • Third Degree 3. Tie-in Sales • Requirements Tie-ins • Package Tie-ins (Bundling) 507 Chapter Twelve Airline Ticket Prices Ticket Price Number of Passengers $2000 18 Average Advance Purchase 12 days $1000-$1999 15 14 days $800-$999 23 32 days $600-$799 49 46 days $400-$599 23 65 days $200-$399 23 35 days $1-$199 34 26 days $0 19 508 Chapter Twelve Uniform Price Vs. Price Discrimination Definition: A monopolist charges a uniform price if it sets the same price for every unit of output sold. While the monopolist captures profits due to an optimal uniform pricing policy, it does not receive the consumer surplus or dead-weight loss associated with this policy. The monopolist can overcome this by charging more than one price for its product. Definition: A monopolist price discriminates if it charges more than one price for its output. 509 Chapter Twelve Uniform Price Vs. Price Discrimination Price Uniform Price Monopoly 1st Degree P.D. Monopoly MC MR D Quantity Chapter Twelve 510 Uniform Price Vs. Price Discrimination Uniform Price Monopoly 1st Degree P.D. Monopoly Price CS: E+F PS: G+H+K+L TS: E+F+G+H+K+L DWL: J+N 0 E+F+G+H+J+K+L+N E+G+G+H+J+K+L+N 0 PU E F H G P1 K MC J N L MR D Quantity Chapter Twelve 511 Forms of Price Discrimination Definition: A policy of first degree (or perfect) price discrimination prices each unit sold at the consumer's maximum willingness to pay. This willingness to pay is directly observable by the monopolist. Definition: The consumer's maximum willingness to pay is called the consumer's reservation price. 512 Chapter Twelve “Willingness to Pay” Curve Think of the demand curve as a "willingness to pay" curve. If the monopolist can observe the willingness to pay of each customer (based on, for example, residence, education, "look", etc), then the monopolist can observe demand perfectly and can "perfectly" price discriminate. 513 Chapter Twelve Is it Reasonable? The monopolist will continue selling units until the reservation price exactly equals marginal cost. Therefore, a perfectly price discriminating monopolist will produce and sell the efficient quantity of output. Note: Only if the monopolist can prevent resale can the monopolist capture the entire surplus. 514 Chapter Twelve Pricing Surplus – Monopoly MC = 2 P = 20 - Q What is producer surplus if uniform pricing is followed? MR = P + (P/Q)Q = 20 - Q - Q = 20 - 2Q MR = MC => 20 - 2Q = 2 => Q* = 9 P* = 11 PS= Revenue-TVC = PQ-2Q = 11(9)-2(9) = 81 515 Chapter Twelve Pricing Surplus – Monopoly What will producer surplus be if the monopolist perfectly price discriminates? P = MC => 20 - Q = 2 =>Q* = 18 Revenue - TVC = [18(20-2)(1/2) + 18(2)]18(2) = 162 This is a gain in captured surplus of 81! 516 Chapter Twelve First Degree Price Discrimination Price 20 11 MC 2 9 18 D 20 Quantity MR (uniform pricing) 517 Chapter Twelve Second Degree Price Discrimination What is the marginal revenue curve for a perfectly price discriminating monopolist? When the monopolist sells an additional unit, it does not have to reduce the price on the other units it is selling. Therefore, MR = P. (i.e., the marginal revenue curve equals the demand curve.) Definition: A policy of second degree price discrimination allows the monopolist to charge a different price to different consumers. While different consumers pay different prices, the reservation price of any one consumer cannot be directly observed. 518 Chapter Twelve Two Part Tariff Definition: A monopolist charges a two part tariff if it charges a per unit fee, r, plus a lump sum fee (paid whether or not a positive number of units is consumed), F. This, effectively, charges demanders of a low quantity a different average price than demanders of a high quantity. Example: hook-up charge plus usage fee for a telephone, club membership, or the like. 519 Chapter Twelve Two Part Tariff P 100 Example: All customers are identical and have demand • P = 100 - QI • MC = AC = 10 4050 10 90 100 Chapter Twelve Q 520 Two Part Tariff What is the optimal two-part tariff? Two steps: (1) maximize the benefits to the consumers by charging r = MC = 10. (2) capture this benefit by setting F = consumer benefits = 4050. 521 Chapter Twelve Two Part Tariff Any higher usage charge would result in a deadweight loss that could not be captured by the monopolist. Any lower usage charge would result in selling at less than marginal cost. In essence, the monopolist maximizes the size of the "pie", then sets the lump sum fee so as to capture the entire "pie" for itself. The total surplus captured is the same as in the case of perfect price discrimination. 522 Chapter Twelve Block Tariff Definition: If a consumer pays one price for one block of output and another price for another block of output, the consumer faces a block tariff 523 Chapter Twelve Block Tariff • P = 100 - Q • MC = AC = 10 Let Q1 be the largest quantity for which the first block rate applies so that p1(Q1) = 100 - Q1. Let Q2 be the largest quantity purchased (so that the second block rate will apply between Q1 and Q2) so that p2(Q2) = 100 - Q2 524 Chapter Twelve Block Tariff Then: = p1(Q1)Q1 + p2(Q2)(Q2-Q1) - TC(Q2) = (100 - Q1)Q1 + (100 - Q2)(Q2-Q1) - 10Q2 and we must choose Q1 and Q2 to maximize this profit… MR1 = (100 - Q1) - Q1 - (100 - Q2) = 0 MR2 = (100 - Q2) - Q2 + Q1 = MC = 10 525 Chapter Twelve Key Equations These are two equations in two unknowns that can be solved to obtain: • Q1* = 30 • Q2* = 60 • P1* = 70 • P2* = 40 (a quantity discount) 526 Chapter Twelve Block Pricing P 100 Demand 450 70 450 40 2700 450 10 0 30 60 100 Q 527 Chapter Twelve Block Pricing P 100 P 100 Demand Demand 450 70 1012.5 55 450 40 2700 450 10 0 2025 30 60 100 Q 0 Chapter Twelve 1012.5 45 MR MC 100 Q 528 Block Pricing If the monopolist could set a different block price for each customer, it would capture the same amount of surplus as a perfectly price discriminating monopolist. 529 Chapter Twelve Utility Pricing D - small D - large MC Chapter Twelve Q 530 Utility Pricing D - small D - large Additional CS P1 Additional PS P2 MC Q1s Q1L Q2L Q 531 Chapter Twelve Third Degree Price Discrimination Definition: A policy of third degree price discrimination offers a different price for each segment of the market (or each consumer group) when membership in a segment can be observed. Example: Movie ticket sales to older people or students at discount • Suppose that marginal costs for the two markets are the same. How does a monopolist maximize profit with this type of price discrimination? 532 Chapter Twelve Optimal Pricing Set the marginal revenue in each market equal to marginal cost. (i.e., the monopolist maximizes total profits by maximizing profits from each group individually.) This implies that MR1 = MC = MR2 at the optimum. Otherwise, the monopolist could raise revenues by switching sales from the low MR group to the high MR group. MC = AC = 20 Example P1 = 100 - Q1 P2 = 80 - 2Q2 533 Chapter Twelve Optimal Pricing MR1 = 100 - 2Q1 = MC = 20 MR2 = 80 - 4Q2 = MC = 20 Q1* = 40 Q2* = 15 Example P1* = 60 P2* = 50 534 Chapter Twelve Third Degree Price Discrimination P 100 Market 1 Demand 1 60 20 0 MR1 100 Q 535 Chapter Twelve Third Degree Price Discrimination P P 100 Market 2 Market 1 Demand 1 80 60 Demand 2 50 20 0 MR1 100 Q 0 Chapter Twelve 20 40 MR2 Q 536 Tie-in Sales – Requirements Definition: A tie-in sale occurs if customer can buy one product only if they agree to purchase another product as well. • Requirements tie-in sales occur when a firm requires customers who buy one product from the firm to buy another product from the firm. A requirements tie-in sale may be used in place of price discrimination when the firm cannot observe the relative willingness to pay of different customers. 537 Chapter Twelve Tie-in Sales – Bundling • Package tie-in sales (or bundling) occur when goods are combined so that customers cannot buy either good separately. Bundling may be used in place of price discrimination to increase producer surplus when consumers have different willingness to pay for the goods sold in the bundle. But bundling does not always pay… 538 Chapter Twelve Tie-in Sales – Bundling Reservation Price Computer Monitor Customer 1 $1,200 $600 Customer 2 $1,500 $400 Marginal Cost $1,000 $300 539 Chapter Twelve Tie-in Sales – Bundling Optimal Pricing Policy Without bundling: pc = $1500 pm = $600 • Profit cm = $800 With bundling: pb = $1800 • Profit b = $1000 540 Chapter Twelve Tie-in Sales – Bundling Reservation Price Computer Monitor Customer 1 $1,200 $400 Customer 2 $1,500 $600 Marginal Cost $1,000 $300 541 Chapter Twelve Tie-in Sales – Bundling Optimal Pricing Policy Without bundling: pc = $1500 pm = $600 • Profit cm = $800 With bundling: pb = $2100 • Profit b = $800 In general, bundling a pair of goods only pays if their demands are negatively correlated (customers who are willing to pay relatively more for good A are not willing to pay as much for good B). 542 Chapter Twelve Reservation Price The reason is that the price is determined by the purchaser with the lowest reservation price. If reservation prices for the two goods are negatively correlated, bundling reduces the dispersion of reservation prices and so raises the price at which additional units can be sold. 543 Chapter Twelve Chapter Thirteen Market Structure And Competition 544 Chapter Thirteen Chapter Thirteen Overview 1. Introduction: Cola Wars 2. A Taxonomy of Market Structures 3. Monopolistic Competition 4. Oligopoly – Interdependence of Strategic Decisions • Bertrand with Homogeneous and Differentiated Products 5. The Effect of a Change in the Strategic Variable • • • • Theory vs. Observation Cournot Equilibrium (homogeneous) Comparison to Bertrand, Monopoly Reconciling Bertrand, and Cournot 6. The Effect of a Change in Timing: Stackelberg Equilibrium 545 Chapter Thirteen A Taxonomy Market Structures • The number of sellers • The number of buyers • Entry conditions • The degree of product differentiation 546 Chapter Thirteen Product Differentiation Definition: Product Differentiation between two or more products exists when the products possess attributes that, in the minds of consumers, set the products apart from one another and make them less than perfect substitutes. Examples: Pepsi is sweeter than Coke, Brand Name batteries last longer than "generic" batteries. 547 Chapter Thirteen Product Differentiation • "Superiority" (Vertical Product Differentiation) i.e. one product is viewed as unambiguously better than another so that, at the same price, all consumers would buy the better product • "Substitutability" (Horizontal Product Differentiation) i.e. at the same price, some consumers would prefer the characteristics of product A while other consumers would prefer the characteristics of product B. 548 Chapter Thirteen A Taxonomy Market Structures Approach Degree of Product Differentiation Firms produce identical products Firms produce differentiated products Many Few One Dominant One Perfect Oligopoly with Dominant Monopoly Competition homogeneous firm products Monopolistic Oligopoly with Competition differentiated ----------------------products 549 Chapter Thirteen Chamberlinian Monopolistic Competition Market Structure • Many Buyers • Many Sellers • Free entry and Exit • (Horizontal) Product Differentiation When firms have horizontally differentiated products, they each face downward-sloping demand for their product because a small change in price will not cause ALL buyers to switch to another firm's product. 550 Chapter Thirteen Monopolistic Competition – Short Run 1. Each firm is small each takes the observed "market price" as given in its production decisions. 2. Since market price may not stay given, the firm's perceived demand may differ from its actual demand. 3.If all firms' prices fall the same amount, no customers switch supplier but the total market consumption grows. 4. If only one firm's price falls, it steals customers from other firms as well as increases total market consumption 551 Chapter Thirteen Perceived vs. Actual Demand Price d (PA=20) Quantity 552 Chapter Thirteen Perceived vs. Actual Demand Price Demand assuming no price matching d (PA=50) d (PA=20) Quantity 553 Chapter Thirteen Perceived vs. Actual Demand Price Demand (assuming price matching by all firms) 50 • Demand assuming no price matching d (PA=50) d (PA=20) Quantity 554 Chapter Thirteen Market Equilibrium The market is in equilibrium if: • Each firm maximizes profit taking the average market price as given • Each firm can sell the quantity it desires at the actual average market price that prevails 555 Chapter Thirteen Short Run Chamberlinian Equilibrium Price d(PA=43) Quantity Chapter Thirteen 556 Short Run Chamberlinian Equilibrium Price Demand assuming no price matching d (PA=50) d(PA=43) Quantity Chapter Thirteen 557 Short Run Chamberlinian Equilibrium Price Demand (assuming price matching by all firms P=PA) • • Demand assuming no price matching d (PA=50) d(PA=43) Quantity Chapter Thirteen 558 Short Run Chamberlinian Equilibrium Price Demand (assuming price matching by all firms P=PA) 50 43 • • 15 Demand assuming no price matching mc 57 d (PA=50) d(PA=43) Quantity MR43 Chapter Thirteen 559 Short Run Monopolistically Competitive Equilibrium Computing Short Run Monopolistically Competitive Equilibrium • MC = $15 • N = 100 • Q = 100 - 2P + PA • Where: PA is the average market price N is the number of firms 560 Chapter Thirteen Short Run Monopolistically Competitive Equilibrium A. What is the equation of d40? What is the equation of D? • d40: Qd = 100 - 2P + 40 = 140 - 2P • D: Note that P = PA so that • QD = 100 - P B. Show that d40 and D intersect at P = 40 • P = 40 => Qd = 140 - 80 = 60 QD = 100 - 40 = 60 C. For any given average price, PA, find a typical firm's profit maximizing quantity 561 Chapter Thirteen Inverse Perceived Demand P = 50 - (1/2)Q + (1/2)PA MR = 50 - Q + (1/2)PA MR = MC => 50 - Q + (1/2)PA = 15 Qe = 35 + (1/2)PA Pe = 50 - (1/2)Qe + (1/2)PA Pe = 32.5 + (1/4)PA 562 Chapter Thirteen Short Run Monopolistically Competitive Equilibrium D. What is the short run equilibrium price in this industry? In equilibrium, Qe = QD at PA so that 100 - PA = 35 + (1/2)PA PA = 43.33 Qe = 56.66 QD = 56.66 563 Chapter Thirteen Monopolistic Competition in the Long Run At the short run equilibrium P > AC so that each firm may make positive profit. Entry shifts d and D left until average industry price equals average cost. This is long run equilibrium is represented graphically by: MR = MC for each firm D = d at the average market price d and AC are tangent at average market price 564 Chapter Thirteen Long Run Chamberlinian Equilibrium Price Residual Demand shifts in as entry occurs P* Marginal Cost P** Average Cost q** q* MR Chapter Thirteen Quantity 565 Oligopoly Assumptions: • Many Buyers and Few Sellers • Each firm faces downward-sloping demand because each is a large producer compared to the total market size • There is no one dominant model of oligopoly. We will review several. 566 Chapter Thirteen Bertrand Oligopoly (homogeneous) Assumptions: • Firms set price* • Homogeneous product • Simultaneous • Non-cooperative *Definition: In a Bertrand oligopoly, each firm sets its price, taking as given the price(s) set by other firm(s), so as to maximize profits. 567 Chapter Thirteen Simultaneously vs. Non-cooperatively Definition: Firms act simultaneously if each firm makes its strategic decision at the same time, without prior observation of the other firm's decision. Definition: Firms act non-cooperatively if they set strategy independently, without colluding with the other firm in any way 568 Chapter Thirteen Setting Price • Homogeneity implies that consumers will buy from the low-price seller. • Further, each firm realizes that the demand that it faces depends both on its own price and on the price set by other firms • Specifically, any firm charging a higher price than its rivals will sell no output. • Any firm charging a lower price than its rivals will obtain the entire market demand. 569 Chapter Thirteen Residual Demand Definition: The relationship between the price charged by firm i and the demand firm i faces is firm is residual demand In other words, the residual demand of firm i is the market demand minus the amount of demand fulfilled by other firms in the market: Q1 = Q - Q2 570 Chapter Thirteen Residual Demand Curve – Price Setting Price Market Demand Residual Demand Curve • (thickened line segments) Quantity 0 571 Chapter Thirteen Residual Demand Curve – Price Setting • Assume firm always meets its residual demand (no capacity constraints) • Assume that marginal cost is constant at c per unit. • Hence, any price at least equal to c ensures nonnegative profits. 572 Chapter Thirteen Price Setting – Homogeneous Products Reaction Function of Firm 1 Price charged by firm 2 45° line Reaction Function of Firm 2 p2* • Price charged by firm 1 0 p1* 573 Chapter Thirteen Best Response Function Thus, each firm's profit maximizing response to the other firm's price is to undercut (as long as P > MC) Definition: The firm's profit maximizing action as a function of the action by the rival firm is the firm's best response (or reaction) function Example: 2 firms Bertrand competitors Firm 1's best response function is P1=P2- e Firm 2's best response function is P2=P1- e 574 Chapter Thirteen Equilibrium If we assume no capacity constraints and that all firms have the same constant average and marginal cost of c then: For each firm's response to be a best response to the other's each firm must undercut the other as long as P> MC Where does this stop? P = MC (!) 575 Chapter Thirteen Equilibrium 1. Firms price at marginal cost 2. Firms make zero profits 3. The number of firms is irrelevant to the price level as long as more than one firm is present: two firms is enough to replicate the perfectly competitive outcome. Essentially, the assumption of no capacity constraints combined with a constant average and marginal cost takes the place of free entry. 576 Chapter Thirteen Bertrand Competition – Differentiated Assumptions: Firms set price* Differentiated product Simultaneous Non-cooperative *As before, differentiation means that lowering price below your rivals' will not result in capturing the entire market, nor will raising price mean losing the entire market so that residual demand decreases smoothly 577 Chapter Thirteen Bertrand Competition – Differentiated Q1 = 100 - 2P1 + P2 "Coke's demand" Q2 = 100 - 2P2 + P1 "Pepsi's demand" MC1 = MC2 = 5 What is firm 1's residual demand when Firm 2's price is $10? $0? Q110 = 100 - 2P1 + 10 = 110 - 2P1 Q10 = 100 - 2P1 + 0 = 100 - 2P1 578 Chapter Thirteen Key Concepts Residual Demand, Price Setting, Differentiated Products Coke’s Price 100 Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Pepsi’s price = $0 for D0 and $10 for D10 MR0 0 Coke’s Quantity Chapter Thirteen 579 Key Concepts Residual Demand, Price Setting, Differentiated Products Coke’s Price 110 100 Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Pepsi’s price = $0 for D0 and $10 for D10 D10 D0 0 Coke’s Quantity Chapter Thirteen 580 Key Concepts Residual Demand, Price Setting, Differentiated Products Coke’s Price 110 100 Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Pepsi’s price = $0 for D0 and $10 for D10 MR10 0 MR0 D10 D0 Coke’s Quantity Chapter Thirteen 581 Key Concepts Residual Demand, Price Setting, Differentiated Products Coke’s Price 110 100 Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Pepsi’s price = $0 for D0 and $10 for D10 D10 5 0 MR10 MR0 D0 Coke’s Quantity Chapter Thirteen 582 Key Concepts Residual Demand, Price Setting, Differentiated Products Coke’s Price 110 100 Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Pepsi’s price = $0 for D0 and $10 for D10 30 27.5 D10 MR10 5 0 45 50 MR0 D0 Coke’s Quantity Chapter Thirteen 583 Key Concepts Residual Demand, Price Setting, Differentiated Products Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Example: MR110 = 55 - Q110 = 5 Q110 = 50 P110 = 30 Therefore, firm 1's best response to a price of $10 by firm 2 is a price of $30 584 Chapter Thirteen Key Concepts Residual Demand, Price Setting, Differentiated Products Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Example: • Solving for firm 1's reaction function for any arbitrary price by firm 2 P1 = 50 - Q1/2 + P2/2 MR = 50 - Q1 + P2/2 MR = MC => Q1 = 45 + P2/2 585 Chapter Thirteen Key Concepts Residual Demand, Price Setting, Differentiated Products Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC And, using the demand curve, we have: • P1 = 50 + P2/2 - 45/2 - P2/4 or • P1 = 27.5 + P2/4 the reaction function 586 Chapter Thirteen Equilibrium and Reaction Functions Pepsi’s Price (P2) Price Setting and Differentiated Products P2 = 27.5 + P1/4 (Pepsi’s R.F.) 27.5 Coke’s Price (P1) 587 Chapter Thirteen Equilibrium and Reaction Functions Pepsi’s Price (P2) Price Setting and Differentiated Products P1 = 27.5 + P2/4 (Coke’s R.F.) P2 = 27.5 + P1/4 (Pepsi’s R.F.) • 27.5 27.5 P1 = 110/3 Coke’s Price (P1) 588 Chapter Thirteen Equilibrium and Reaction Functions Pepsi’s Price (P2) P2 = 110/3 Price Setting and Differentiated Products P1 = 27.5 + P2/4 (Coke’s R.F.) Bertrand Equilibrium P2 = 27.5 + P1/4 (Pepsi’s R.F.) • 27.5 27.5 P1 = 110/3 Coke’s Price (P1) 589 Chapter Thirteen Equilibrium Equilibrium occurs when all firms simultaneously choose their best response to each others' actions. Graphically, this amounts to the point where the best response functions cross. 590 Chapter Thirteen Equilibrium Example: Firm 1 and Firm 2, continued • P1 = 27.5 + P2/4 • P2 = 27.5 + P1/4 Solving these two equations in two unknowns. • P1* = P2* = 110/3 Plugging these prices into demand, we have: • Q1* = Q2* = 190/3 • 1* = 2* = 2005.55 • = 4011.10 591 Chapter Thirteen Equilibrium Profits are positive in equilibrium since both prices are above marginal cost! Even if we have no capacity constraints, and constant marginal cost, a firm cannot capture all demand by cutting price. This blunts price-cutting incentives and means that the firms' own behavior does not mimic free entry 592 Chapter Thirteen Equilibrium Only if I were to let the number of firms approach infinity would price approach marginal cost. Prices need not be equal in equilibrium if firms not identical (e.g. Marginal costs differ implies that prices differ) The reaction functions slope upward: "aggression => aggression" 593 Chapter Thirteen Theory vs. Observation US Manufacturing Industries CR8 >70 <70 Average Profit Rate 12.1% 6.9% Source: Bain, Joe S., "Relation of Profit Rate to Industry Concentration: American Manufacturing, 1936-1940," Quarterly Journal of Economics, v. 65 (August 1951), pp. 293-324 and Barriers to New Competition (Cambridge: Harvard University Press, 1956). 594 Chapter Thirteen Cournot Oligopoly Assumptions • Firms set outputs (quantities)* • Homogeneous Products • Simultaneous • Non-cooperative *Definition: In a Cournot game, each firm sets its output (quantity) taking as given the output level of its competitor(s), so as to maximize profits. Price adjusts according to demand. Recall our reasoning from the Bertrand case… Residual Demand: Firm i's guess about its rival's output determines its residual demand. 595 Chapter Thirteen Residual Demand Price 10 units Residual Marginal Revenue when q2 = 10 Residual Demand when q2 = 10 MC Demand 0 Quantity q1* 596 Chapter Thirteen Profit Maximization Profit Maximization: Each firm acts as a monopolist on its residual demand curve, equating MRR to MC. MRR = p + q1(p/q) = MC Best Response Function: The point where (residual) marginal revenue equals marginal cost gives the best response of firm i to its rival's (rivals') actions. For every possible output of the rival(s), we can determine firm i's best response. The sum of all these points makes up the best response (reaction) function of firm i. 597 Chapter Thirteen Profit Maximization q2 Example: Reaction Functions, Quantity Setting Reaction Function of Firm 1 0 q1 Chapter Thirteen 598 Profit Maximization q2 Example: Reaction Functions, Quantity Setting Reaction Function of Firm 1 q2* 0 • q1* Reaction Function of Firm 2 q1 Chapter Thirteen 599 Equilibrium Equilibrium: No firm has an incentive to deviate in equilibrium in the sense that each firm is maximizing profits given its rival's output Example A: P = 100 - Q1 - Q2 MC = AC = 10 What is firm 1's profit-maximizing output when firm 2 produces 50? Firm 1's residual demand: • P = (100 - 50) - Q1 • MR50 = 50 - 2Q1 • MR50 = MC 50 - 2Q1 = 10 • Q150 = 20 600 Chapter Thirteen Profit Maximization Example B: What is the equation of firm 1's reaction function? Firm 1's residual demand: • P = (100 - Q2) - Q1 • MRr = 100 - Q2 - 2Q1 • MRr = MC 100 - Q2 - 2Q1 = 10 • Q1r = 45 - Q2/2 firm 1's reaction function 601 Chapter Thirteen Profit Maximization Example C: Similarly, one can compute that Q2r = 45 - Q1/2. Now, calculate the Cournot equilibrium. • Q1 = 45 - (45 - Q1/2)/2 • Q1* = 30 • Q2* = 30 • P* = 40 • 1* = 2* = 30(30) = 900 602 Chapter Thirteen Cournot, Bertrand, and Monopoly Equilibriums P > MC for Cournot competitors, but P < PM: If the firms were to act as a monopolist (perfectly collude), they would set market MR equal to MC: • P = 100 - Q • MC = AC = 10 • MR = MC => 100 - 2Q = 10 => QM = 45 • PM = 55 • M= 45(45) = 2025 • c = 1800 603 Chapter Thirteen Cournot, Bertrand, and Monopoly Equilibriums A perfectly collusive industry takes into account that an increase in output by one firm depresses the profits of the other firm(s) in the industry. A Cournot competitor takes into account the effect of the increase in output on its own profits only. Therefore, Cournot competitors "overproduce" relative to the collusive (monopoly) point. Further, this problem gets "worse" as the number of competitors grows because the market share of each individual firm falls, increasing the difference between the private gain from increasing production and the profit destruction effect on rivals. Therefore, the more concentrated the industry in the Cournot case, the higher the price-cost margin. 604 Chapter Thirteen Cournot, Bertrand, and Monopoly Equilibriums Homogeneous product Bertrand resulted in zero profits, whereas the Cournot case resulted in positive profits. Why? The best response functions in the Cournot model slope downward. In other words, the more aggressive a rival (in terms of output), the more passive the Cournot firm's response. The best response functions in the Bertrand model slope upward. In other words, the more aggressive a rival (in terms of price) the more aggressive the Bertrand firm's response. 605 Chapter Thirteen Cournot, Bertrand, and Monopoly Equilibriums Cournot: Suppose firm j raises its output…the price at which firm i can sell output falls. This means that the incentive to increase output falls as the output of the competitor rises. Bertrand: Suppose firm j raises price the price at which firm i can sell output rises. As long as firm's price is less than firm's, the incentive to increase price will depend on the (market) marginal revenue. 606 Chapter Thirteen Cournot, Bertrand, and Monopoly Equilibriums What if one firm moves before the other? Call the first mover the “leader” and the second mover the “follower”. Let both firms choose quantities once and for all. The second firm is in the same situation as a Cournot firm: it takes the leader’s output as given and maximizes profits accordingly, using its residual demand. The second firm’s behavior can, then, be summarized by a Cournot reaction function. 607 Chapter Thirteen Stackelberg Equilibrium vs. Cournot q2 A Profit for firm 1 at A…0 at B…0 at C…1012.5 at Cournot Eq…900 • Former Cournot Equilibrium • • C B (q1= 90) • Chapter Thirteen Follower’s Cournot Reaction Function q1 608 Summary 1. Market structures are characterized by the number of buyers, the number of sellers, the degree of product differentiation and the entry conditions. 2. Product differentiation alone or a small number of competitors alone is not enough to destroy the long run zero profit result of perfect competition. This was illustrated with the Chamberlinian and Bertrand models. 3. Chamberlinian) monopolistic competition assumes that there are many buyers, many sellers, differentiated products and free entry in the long run. 609 Chapter Thirteen Summary 4. Chamberlinian sellers face downward-sloping demand but are price takers (i.e. they do not perceive that their change in price will affect the average price level). Profits may be positive in the short run but free entry drives profits to zero in the long run. 5. Bertrand and Cournot competition assume that there are many buyers, few sellers, and homogeneous or differentiated products. Firms compete in price in Bertrand oligopoly and in quantity in Cournot oligopoly. 6. Bertrand and Cournot competitors take into account their strategic interdependence by means of constructing a best response schedule: each firm maximizes profits given the rival's strategy. 610 Chapter Thirteen Summary 7. Equilibrium in such a setting requires that all firms be on their best response functions. 8. If the products are homogeneous, the Bertrand equilibrium results in zero profits. By changing the strategic variable from price to quantity, we obtain much higher prices (and profits). Further, the results are sensitive to the assumption of simultaneous moves. 9. This result can be traced to the slope of the reaction functions: upwards in the case of Bertrand and downwards in the case of Cournot. These slopes imply that "aggressivity" results in a "passive" response in the Cournot case and an "aggressive" response in the Bertrand case. 611 Chapter Thirteen Chapter Fourteen Game Theory and Strategic Behavior 612 Chapter Fourteen Chapter Fourteen Overview 1. Motivation: Honda and Toyota 2. Nash Equilibrium 3. The Prisoner's Dilemma 4. Dominant Strategy Equilibrium 5. Limitations of the Nash Equilibrium 6. Sequential Moves Games • The Value of Limiting One’s Opinion 613 Chapter Fourteen Capacity Expansion Game What is the likely outcome of this game? Toyota Honda Build a new plant Do not Build Build a new plant 16,16 20,15 Do not Build 15,20 18,18 614 Chapter Fourteen Capacity Expansion Game Game Elements Players: agents participating in the game (Toyota, Honda) Strategies: Actions that each player may take under any possible circumstance (Build, Don't build) Outcomes: The various possible results of the game (four, each represented by one cell of matrix) Payoffs: The benefit that each player gets from each possible outcome of the game (the profits entered in each cell of the matrix) 615 Chapter Fourteen Capacity Expansion Game Information: A full specification of who knows what when (full information) Timing: Who can take what decision when and how often the game is repeated (simultaneous, one-shot) Solution concept of the game: "What is the likely outcome"? (Dominant Strategy Equilibrium, Nash Equilibrium) 616 Chapter Fourteen Nash Equilibrium Definition: A Nash Equilibrium occurs when each player chooses a strategy that gives him/her the highest payoff, given the strategy chosen by the other player(s) in the game. ("rational self-interest") Toyota vs. Honda: A Nash equilibrium: Each Firm Builds a New Plant 617 Chapter Fourteen Nash Equilibrium • Given Toyota builds a new plant, Honda's best response is to build a new plant. • Given Honda builds a new plant, Toyota's best response is to build a plant. • Why is the Nash Equilibrium plausible? • It IS "self enforcing” Even though it DOES NOT necessarily maximise collective interest. 618 Chapter Fourteen Prisoner's Dilemma Definition: If a game is such that the players choose a set of payoffs that is Pareto dominated by another set of payoffs, the game is called a Prisoner's Dilemma. Ron Confess Don't Confess -5,-5 0,-10 Don't Confess -10,0 -1,-1 Confess 619 Chapter Fourteen Other Considerations Nash Equilibrium: both confess Pareto Dominant Point: Neither confesses Example: Bertrand and Cournot Equilibriums Example: The Prisoner's Dilemma and Excessive Litigation Definition: A dominant strategy is a strategy that is better than any other strategy that a player might choose, no matter what strategy the other player follows. Note: When a player has a dominant strategy, that strategy will be the player's Nash Equilibrium strategy. 620 Chapter Fourteen Dominant Strategy Equilibrium Definition: A Dominant Strategy Equilibrium occurs when each player uses a dominant strategy. Example: Game Matrix 1, Game Matrix 2 Toyota Build a Don’t New Plant Build Honda Build a 12,4 New Plant 20,3 Don’t Build 18,5 15,6 621 Chapter Fourteen Dominated Strategy Game Matrix 3: Capacity Expansion: Revisited Honda does not have a dominant strategy, but a Nash Equilibrium exists: Toyota builds, Honda Doesn't Definition: A player has a dominated strategy when the player has another strategy that gives it a higher payoff no matter what the other player does. Example: "Do not build" in Game Matrix 1. Example: "Do not build" for Toyota only in Game Matrix 3. 622 Chapter Fourteen Dominant or Dominated Strategy Why look for dominant or dominated strategies? A dominant strategy equilibrium is particularly compelling as a "likely" outcome Similarly, because dominated strategies are unlikely to be played, these strategies can be eliminated from consideration in more complex games. This can make solving the game easier. 623 Chapter Fourteen Dominated Strategy Game Matrix 4: Dominated Strategies Toyota Build Large Build Small Do Not Build Build Large 0,0 12,8 18,9 Build Small 8,12 16,16 20,15 Do Not Build 9,18 15,20 18,18 Honda "Build Large" is dominated for each player By eliminating the dominated strategies, we can reduce the game to matrix #1! 624 Chapter Fourteen Nash Equilibrium Limitations Game Matrix 4: Dominated Strategies Limitations of Nash Equilibrium The Nash Equilibrium need not be unique Slick Luke Swerve Stay Swerve 0,0 -10,10 Stay 10,-10 -100,-100 625 Chapter Fourteen Nash Equilibrium Limitations In the above example, Nash Equilibriums: (Swerve, Stay) and (Stay, Swerve). Now, compare to the following case: Sirius Stay Exit Stay -200, -200 300,0 Exit 0,300 0,0 XM 626 Chapter Fourteen Nash Equilibrium Limitations Example: Bank Runs Depositor 2 Withdraw Don't Withdraw Withdraw 25,25 50,0 Don't Withdraw 0,50 110,110 Depositor 1 627 Chapter Fourteen Nash Equilibrium Limitations Nash Equilibrium need not exist Example: Matching Pennies Game Matrix 6: Non-existence of Nash Equilibrium Player 1 Heads Tails Heads 1,-1 -1,1 Tails -1,1 1,-1 628 Chapter Fourteen Sequential Move Games – Game Tree Definition: A game tree shows the different strategies that each player can follow in the game and the order in which those strategies get chosen. 629 Chapter Fourteen Sequential Move Games – Game Tree Game Tree 1: Toyota and Honda, Revisited 630 Chapter Fourteen Sequential Move Games – Game Tree Game trees often are solved by starting at the end of the tree and, for each decision point, finding the optimal decision for the player at that point. Keeps analysis manageable. Ensures optimality at each point. The solution to the revisited game differs from that of the simultaneous game. Why – the first mover can force second mover's hand Illustrates the value of commitment (i.e. limiting one's own actions) rather than flexibility Example: Irreversibility of Business Decisions in the Airline Industry. 631 Chapter Fourteen Summary 1. Game Theory is the branch of economics concerned with the analysis of optimal decision making when all decision makers are presumed to be rational, and each is attempting to anticipate the actions and reactions of the competitors 2. A Nash Equilibrium in a game occurs when each player chooses a strategy that gives him/her the highest payoff, given the strategies chosen by the other players in the game. 3. The Nash Equilibrium may be a good predictor when it coincides with the Dominant Strategy Equilibrium. 632 Chapter Fourteen Summary 4. When there are multiple Nash Equilibriums, we must appeal to other concepts to choose the "likely" outcome of the game. 5.An analysis of sequential move games reveals that moving first in a game can have strategic value if the first mover can gain from making a commitment. 633 Chapter Fourteen Chapter Fifteen Risk and Information 634 Chapter Fifteen Chapter Fifteen Overview 1. Introduction: Amazon.com 2. Describing Risky Outcome – Basic Tools • • • Lotteries and Probabilities Expected Values Variance 3. Evaluating Risky Outcomes • Risk Preferences and the Utility Function 4. Avoiding and Bearing Risk • • • The Demand for Insurance and the Risk Premium Asymmetric Information and Insurance The Value of Information and Decision Trees 635 Chapter Fifteen Tools for Describing Risky Outcomes Definition: A lottery is any event with an uncertain outcome. Examples: Investment, Roulette, Football Game. Definition: A probability of an outcome (of a lottery) is the likelihood that this outcome occurs. Example: The probability often is estimated by the historical frequency of the outcome. 636 Chapter Fifteen Probability Distribution Definition: The probability distribution of the lottery depicts all possible payoffs in the lottery and their associated probabilities. Property: • The probability of any particular outcome is between 0 and 1 • The sum of the probabilities of all possible outcomes equals 1. Definition: Probabilities that reflect subjective beliefs about risky events are called subjective probabilities. 637 Chapter Fifteen Probability Distribution Probability 1 .90 .80 .70 .60 .50 .40 .30 .20 .10 0 67% chance of losing Payoff $25 638 Chapter Fifteen Probability Distribution Probability 1 .90 .80 .70 .60 .50 .40 .30 .20 .10 0 67% chance of losing 33% chance of winning $25 $100 Payoff 639 Chapter Fifteen Expected Value Definition: The expected value of a lottery is a measure of the average payoff that the lottery will generate. EV = Pr(A)xA + Pr(B)xB + Pr(C)xC Where: Pr(.) is the probability of (.) A,B, and C are the payoffs if outcome A, B or C occurs. 640 Chapter Fifteen Expected Value In our example lottery, which pays $25 with probability .67 and $100 with probability 0.33, the expected value is: EV = .67 x $25 + .33 x 100 = $50. Notice that the expected value need not be one of the outcomes of the lottery. 641 Chapter Fifteen Variance & Standard Deviation Definition: The variance of a lottery is the average deviation between the possible outcomes of the lottery and the expected value of the lottery. It is a measure of the lottery's riskiness. Var = (A - EV)2(Pr(A)) + (B - EV)2(Pr(B)) + (C - EV)2(Pr(C)) Definition: The standard deviation of a lottery is the square root of the variance. It is an alternative measure of risk 642 Chapter Fifteen Variance & Standard Deviation For the example lottery The squared deviation of winning is: • ($100 - $50)2 = 502 = 2500 The squared deviation of losing is: • ($25 - $50)2 = 252 = 625 The variance is: • (2500 x .33)+ (625 x .67) = 1250 643 Chapter Fifteen Evaluating Risky Outcomes Example: Work for IBM or Amazon.Com? Suppose that individuals facing risky alternatives attempt to maximize expected utility, i.e., the probability-weighted average of the utility from each possible outcome they face. Note: EV(Amazon) = .5($4000)+.5($104,000) = $54,000 U(IBM) = U($54,000) = 230 U(Amazon) = • .5xU($4,000) + .5xU($104,000) = .5(60) + .5(320) = 190 644 Chapter Fifteen Evaluating Risky Outcomes Utility Utility function U(104) = 320 0 4 104 Income (000 $ per year) 645 Chapter Fifteen Evaluating Risky Outcomes Utility Utility function U(104) = 320 U(54) = 230 .5u(4) + .5U(104) = 190 U(4) = 60 0 4 54 104 Income (000 $ per year) 646 Chapter Fifteen Risk Preferences Notes: • Utility as a function of yearly income only • Diminishing marginal utility of income Definition: The risk preferences can be classified as follows: An individual who prefers a sure thing to a lottery with the same expected value is risk averse An individual who is indifferent about a sure thing or a lottery with the same expected value is risk neutral An individual who prefers a lottery to a sure thing that equals the expected value of the lottery is risk loving (or risk preferring) 647 Chapter Fifteen Risk Preferences Suppose that an individual must decide between buying one of two stocks: the stock of an Internet firm and the stock of a Public Utility. The values that the shares of the stock may take (and, hence, the income from the stock, I) and the associated probability of the stock taking each value are: Internet firm Public Utility I Probability I $80 .3 $80 $100 .4 $100 $120 .3 $120 Probability .1 .8 .1 648 Chapter Fifteen Risk Preferences Which stock should the individual buy if she has utility function U = (100I)1/2? Which stock should she buy if she has utility function U = I? EU(Internet) = .3U(80) + .4U(100) + .3U(120) EU(P.U.) = .1U(80) + .8U(100) + .1U(120) a. U = (100I)1/2: • U(80) = (8000)1/2 = 89.40 • U(100) = (10000)1/2 = 100 • U(120) = (12000)1/2 = 109.5 649 Chapter Fifteen Risk Preferences EU(Internet) = .3(89.40)+.4(100)+.3(109.50) = 99.70 EU(P.U.) = .1(89.40) + .8(100) + .1(109.50) = 99.9 The individual should purchase the public utility stock 650 Chapter Fifteen Risk Preferences U = I: EU(Internet) = .3(80)+.4(100)+.3(120)=100 EU(P.U.) .1(80) + .8(100) + .3(120) = 100 This individual is indifferent between the two stocks. 651 Chapter Fifteen Utility Function – Risk Averse Decision Maker Utility Utility function U(100) U(50) U(25) 0 $25 $50 $100 Income 652 Chapter Fifteen Utility Function – Risk Averse Decision Maker Utility Utility function U(100) U(50) •A U(25) 0 $25 $100 $50 Income 653 Chapter Fifteen Utility Function – Risk Averse Decision Maker Utility Utility function U1 I 0 I Income 654 Chapter Fifteen Utility Function – Risk Averse Decision Maker Utility Utility function U2 U1 I 0 I Income 655 Chapter Fifteen Utility Function – Two Risk Approaches Risk Neutral Preferences Risk Loving Preferences Utility Utility Utility Function 0 Utility Function Income Income 656 Chapter Fifteen Avoiding Risk - Insurance Utility Risk premium = horizontal distance $17000 Utility function U(104) = 320 U(54) = 230 E • .5u(4) + .5U(104) = 190 17000 •D U(4) = 60 0 4 37 54 104 Income (000 $ per year) 657 Chapter Fifteen Risk Premium Definition: The risk premium of a lottery is the necessary difference between the expected value of a lottery and the sure thing so that the decision maker is indifferent between the lottery and the sure thing. pU(I1) + (1-p)U(I2) = U(pI1 + (1-p)I2 - RP) The larger the variance of the lottery, the larger the risk premium 658 Chapter Fifteen Computing Risk Premium Example: Computing a Risk Premium • U = I1/2; p = .5 • I1 = $104,000 • I2 = $4,000 659 Chapter Fifteen Computing Risk Premium A. Verify that the risk premium for this lottery is approximately $17,000 .5(104,000)1/2 + .5(4,000)1/2 = (.5(104,000) + .5(4,000) - RP)1/2 $192.87 = ($54,000 - RP)1/2 $37,198 = $54,000 - RP RP = $16,802 660 Chapter Fifteen Computing Risk Premium B. Let I1 = $108,000 and I2 = $0. What is the risk premium now? .5(108,000)1/2 + 0 = (.5(108,000) + 0 - RP)1/2 .5(108,000)1/2 = (54,000 - RP)1/2 RP = $27,000 (Risk premium rises when variance rises, EV the same…) 661 Chapter Fifteen The Demand for Insurance Lottery: $50,000 if no accident (p = .95) $40,000 if accident (1-p = .05) (i.e. "Endowment" is that income in the good state is 50,000 and income in the bad state is 40,000) EV = .95($50000)+.05($40000) = $49,500 662 Chapter Fifteen The Demand for Insurance Insurance: Coverage = $10,000 Price = $500 $49,500 sure thing. Why? In a good state, receive 50000-500 = 49500 In a bad state, receive 40000+10000-500=49500 663 Chapter Fifteen The Demand for Insurance If you are risk averse, you prefer to insure this way over no insurance. Why? Full coverage ( no risk so prefer all else equal) Definition: A fairly priced insurance policy is one in which the insurance premium (price) equals the expected value of the promised payout. i.e.: 500 = .05(10,000) + .95(0) 664 Chapter Fifteen The Supply of Insurance Insurance company expects to break even and assumes all risk – why would an insurance company ever offer this policy? Definition: Adverse Selection is opportunism characterized by an informed person's benefiting from trading or otherwise contracting with a less informed person who does not know about an unobserved characteristic of the informed person. 665 Chapter Fifteen Insurance & Moral Hazard Definition: Moral Hazard is opportunism characterized by an informed person's taking advantage of a less informed person through an unobserved action. 666 Chapter Fifteen Adverse Selection & Market Failure Lottery: • $50,000 if no blindness (p = .95) • $40,000 if blindness (1-p = .05) • EV = $49,500 (fair) insurance: • Coverage = $10,000 • Price = $500 • $500 = .05(10,000) + .95(0) 667 Chapter Fifteen Adverse Selection & Market Failure Suppose that each individual's probability of blindness differs [0,1]. Who will buy this policy? Now, p' = .10 so that: EV of payout = .1(10,000) + .9(0) = $1000 while price of policy is only $500. The insurance company no longer breaks even. 668 Chapter Fifteen Adverse Selection & Market Failure Suppose we raise the price of policy to $1000. Now, p'' = .20 so that. EV of payout = .2(10,000) + .8(0) = $2000. So the insurance company still does not break even and thus the Market Fails. 669 Chapter Fifteen Decision Trees Definition: A decision tree is a diagram that describes the options available to a decision maker, as well as the risky events that can occur at each point in time. 1. 2. 3. 4. Decision Nodes Chance Nodes Probabilities Payoffs We analyze decision problems by working backward along the decision tree to decide what the optimal decision would Be. 670 Chapter Fifteen Decision Trees 671 Chapter Fifteen Decision Trees Steps in constructing and analyzing the tree: 1. 2. 3. 4. 5. 6. Map out the decision and event sequence Identify the alternatives available for each decision Identify the possible outcomes for each risky event Assign probabilities to the events Identify payoffs to all the decision/event combinations Find the optimal sequence of decisions 672 Chapter Fifteen Perfect Information Definition: The value of perfect information is the increase in the decision maker's expected payoff when the decision maker can -- at no cost -- obtain information that reveals the outcome of the risky event. 673 Chapter Fifteen Perfect Information Example: • Expected payoff to conducting test: $35M • Expected payoff to not conducting test: $30M The value of information: $5M The value of nformation reflects the value of being able to tailor your decisioins to the conditions that will actually prevail in the future. It should represent the agent's willingness to pay for a "crystal ball". 674 Chapter Fifteen Summary 1. We can think of risky decisions as lotteries. 2. We can think of individuals maximizing expected utility when faced with risk. 3. Individuals differ in their attitudes towards risk: those who prefer a sure thing are risk averse. Those who are indifferent about risk are risk neutral. Those who prefer risk are risk loving. 4. Insurance can help to avoid risk. The optimal amount to insure depends on risk attitudes. 675 Chapter Fifteen Summary 5. The provision of insurance by individuals does not require risk lovers. 6. Adverse Selection and Moral Hazard can cause inefficiency in insurance markets. 7. We can calculate the value of obtaining information in order to reduce risk by analyzing the expected payoff to eliminating risk from a decision tree and comparing this to the expected payoff of maintaining risk. 676 Chapter Fifteen Chapter Sixteen General Equilibrium Theory 677 Chapter Sixteen Chapter Sixteen Overview 1. General Equilibrium – Analysis I • Partial Equilibrium Bias 2. Efficiency and Perfect Competition 3. General Equilibrium – Analysis II • • • • The Efficiency if Competition The Edgeworth Box Analysis of Allocation: A Pure Exchange Economy Analysis of Production 678 Chapter Sixteen Partial vs. General Equilibrium If there are spillover effects from one market to another, then the effects of a change in one market on the economy must be analyzed by examining its effect on all markets 679 Chapter Sixteen Partial vs. General Equilibrium Further, many exogenous events (or policy changes) affect many markets simultaneously (example: discovery of a major oil deposit that raises the income of all citizens in an economy and so affects equilibrium in all markets). If we do not take into account all markets in our equilibrium calculation, we induce a bias in our analysis 680 Chapter Sixteen Partial vs. General Equilibrium Definition: General Equilibrium analysis is the study of how equilibrium is determined in all markets simultaneously (e.g. product markets and labor markets). Definition: Partial Equilibrium analysis is the study of how equilibrium is determined in only a single market (e.g. a single product market). 681 Chapter Sixteen Partial vs. General Equilibrium Example: Equilibrium in two markets Q1D = 12 – 3p1 + p2 Q2D = 4 – 2p2 + p1 Q1s = 2 + p1 Q2s = 1 + p2 What is the general equilibrium level of prices and output in this economy? Market 1 equilibrium: • 12 – 3p1 + p2 = 2 + p1 • p1 = 10/4 + p2/4 Market 2 equilibrium: • 4 – 2p2 + p1 = 1 + p2 • p2 = 1 + p1/3 682 Chapter Sixteen Partial vs. General Equilibrium Substituting condition 1 into condition 2: 4 – 2p2 + 10/4 + p2/4 = 1 + p2 • 2 = p2e • 3 = p1e • Q1e = 5 • Q2e = 3 683 Chapter Sixteen Equilibrium in Two Markets P1 Market 1 4.67 P1 = 4 + P2/3 – QD1/3 14 Chapter Sixteen Q1 684 Equilibrium in Two Markets P1 P1 = Q1s - 2 Market 1 4.67 2 14 Chapter Sixteen Q1 685 Equilibrium in Two Markets P1 P1 = Q1s - 2 Market 1 4.67 e1 • 3 2 P1 = 4 + P2/3 - Q1D/3 5 14 Chapter Sixteen Q1 686 Equilibrium in Two Markets P2 P2 = Q2s - 1 Market 2 Q2 1 687 Chapter Sixteen Equilibrium in Two Markets P2 P2 = Q2s - 1 Market 2 5.5 P2 = 4 + P1/2 - Q2D/2 1 11 Q2 688 Chapter Sixteen Equilibrium in Two Markets P2 P2 = Q2s - 1 Market 2 5.5 e2 • 2 1 4 P2 = 4 + P1/2 - Q2D/2 11 Q2 689 Chapter Sixteen Equilibrium in Two Markets Suppose an exogenous shock increases demand in market 1 to: Q1D = 22 – 3p1 + p2 . What is the new general equilibrium? • Market 1 equilibrium: p1 = 22/4 + p2/4 • Market 2 equilibrium: p2 = 1 + p1/3 • 32/11 = p2e • 63/11 = p1e • Q1e = 85/11 • Q2e = 43/11 690 Chapter Sixteen Equilibrium in Two Markets Suppose you used the partial equilibrium price and output level in market 2 in order to compute the market 1 equilibrium. What would be the bias in your conclusions for market 1? If we re-solve for market 1 price with the new demand but p2e = 2, we obtain p1e = 11/2 = 5.5 – but in part (b), p1e = 63/11 = 5.72. In other words, we would underestimate the true price for good 1. 691 Chapter Sixteen Efficiency and Competitive Markets Definition: An economic situation is Pareto Efficient if there is no way to make any person better off without hurting somebody else. Result 1 – Production Efficiency: A perfectly competitive market produces a Pareto efficient amount of output. Because the price at which someone is willing to buy an extra unit exactly equals the price that must be paid to induce someone else to sell an extra unit: Or 692 Chapter Sixteen Efficiency and Competitive Markets Since price equals marginal cost at the competitive equilibrium, consumers value the last unit of output by exactly the amount that it costs to produce (in the sense of opportunity cost) so that no reallocation of consumption towards this good or away from this good could increase the value obtained from resources in the economy. 693 Chapter Sixteen Efficiency and Competitive Markets As long as Pi > MCi, the total size of the “economic pie” could be increased by increased consumption of good i since MRi reflects the opportunity cost of producing i. As long as Pi < MCi, the total size of the “economic pie” could be increased by decreased consumption of good i. 694 Chapter Sixteen Efficiency and Competitive Markets Result 2 – Allocative Efficiency: A competitive market allocates goods in a way that is Pareto efficient. because it equalizes the marginal rates of substitution across consumers. i.e., If all consumers are willing to trade goods at the same rate then it is not possible for any pair to get together and improve their joint utilities by reallocating goods. 695 Chapter Sixteen Summarizing Perfect Competition Perfect competition maximizes the sum of consumers’ surplus plus producers’ surplus (minimizes deadweight loss) and allocates that output in a Pareto Efficient way. Is Prefect Competition Really Desirable? We know that consumers’ surplus is not the “ideal” measure of consumer benefit from consumption when there are income effects…but if income affects the placement of demand, have we calculated our measure of “efficiency” correctly? Where does “income” come from and does our result depend on the allocation of income across consumers? 696 Chapter Sixteen Summarizing Perfect Competition Producers’ surplus measures producers’ benefits net of costs (i.e., costs affect the placement of supply)…but what determines these “opportunity costs”? Our discussion has taken “income” and “costs” as, at least partially, given. But these come, in fact, from other markets (labor markets, for example). Further, these concepts are related. If we wish to make a stronger statement about economic efficiency, we need to measure economic efficiency while allowing income and all costs to be endogenous. 697 Chapter Sixteen Pure Exchange Economy Efficiency Simplifying Assumptions 1. Consumers and producers are price takers. 2. There are only two individuals and two goods in the economy. 3. Individuals have fixed allocations (endowments) of goods that they might trade. No production occurs for now. 4. Consumers maximize utility with usually-shaped indifference curves (and non-satiation). Utilities are not interdependent. 698 Chapter Sixteen Edgeworth Box Diagram 699 Chapter Sixteen Edgeworth Box Diagram 700 Chapter Sixteen Edgeworth Box Diagram 701 Chapter Sixteen Edgeworth Box Diagram 1. The length of the side of the box measures the total amount of the good available. 2. Person A’s consumption choices are measured from the lower left hand corner, Person B’s consumption choices are measured from the upper right hand corner. 3. We can represent an initial endowment, (wA1,wA2), (wB1,wB2) as a point in the box. This is the allocation that consumers have before any exchange occurs. 702 Chapter Sixteen Edgeworth Box Diagram 4. Any other feasible consumption allocation is a point in the box such that, for each individual: "final demand" < "initial supply" • xA1+xB1 < wA1 + wB1 • xA2+xB2 < wA2 + wB2 5. We can represent indifference curves of the individuals between the goods in the standard way measured from the appropriate corners. 703 Chapter Sixteen Exchange • Any voluntary barter trade (a point that makes at least one consumer better off) must lie in a “lens” formed by the indifference curves that intersect the initial endowment. • Allocation through trading that potentially improves utility…but is infeasible: There is excess demand for good 1 and excess supply of good 2. Neither the market for good 1 nor the market for good 2 is in equilibrium. 704 Chapter Sixteen Edgeworth Box – Infeasible Allocation 705 Chapter Sixteen Edgeworth Box – Infeasible Allocation 706 Chapter Sixteen Edgeworth Box – Infeasible Allocation 707 Chapter Sixteen Edgeworth Box –Allocation Can be Improved 708 Chapter Sixteen Edgeworth Box –Allocation Can be Improved 709 Chapter Sixteen Edgeworth Boxes Trading will continue until no mutually improving trades are possible. (e.g. at M) 710 Chapter Sixteen Edgeworth Box – Economically Efficient Allocation 711 Chapter Sixteen Edgeworth Box – Economically Efficient Allocation 712 Chapter Sixteen Edgeworth Box – Economically Efficient Allocation 713 Chapter Sixteen Edgeworth Box – Economically Efficient Allocation 714 Chapter Sixteen Pareto Set / Contract Curves 1. M is Pareto efficient 2. M is at a tangency point of the two individuals’ indifference curves MRSA1,2 = MRSB1,2 3. Definition: The set of all Pareto efficient points in the Edgeworth box is known as the Pareto set or the Contract Curve. This set typically will stretch from one corner to the other of the box (M not unique). A subset of this set will contain the points that are Pareto efficient with respect to the initial endowment. 715 Chapter Sixteen The Contract Curve 716 Chapter Sixteen The Contract Curve 717 Chapter Sixteen The Contract Curve 718 Chapter Sixteen The Contract Curve 719 Chapter Sixteen Pure Exchange Economy • A pure exchange economy in which completely decentralized trading is allowed such that agents have access to each other and each is able to maximize utility subject to a feasibility constraint gets the economy to A Pareto Efficient Allocation. • This requires each individual to have information on his endowment and preferences only 720 Chapter Sixteen Calculating a Contract Curve Two individuals, A and B with "Cobb-Douglas" utility functions over 2 goods, X and Y. UA = (XA)(YA)1- UB = (XB)(YB)1- MUYA = (1-)XAY- MUXB = XA-1Y1- MUYB = (1-)XAY- XA + XB = 100 – This gives the size of the Edgeworth Box YA + YB = 200 Therefore: MRSX,YA = MUXA/MUYA = [/(1-)][YA/XA] MRSX,YB = MUXB/MUYB = [/(1-)][YB/XB] 721 Chapter Sixteen Calculating a Contract Curve And XA = 100 – XB – feasibility constraints YA = 200 - YB MRSX,YA = MRSX,YB – tangency condition for contract curve [/(1-)][(200 – YB)/(100 – XB)] = [/(1-)][YB/XB] Or (-)YBXB - (1-)(100YB) + (1-)200XB = 0 or (-)YAXA + (1-)(100YA) - (1-)200XA = 0 722 Chapter Sixteen Calculating a Contract Curve Draw the contract curve for ==½ The equations for the contract curves simplify to: YA = 2XA and YB = 2XB 723 Chapter Sixteen The Role of Prices Suppose that agents are presented with prices, (p1,p2) that they take as given and can use to value their initial endowment of goods p1w1 + p2w2 = I Hence, these prices define a budget constraint for each individual…tangency with the budget constraint determines where the individuals will desire to consume: 724 Chapter Sixteen Prices & Equilibrium MRS = p1/p2 So that in the General Equilibrium – MRSA1,2 = MRSB1,2 = p1/p2 Definition: If, at the announced prices, the amount that A wants to buy (sell) of good 1 exactly equals the amount B wants to sell (buy) of good 1 and if the same holds for good 2 as well, the market is in equilibrium. 725 Chapter Sixteen Economically Efficient Price Allocation 726 Chapter Sixteen Economically Efficient Price Allocation 727 Chapter Sixteen Economically Efficient Price Allocation 728 Chapter Sixteen Economically Efficient Price Allocation 729 Chapter Sixteen Economically Efficient Price Allocation • In other words, income is determined by the value of the endowment and equilibrium holds when, in every market, demand equals supply. • Further, since the market equilibrium holds where the marginal rates of substitution are equal and the preferred bundles of each agent lie above the budget set, the market equilibrium is Pareto Efficient. 730 Chapter Sixteen Economically Efficient Price Allocation This means that society can achieve efficiency by allowing competition This equilibrium requires very little information (prices only) or co-ordination. In fact, any Pareto-efficient equilibrium can be obtained by competition, given an appropriate endowment. For example, any Pareto efficient allocation, x, can be obtained as a competitive equilibrium if the initial endowment is x. 731 Chapter Sixteen Economically Efficient Price Allocation • This means that society can obtain a particular efficient allocation by appropriately redistributing endowments (income). • This can be achieved through taxes/subsidies to endowments (lump sum taxes) that do not affect choice (prices) • In fact, this redistribution could be viewed as the main role of government in the perfectly competitive model 732 Chapter Sixteen At Equilibrium Prices: 1. Allocative Efficiency: MRSX,Y for all the individuals must be equal 2. Private Utility Maximization: MRSX,Y for each and every individual must equal pX/pY 3. Market Equilibrium: Qd = QS must hold for each and every good. 4. Feasibility: Total supply must equal the original endowment for each and every good. 733 Chapter Sixteen Production Suppose that all individuals in the economy have a dual role: they are consumers, but they also are the producers. In other words, the individual's role as a producer will determine their income. Definition: The production possibility frontier (PPF) of an individual is the maximum combinations of goods A and B that can be produced with the individual’s input (e.g., labor) per unit of time. Definition: An individual achieves efficiency in production if s/he produces combinations of goods on the PPF (so that there is no "slacking off"). 734 Chapter Sixteen Marginal Rate of Transformation Definition: The slope of the production possibility frontier is the marginal rate of transformation (MRT). The MRT tells us how much more of good Y can be produced if the production of good X is reduced by a small amount. Or…the MRT tells us how much it costs to produce one good in terms of foregone production of the other good (opportunity cost). 735 Chapter Sixteen Production Possibility Frontier (PPF) Kate’s Production Y 6 PPFK MRTK= 2 2 3 X 736 Chapter Sixteen Production Possibility Frontier Kate’s Production Y Pierre’s Production Y 6 PPFK MRTK= 2 PPFP 2 MRTP= 1/2 3 3 X 2 6 X 737 Chapter Sixteen Production Possibility Frontier Kate’s Production Y Pierre’s Production Joint Production Y Y PPFJ MRTJ= 1/2 6 6 MRTJ= 2 PPFK MRTK= 2 PPFP 2 MRTP= 1/2 3 3 X 2 6 X 6 X 738 Chapter Sixteen Joint PPF Definition: The joint PPF for all possible technologies and all producers in the economy depicts the maximum amount of each good that could be produced in total by all producers. Definition: A producer who, when producing one good, reduces production of a second good less compared to another producer is said to have a comparative advantage in producing the first good. 739 Chapter Sixteen Joint PPF • If the MRT of two different producers (and consumers) differs, then the individuals can potentially gain from trade • If many production methods are available, the joint PPF takes a typically “rounded” shape, representing the various MRT’s available to the economy. 740 Chapter Sixteen The Efficient Product Mix • Now, let’s look at the efficient product mix. At which point along the joint PPF would society operate? • Any individual consumer would prefer production to occur at a point where the consumer's indifference curve is just tangent to the PPF. 741 Chapter Sixteen The Efficient Product Mix Y Preference Direction PPFJ X 742 Chapter Sixteen The Efficient Product Mix Y Preference Direction IC PPFJ X 743 Chapter Sixteen The Efficient Product Mix Y Preference Direction • MRSX,Y = MRTX,Y IC PPFJ X 744 Chapter Sixteen The Efficient Product Mix At this point, the consumer’s willingness to give up good X in order to get good Y just equals the rate at which a producer has to give up good X in order to produce more of good Y. MRTX,Y = MRSX,Y But this must be true for all consumers if the economy is to produce optimally for each consumer. 745 Chapter Sixteen Comparative Markets & Optimality Can the competitive market help us to achieve this optimality? At the Pareto efficient allocations, it is true for all consumers that: MRSX,Y = pX/pY 746 Chapter Sixteen The Producers’ Problem Suppose that the producers produce goods X and Y and choose the product mix so as to maximize profits given the prices pX and pY: Max = pXQX + pYQY – C*QX,QY Where: we will suppose that the cost of production is fixed whatever the optimal output mix (e.g., we just want to know how to employ the labor we have contracted) 747 Chapter Sixteen Isoprofit Definition: an isoprofit line shows the output combinations that result in a given level of profit, 0 or QY = (0 + C*)/pY – pXQX/pY 748 Chapter Sixteen The Profit Maximizing Product Mix Y PPFJ X Chapter Sixteen 749 The Profit Maximizing Product Mix Y Isoprofit Lines (0+C*)/PY • -pX/pY PPFJ X Chapter Sixteen 750 The Profit Maximizing Product Mix Y Isoprofit Lines (0+C*)/PY Direction of increasing profits • Profit maximising product mix -pX/pY PPFJ X Chapter Sixteen 751 The Profit Maximizing Product Mix Hence, If the firm maximizes profits, then, it chooses the product mix that shifts out the isoprofit line as much as possible while remaining feasible. This is a tangency point such that for all producers: MRTX,Y = pX/pY 752 Chapter Sixteen The Profit Maximizing Product Mix In other words, in equilibrium, the price ratio will measure the opportunity cost of production of one good in terms of production of the other good. Therefore Because competition ensures that both the MRS and the MRT equal the (same) price ratio for all producers and all consumers, a competitive equilibrium achieves an efficient product mix for all producers and all consumers Earlier allocative efficiency results still hold with production 753 Chapter Sixteen General Equilibrium Y PPF X 754 Chapter Sixteen General Equilibrium Y Ys XeB • YeB PPF Xs X 755 Chapter Sixteen General Equilibrium Y Ys XeB • • Slope = -p1e/p2e YeB PPF XeA X Xs 756 Chapter Sixteen General Equilibrium Y Ys YeA XeB • • Slope = -p1e/p2e YeB PPF XeA Xs X 757 Chapter Sixteen General Equilibrium Ys and Xs are the amounts of X produced in the economy; (XeA,YeA) is the amount of X and Y consumed by person A and (XeB,YeB) is the amount of X and Y consumed by person B. • Efficiency in exchange (on contract curve) • Efficiency in use of inputs (on PPF) • Efficiency in product mix (tangency with PPF) 758 Chapter Sixteen Summary 1. If there are spillover effects among markets in the economy, we need to calculate equilibrium by determining equilibrium in all markets simultaneously. Otherwise, our results for equilibrium prices and quantities will be biased. This bias can be large. 2. In partial equilibrium analysis, a perfectly competitive and allocates goods in a way market produces a Pareto efficient amount of output that is Pareto efficient. 759 Chapter Sixteen Summary 3. We can make a similar statement about perfect competition in a general equilibrium analysis. In other words, taking into account that income is determined endogenously and costs are determined endogenously was well, we can still state that perfect competition produces a Pareto efficient amount of output and allocates it in a Pareto efficient way. 4. More specifically, competitive allocations are efficient in exchange, efficient in the use of inputs in production, and efficient in the mix of outputs. 760 Chapter Sixteen Chapter Seventeen Externalities and Public Goods 761 Chapter Seventeen Chapter Seventeen Overview 1. Motivation 2. Inefficiency of Competition with Externalities 3. Allocation Property Rights to Restore Optimality • • • The Coase Theorem Problems with the Coase Approach Other Methods to Restore Optimality – Standards and Fees 4. Public Goods • • • A Taxonomy Demand for Public Goods Free Riders and the Supply of Public Goods 762 Chapter Seventeen Externalities Definition: If one agent's actions imposes costs on another party, the agent exerts a negative externality, while if the agent's actions have benefits for another party, the agent exerts a positive externality. • Network externalities, snob effects • Wind chimes When externalities are present, the competitive market may not attain the Pareto Efficient outcome. 763 Chapter Seventeen Inefficiency of Competition with Externalities Competitive firms and consumers do not have to pay for the harms of their negative externalities, they produce too many. Since they are not compensated for the benefits of their positive externalities, they create too little. Example – Firm produces paper and harmful by-products: 1 ton paper 1 unit waste • Private cost of production does not include harm from waste. • Social cost of production includes the harm from the externality and is, then, greater than the private cost. 764 Chapter Seventeen Inefficiency of Competition with Externalities MCS = MCP + MCW Pp ($/ton) MCP MCW Demand 0 Qp (tons/day) W (units/day) 765 Chapter Seventeen Inefficiency of Competition with Externalities MCS = MCP + MCW Pp ($/ton) PS MCP •e s PC •e c MCW QS 0 Demand QC Qp (tons/day) W (units/day) 766 Chapter Seventeen Inefficiency of Competition with Externalities MCS = MCP + MCW Pp ($/ton) MCP A PS PC •e B F C E S D H G •e •MC C MCW P • MC Demand W QS 0 QC Qp (tons/day) W (units/day) 767 Chapter Seventeen Inefficiency of Competition with Externalities Social Optimum Private Change B+C+D • Consumers Surplus A A+B+C+D • Private Producers Surplus PSP B+C+F+G F+G+H H-B-C • Externality Cost, CG • Social Producers Surplus PSS = PSP-CG • Welfare W = CS + PSS C+G A+B+F C+D+E+ G+H B+F D+E+H F-C-D-E -B-C-D-E A+B+F-E -E=DWL 768 Chapter Seventeen Competitive Market & Social Optimum Competitive market: p = MPP Social optimum: p = MCS Competitive market creates a dead-weight loss (socially excessive negative externalities) This is because the polluter does not have to pay for pollution Socially optimal amount of waste is non-zero. How can we restore optimality? 769 Chapter Seventeen Restoring Optimality Definition: A property right is a legal rule that describes what economic agents can do with an object or idea. Deed to parcel of land; patent on a method 770 Chapter Seventeen Restoring Optimality – Paper Mill & Fishermen Suppose that paper mill may reduce its emissions of gunk by installing filters and fishermen can reduce emissions by installing a water treatment plant. Mill Fishermen No Treatment treatment No filter 500,100 500,200 filter 300,500 300,300 771 Chapter Seventeen Restoring Optimality – Paper Mill & Fishermen Case 1: No explicit rights allocation • Nash outcome: no filter, treatment plant • Joint payoff = 700 (not Pareto efficient) 772 Chapter Seventeen Restoring Optimality – Paper Mill & Fishermen Case 2: Fishermen have property right to no Pollution (and so, set a fee of, say, $500 for receiving pollution) Fishermen Nash Outcome: Filter, No treatment Joint Payoff = 800 (Pareto Efficient) Mill No Treatment treatment No filter 0,600 0,700 Filter 300,500 300,300 773 Chapter Seventeen Restoring Optimality – Paper Mill & Fishermen Case 3: Mill has right to pollute. Suppose the mill "sells" right to fresh water (i.e. obligation to install filter) for $250: Fishermen Nash Outcome: Filter, No Treatment Joint Payoff = 800 (Pareto Efficient) Mill No Treatment treatment No filter 500,100 500,200 filter 550,250 550,50 774 Chapter Seventeen The Coase Theorem • If there are no impediments to bargaining, assigning property rights results in the efficient outcome (at which joint profits are maximized). • Efficiency is achieved regardless of who receives the property rights. • Who gets the property rights affects the income distribution: the property rights are valuable. (The party with the property rights is compensated by the other party.) 775 Chapter Seventeen The Coase Theorem • Transaction Costs may be high; • Large numbers of injured parties; • Incomplete/Asymmetric Information. e.g. What are the long run effects of genetic engineering? 776 Chapter Seventeen Other Methods to Restore Optimality Pp ($/ton) MCS = MCP + MCW Emissions Standards (quota) MCP MCW Demand for Paper Qp (tons/day) W (units/day) 0 Chapter Seventeen 777 Other Methods to Restore Optimality MCS = MCP + MCW Pp ($/ton) Emissions Standards (quota) MCP •e What is the marginal cost of pollution at the social optimum? S T MCW •MC P • MC Demand for paper G 0 Qp (tons/day) W (units/day) QS= Quota Chapter Seventeen 778 Public Goods Definition: Rivalry in consumption means that only one person can consume a good: the good is used up in consumption (it can be depleted). Definition: Exclusion in consumption means that others can be prevented from consuming a good. 779 Chapter Seventeen Public Goods Definition: Private goods have properties of rivalry and exclusion. Pure Public goods lack both rivalry and exclusion. Club goods lack rivalry but have property of exclusion. Common property lacks exclusion but does have the property of rivalry. Exclusion No exclusion Rivalry Pure Private Commons: goods: Apple Fisheries No Rivalry Club goods: concert Pure public good: clean air 780 Chapter Seventeen Demand for Public Goods Because public goods lack rivalry, the aggregate demand is the aggregate willingness to pay curve: the vertical sum of the individual demand curves. 781 Chapter Seventeen Efficient Provision of a Public Good 400 Price ($/unit) 300 200 100 D1 0 30 Quantity of Public Good 100 782 Chapter Seventeen Efficient Provision of a Public Good 400 Price ($/unit) 300 200 100 D2 D1 0 30 100 Quantity of Public Good 200 Chapter Seventeen 783 Efficient Provision of a Public Good 400 Price ($/unit) 300 MC = 240 200 100 D2 MC = 50 D1 0 30 100 Quantity of Public Good 200 Chapter Seventeen 784 Efficient Provision of a Public Good 400 Price ($/unit) MSB 300 MC = 240 200 100 D2 MC = 50 D1 0 30 100 Quantity of Public Good 200 Chapter Seventeen 785 Efficient Provision of a Public Good 400 MC = 400 Price ($/unit) MSB 300 MC = 240 200 100 D2 MC = 50 D1 0 30 100 Quantity of Public Good 200 Chapter Seventeen 786 Efficient Provision of a Public Good Example Consumer 1: P1 = 100 - Q Consumer 2: P2 = 200 - Q How would we determine the efficient level of the public god algebraically assuming the marginal cost of the public good is $240? Summing P1 and P2, we obtain MSB = P1 + P2 = 100 - Q + 200 - Q = 300 - 2Q 787 Chapter Seventeen Efficient Provision of a Public Good Setting MSB = MC, we have: 300 - 2Q = 240 Or Q* = 30 788 Chapter Seventeen Free Rider Definition: a free rider benefits from an action of other (s) without paying for that action. Solutions to the free rider problem 789 Chapter Seventeen Summary 1. When one agent's actions affect another agent, the agent exerts an externality. 2. When externalities are present the competitive market may not attain the Pareto Efficient outcome. 3. We can restore optimality by assigning property rights to the cause of the externality (The Coase Theorem). 4. If we follow this approach, efficiency is achieved regardless of who receives the property rights; however, the property rights affect the income distribution. 790 Chapter Seventeen Summary 5. When transaction costs are high or there is asymmetric or incomplete information, allocating property rights may not restore optimality. 6. Other methods of restoring optimality include standards and fees. 7. Private goods have the properties of rivalry and exclusion. Other types of goods exist that do not have these properties. 791 Chapter Seventeen Summary 8. Goods that lack rivalry and exclusion are called pure public goods. 9. The demand for pure public goods is the vertical sum of the individual willingness to pay for the good. 10. Pure public goods tend to be undersupplied by the market. 792 Chapter Seventeen Index – Alphabetical Topics Take me to the Text: Analyzing Economic Problems Demand and Supply Analysis Capturing Surplus Competitive Markets: Applications Consumer Choice Consumer Preferences and the Concept of Utility Costs and Cost Minimization Cost Curves Demand Theory Equilibrium Theory Externalities Game Theory and Strategic Behavior Inputs and Production Functions Market Structure and Competition Monopoly and Monopsony Perfectly Competitive Markets Public Goods Risk and Information 793