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Economics of the Firm Some Introductory Material Introducing homo economicus….also known as “Economic Man” Economic man is a RATIONAL being Every decision we make involves both incremental benefits and costs…if we are acting rationally, we will undertake any action where the benefits outweigh the costs. Example: Suppose that you have been wandering in the desert for 5 days when you come across a lemonade stand. How much would you pay for a glass of lemonade? Suppose that you have been wandering in the desert for 5 days when you come across a lemonade stand. How much would you pay for a glass of lemonade? “Utility” is a function of lemonade (among other things) U L, A glass of lemonade will raise your utility… MU L A glass of lemonade isn’t free..it has a price PL You will buy a glass of lemonade as long as the benefits are greater than the costs We can complicate the example by adding an alternative choice…a hot dog stand “Utility” is a function of lemonade and hot dogs (among other things) U L, H , A glass of lemonade will raise your utility… MU L PL Every dollar spent on lemonade is a dollar that won’t be spent on hot dogs MU H PH You will buy a glass of lemonade as long as the benefits are greater than the costs In either case, we can say that, given a representation of individual tastes, price should have a negative relationship with quantity purchased “Utility” is a function of lemonade and hot dogs (among other things) U L, H , Rational Behavior (-) (+) QD DPL , PH Purchases of lemonade are negatively related to the price of lemonade and positively related to the price of hot dogs We can easily add another variable to our demand story…most of us are constrained by our disposable income. Expenditures on Lemonade Expenditures on Hot Dogs Available Income PL L PH H I (Constraint) U L, H , (Preferences) + Rational Behavior (-) (+) (+) QD DPL , PH , I Purchases of lemonade are negatively related to the price of lemonade and positively related to income and the price of hot dogs We have a similar situation on the supply side…with one complication. Stockholders/Bondholders provide capital for the firm Stockholders/Bondholders receive payments from the firm Managers provide effort to the firm Managers receive compensation from the firm Stockholders own the company, but managers make the decisions…how do we align their incentives? If we assume that the institutional details have been worked out, then the job of the decision maker is to maximize firm value Profits one year in the future Profits two years in the future 3 1 2 FV 0 ... 2 3 1 r 1 r 1 r Current Profits Risk adjusted rate of return While it is not necessary, it is sufficient to say that maximizing each year’s profits will maximize firm value Variable costs are influenced by sales decisions PLQ VC FC Price times quantity equals current revenues Fixed costs (overhead) is not affected by the level of sales and, hence, has no impact on sales decisions As with the average consumer, a firm’s decisions are made at the margin!!! For each sale that is made, it must be profitable at the margin. For now, lets assume that the firm has no control over the price it charges PLQ VC FC How does an additional sale affect revenues? PL How does an additional sale affect costs? MC A sale will be made as long as it has a bigger impact on revenues than costs. As with the average consumer, a firm’s decisions are made at the margin!!! In either case, we can say that, given a representation of a firm’s cost structure, price should have a positive relationship with sales (higher price raises profit margin) while anything that influences costs at the margin should have a negative relationship with sales Costs are a function of wages, material prices, etc. PLQ VC FC Rational Behavior (+) (-) QS S PL , MC Sales of lemonade are positively related to the price of lemonade and negatively related to marginal costs A Demand Function represents the rational decisions made by a representative consumer(s) “Is a function of” Quantity Purchased QD DPL , I Market Price (-) For example, suppose that at a market price of $2.50, an individual with an annual income of $50,000 chooses to buy 5 glasses of lemonade per week. Income (+) 5 D$2.50,$50,000 A Demand Curve is simply a graphical representation of a demand function For example, suppose that at a market price of $2.50, an individual with an annual income of $50,000 chooses to buy 5 glasses of lemonade per week. Price DI $50,000 $2.50 Quantity 5 5 D$2.50,$50,000 A Demand Curve is simply a graphical representation of a demand function Suppose that an increase in the market price from $2.50 to $2.75 causes this individual to reduce his/her lemonade purchases to 4 glasses per week Price $2.75 $2.50 DI $50,000 Quantity 4 5 4 D$2.75,$50,000 Demand curves slope downwards – this reflects the negative relationship between price and quantity. Elasticity of Demand measures this effect quantitatively %Q 20 D 2 % P 10 Price 2.75 2.50 *100 10% 2.50 $2.75 $2.50 DI $50,000 Quantity 4 5 45 *100 20% 5 A Supply Function represents the rational decisions made by a representative firm(s) “Is a function of” QS S PL , MC Quantity Supplied Market Price (+) For example, suppose that at a market price of $2.00, a firm facing a wage rate of $6/hr will supply 200 glasses per week. Marginal Costs (-) 200 S $2.00,$6 A Supply Curve is simply a graphical representation of a supply function For example, suppose that at a market price of $3.00, a firm facing a wage rate of $6/hr will supply 200 glasses of lemonade per week. Price S C $6 $2.00 Quantity 200 200 S $3.00,$6 A Supply Curve is simply a graphical representation of a supply function Suppose that an increase in the market price from $3.00 to $3.90 causes this firm to increase it’s lemonade sales to 250 cups per week S C $6 Price $3.00 $2.00 Quantity 200 250 250 S $3.50,$6 Supply curves slope upwards – this reflects the positive relationship between price and quantity. Elasticity of Supply measures this effect quantitatively S C $6 Price 3.00 2.00 *100 50% 2 . 00 $3.00 $2.00 Quantity 200 %QS 25 s .5 %P 50 250 250 200 *100 25% 200 Suppose that the overall market consists of 5,000 identical lemonade drinkers and 100 lemonade suppliers Price $2.75 At a price of $2.50, each of the 5,000 lemonade drinkers buys 5 glasses per week. $2.50 DI $50,000 Quantity 20,000 25,000 S C $6 Price At a price of $3.00, each of the 100 lemonade suppliers is willing to sell 250 glasses per week. $3.00 $2.00 Quantity 20,000 25,000 Given the behavior of suppliers and consumers, the market price would need to settle in between $2.50 and $2.75 S C $6 Price $2.00 DI $50,000 At a price of $2.00, total supply is 20,000, but demand is at least 25,000 Quantity 20,000 Q>25,000 Given the behavior of suppliers and consumers, the market price would need to settle in between $2.50 and $2.75 S C $6 Price $3.00 At a price of $3.00, total supply is 25,000, but demand is less than 20,000 DI $50,000 Quantity Q<20,000 25,000 Given the behavior of suppliers and consumers, the market price would need to settle in between $2.50 and $2.75 S C $6 Price 22,500 S $2.60, C $6 D$2.60, I $50,000 $2.60 DI $50,000 Quantity 22,500 We would call the $2.60 price the equilibrium price Suppose that average income in the area rose to $75,000. Higher income levels should raise demand at any market price S C $6 Price At the current $2.60 market price, supply is still 22,500, but with a higher level of income, demand has risen to 28,000 $2.60 DI $75,000 DI $50,000 Quantity 22,500 28,000 At the new income level of $75,000, $2.60 can no longer be the equilibrium price Suppose that average income in the area rose to $75,000. Higher income levels should raise demand at any market price S C $6 Price 25,000 S $3.00, C $6 D$3.00, I $75,000 $3.00 $2.60 DI $75,000 DI $50,000 Quantity 22,500 25,000 The increase in income causes a rise in sales and a rise in market price Suppose that lemonade store wages rose to $10/hr. Higher wages should lower supply at any market price S C $6 Price At the current $2.60 market price, supply has fallen to 18,000, but demand is still at 22,500 $2.60 DI $50,000 Quantity 18,000 22,500 At the wage level of $10, $2.60 can no longer be the equilibrium price Suppose that lemonade store wages rose to $10/hr. Higher wages should lower supply at any market price S C $6 Price 20,000 S $2.75, C $10 D$2.75, I $50,000 $2.75 $2.60 DI $50,000 Quantity 20,000 22,500 Higher wages cause a rise in market price and a drop in sales Supply, Demand, and equilibrium prices/sales PL L PH H I (Constraint) U L, H , (Preferences) + Rational Behavior PQ VC FC Rational Behavior (+) (-) QS S P, MC (-) (+) QD DPL , I With the additional assumption that prices adjust and that markets clear (equilibrium), we have the following… (+) (-) Q QI , MC P PI , MC (+) (+) Sales are related to average income and marginal costs Prices are related to average income and marginal costs If we truly believe in competitive markets, we can sleep well at nigh knowing several things…goods are being produced by the most efficient producers (i.e. those with the lowest costs) and given to individuals with the highest values. Somebody who bought a glass of lemonade paid $2.60 when they actually valued it at much higher. We call this consumer surplus Price S P* $2.60 Somebody who sold this glass of lemonade collected $2.60 when the marginal production cost was much lower. We call this producer surplus (a.k.a Profit) D Q* 22,500 Q 17,750 Quantity We also can rest assured that we are producing exactly the right goods and services Price S P* $2.60 Price S P* $2.60 D' D' Q* 22,500 Lemonade D D Quantity Q* 22,500 Quantity Hot Dogs If consumer preferences suddenly shifted away from lemonade and towards hot dogs, the lemonade market would shrink (as the price of lemonade falls) while the hot dog market expands (and the price rises) Can we use our market model to explain differences in salaries? Kobe Bryant: Salary = $23,000,000,000 High School Teacher: Salary = $50,000 Price S Price S $50K $23M D D Quantity $15K 3,000,000 Quantity 1 Microsoft’s new Xbox 360 gaming console was released in North America on November 22 at a retail price of $299.99. Available supply sold out almost immediately as Christmas shoppers stood in line for this year’s hot item. (Microsoft has increased its sales target from 3M units to 6M units). What’s odd about this?? Why didn’t Microsoft raise their price? S Price ??? $299.99 D Quantity 3M Clearly, $299.99 is not an equilibrium price ! When do our rationality assumptions begin to break down? Situations involving interactions among small groups of people: Example: How to split $20. Situations involving the immediate present vs. the future: Example: Instant gratification and the time value of money Situations involving uncertainty Example: The Monty Hall Problem And now for something completely different…. What are the odds that a fair coin flip results in a head? What are the odds that the toss of a fair die results in a 5? What are the odds that tomorrow’s temperature is 95 degrees? The answer to all these questions come from a probability distribution Probability 1/2 Head Tail Probability 1/6 1 2 3 4 5 6 A probability distribution is a collection of probabilities describing the odds of any particular event The distribution for temperature in south bend is a bit more complicated because there are so many possible outcomes, but the concept is the same Probability Standard Deviation Temperature Mean We generally assume a Normal Distribution which can be characterized by a mean (average) and standard deviation (measure of dispersion) Without some math, we can’t find the probability of a specific outcome, but we can easily divide up the distribution Probability Temperature Mean-2SD 2.5% Mean -1SD 13.5% Mean 34% Mean+1SD 34% Mean+2SD 13.5% 2.5% Annual Temperature in South Bend has a mean of 59 degrees and a standard deviation of 18 degrees. Probability 95 degrees is 2 standard deviations to the right – there is a 2.5% chance the temperature is 95 or greater (97.5% chance it is cooler than 95) Temperature 23 41 Can’t we do a little better than this? 59 77 95 Conditional distributions give us probabilities conditional on some observable information – the temperature in South Bend conditional on the month of July has a mean of 84 with a standard deviation of 7. Probability 95 degrees falls a little more than one standard deviation away (there approximately a 16% chance that the temperature is 95 or greater) Temperature 70 77 84 91 95 Conditioning on month gives us a more accurate forecast! 98 We know that there should be a “true” probability distribution that governs the outcome of a coin toss (assuming a fair coin) PrHeads PrTails .5 Suppose that we were to flip a coin over and over again and after each flip, we calculate the percentage of heads & tails # of Heads Total Flips (Sample Statistic) .5 (True Probability) That is, if we collect “enough” data, we can eventually learn the truth! We can follow the same process for the temperature in South Bend Temperature ~ N , 2 We could find this distribution by collecting temperature data for south bend Sample Mean (Average) Sample Variance 1N x xi N i 1 N 1 2 s 2 xi x 2 N i 1 Note: Standard Deviation is the square root of the variance. Conditional Distributions Obviously, the temperature in South Bend is different in the winter and the summer. That is, temperature has a conditional distribution Temp (Summer) ~ Temp (Winter) ~ N s, N W , W2 Regression is based on the estimation of conditional distributions 2 s Some useful properties of probability distributions x N μ,σ 2 y kx Probability distributions are scalable y N k,k 2σ 2 = 3X Mean = 1 Mean = 3 Variance = 4 Variance = 36 (3*3*4) Std. Dev. = 2 Std. Dev. = 6 y N ,σ x y N ,σ x N μ x ,σ x2 Probability distributions are additive y 2 y x y 2 x σ y2 2 cov xy = + Mean = 1 Mean = 2 Mean = 3 Variance = 1 Variance = 9 Variance = 14 (1 + 9 + 2*2) Std. Dev. = 1 Std. Dev. = 3 Std. Dev. = 3.7 COV = 2 Suppose we know that the value of a car is determined by its age Value = $20,000 - $1,000 (Age) Car Age Value Mean = 8 Mean = $ 12,000 Variance = 4 Variance = 4,000,000 Std. Dev. = 2 Std. Dev. = $ 2,000 We could also use this to forecast: Value = $20,000 - $1,000 (Age) How much should a six year old car be worth? Value = $20,000 - $1,000 (6) = $14,000 Note: There is NO uncertainty in this prediction. Searching for the truth…. You believe that there is a relationship between age and value, but you don’t know what it is…. 1. Collect data on values and age 2. Estimate the relationship between them Note that while the true distribution of age is N(8,4), our collected sample will not be N(8,4). This sampling error will create errors in our estimates!! 18000.00 16000.00 Slope = b 14000.00 12000.00 10000.00 a 8000.00 6000.00 4000.00 2000.00 0.00 0 2 4 6 Value = a + b * (Age) + error 8 10 12 14 error N 0,σ 2 We want to choose ‘a’ and ‘b’ to minimize the error! Regression Results Variable Intercept Age Coefficients Standard Error t Stat 12,354 653 18.9 - 854 80 -10.60 We have our estimate of “the truth” Value = $12,354 - $854 * (Age) + error Intercept (a) Age (b) Mean = $12,354 Mean = -$854 Std. Dev. = $653 Std. Dev. = $80 T-Stats bigger than 2 in absolute value are considered statistically significant! Regression Statistics R Squared 0.36 Standard Error 2250 Percentage of value variance explained by age Error Term Mean = 0 Std, Dev = $2,250 We can now forecast the value of a 6 year old car 6 Salary = $12,354 - $854 * (Age) + error Mean = $12,354 Mean = $854 Mean = $0 Std. Dev. = $653 Std. Dev. = $ 80 Std. Dev. = $2,250 StdDev Var a X 2Var b 2 XCova, b Var error Cova, b XVarb (Recall, Shoe size has a mean of 6) StdDev 6532 6 2 80 2 26880 2 2250 2 $2,259 Value 12,354 854 * 6 $7,230 StdDev 653 2 6 80 2 2 2 2 2 6 8 80 2250 $2,259 Value +95% Forecast Interval -95% Age 6 x 8 Age Note that your forecast error will always be smallest at the sample mean! Also, your forecast gets worse at an increasing rate as you depart from the mean What are the odds that Pat Buchanan received 3,407 votes from Palm Beach County in 2000? The Strategy: Estimate a conditional distribution for Pat Buchanan’s votes using every county EXCEPT Palm Beach Using Palm Beach data, forecast Pat Buchanan’s vote total for Palm Beach The Data: Demographic Data By County County Black (%) Age 65 (%) Hispanic (%) College (%) Income (000s) Buchanan Total Votes Votes Alachua 21.8 9.4 4.7 34.6 26.5 262 84,966 Baker 16.8 7.7 1.5 5.7 27.6 73 8,128 LN P a1 a2 B a2 A65 a3 H a4C a5 I Buchanan Votes Total Votes Error term *100 Parameters to be estimated Side note: Why logs? Option #1: Linear P 3 .5B A 10% increase in the black percentage (say, from 30% to 40%) increases Pat Buchanan’s vote percentage by 5% (Say, from 1% to 6%) P = Buchanan’s Vote Percentage B = Percentage Black Option #2: Semi –Log Linear LN P 3 .5B A 10% increase in the black percentage (say, from 30% to 40%) increases Pat Buchanan’s vote percentage by 5% (Say, from 1% to 1(1.05) = 1.05%) Option #3: Log Linear LN P 3 .5LN B A 10% increase in the black percentage (say, from 30% 30(1.10) = 33% increases Pat Buchanan’s vote percentage by 5% (Say, from 1(1.05) = 1.05%) The Results: Variable Coefficient Standard Error t - statistic Intercept 2.146 .396 5.48 Black (%) -.0132 .0057 -2.88 Age 65 (%) -.0415 .0057 -5.93 Hispanic (%) -.0349 .0050 -6.08 College (%) -.0193 .0068 -1.99 .00113 -4.58 Income (000s) -.0658 LN P 2.146 .0132B .0415 A65 .0349H .0193C .0658I Now, we can make a forecast! County Black (%) Age 65 (%) Hispanic (%) College (%) Income (000s) Buchanan Total Votes Votes Palm Beach 21.8 23.6 9.8 22.1 33.5 3,407 431,621 LN P 2.146 .0132B .0415 A65 .0349H .0193C .0658I LN P 2.004 P e 2.004 .134% .00134431,621 578 This would be our prediction for Pat Buchanan’s vote total! LN P 2.004 We know that the log of Buchanan’s vote percentage is distributed normally with a mean of -2.004 and with a standard deviation of .2556 Probability LN(%Votes) -2.004 – 2*(.2556) = -2.5152 -2.004 + 2*(.2556) = -1.4928 There is a 95% chance that the log of Buchanan’s vote percentage lies in this range P e 2.004 .134% Next, lets convert the Logs to vote percentages Probability % of Votes e 2.5152 .08% e 1.4928 .22% There is a 95% chance that Buchanan’s vote percentage lies in this range .00134431,621 578 Finally, we can convert to actual votes Probability .0008431,621 348 Votes .0022431,621 970 There is a 95% chance that Buchanan’s total vote lies in this range