Transcript Microeconomics - University of Utah

MICROECONOMICS
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Price Theory
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How much does Windows 7 sell for?
How much does Linux sell for?
If a negligent driver kills an 85 year old woman, how
much money will the jury award the estate of the
family?
In a similar accident, but involving a 20 year old man,
how much will the award be?
How much more money does a white male make
compared with a white female make doing similar work?
How much more money can you expect to earn over your
lifetime with a Master’s Degree from Chulalongkorn
University compared with if you did not go to school?
SUPPLY & DEMAND
 One
of the most persuasive models in the
business, social, and behavioral sciences.
 Wide applications in fields such as
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Economics
Finance
Labor
Statistics
Health
 Major
Goal: Price Determination.
THE LAW OF DEMAND
An inverse relationship between a measure of
price and a measure of the quantity demanded.
 As the price of something goes up less of that
something is demanded.
 What is price?
 What is demand?
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PRICES
 In
microeconomics a price is a ratio that
represents terms of trade.
 Prices, in micro, are real.
 Opportunity costs represent real prices.
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In order to get something you have to give
something up.
 We
will use monetary units for
convenience. Thus Baht or Dollars
represent a medium of exchange…dollars
per shirt or dollars per baht represent the
price of shirts (in $’s) or the price of baht
(in $’s).
A MODEL
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Maybe your first economic model was the PPF
model…it represents prices in real terms:
PPF
 In
this model we see the terms of trade,
i.e., how much Y we get (or give up) when
we give up (or get) some amount of X.
 Did you notice the curvature of the PPF?
It doesn’t need to be this way, but the
curve represents increasing marginal cost.
That is a standard (and useful
assumption):
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As we get more X we have to give up
increasing amounts of Y.
GOODS & SERVICES
Production is transformation.
 It might be a physical transformation of
resources.
 It might be a spatial transformation of resources.
 It might be a temporal transformation of
resources.
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THE LAW OF DEMAND
Intuitive.
 Applicable to individual decision making.
 Applicable to market activity.
 Applicable to non-market activity:
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Demand for drunk driving.
Demand for quality of life.
DEMAND
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Demand exists in the output market.
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Demand exists in the input market.
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For example: demand for automobiles.
For example: demand for labor.
Some goods & services are both inputs and
outputs.
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For example: tomatoes.
MARKET DEMAND
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Generated from individual demand.
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For example, at a price of 10 baht
Miss Kawita wants 5 units
 Mr Chayanin wants 4 units
 Mr Satta does not want any units
 Miss Utumporn wants 1 unit
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At this price 10 units are demanded.
DEMAND MAY BE BINARY
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At a price of Bt 3.95 million (Mercedes E220 CDI)
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Richard has zero effective demand – is not in the
market
Miss Ungkana has non-zero effective demand – is in
the market (do not let BMW know this!)
Aggregation of many zeroes and ones leads to
market demand
THE LAW OF DEMAND
Sometimes we can quantify Qd and P
 We might model Qd
 QdRichard = f(…,P,YRichard, …)
 QdRichard = a + bP + cY
 b might be -5
 c might be .025
 a represents other determinants
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LAW OF DEMAND
 QdRichard
= a + bP + cY
 This is a linear model
and looks like this:
LINEAR DEMAND
If we examine our demand function holding Y
constant (=1000) then we have
 Qd = 35 – 5P
 This is the same as
 P = 7 – Qd/5
 Graphing P against Q – Alfred Marshall
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P = 7 – QD/5
 Which
Graphs as:
DEMAND AS WILLINGNESS TO PAY
The demand function for an individual represents
the maximum amount of money that a person
would be willing to pay to purchase a given
quantity of a good or service.
 The law of demand in this case is a reflection of
diminishing marginal utility.
 Marginal: incremental.
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THE SUPPLY FUNCTION
 If
I offered to buy all the chocolate chip
cookies you brought to class on Saturday
for Bt 1000 each, how many cookies would
you bring?
 If I offered to buy all of the cookies you
brought for Bt 2 each, how many would
you bring?
 In this sense, the Supply Function
represents the minimum amount of
money a person would be willing to accept
to provide a given quantity of a good or
service.
SUPPLY PREVIEW
Because of the profit motive there is a direct or
positive relationship between the quantity
supplied of a good or service and its price.
 We might model this like:
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Qs = f(…, P, …)
 Qs = 10P, for example.
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EQUILIBRIUM
When we have a demand function (Qd) and a
supply function (Qs) we can think about the price
(P) which equilibrates Qd and Qs. This is Pe.
 Typically when an observed price Po is greater
than Pe we see excess supply and when Po < Pe we
have excess demand. Does this make sense to
you?
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QD = 10 – P; QS = P; PE = 5
IN LABOR ECONOMICS
There is a demand for labor by firms and there is
a supply of labor by households.
 The price of labor is the wage.
 The demand for labor depends on what sorts of
things?
 The supply of labor depends on what sorts of
things?
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WAGE DETERMINATION
As we will see, the demand for labor is called a
derived demand. As more consumers want a
particular good or service that creates demand
for labor in the industry that produces that
particular good or service.
 What is We in a particular industry?
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COMMODIFICATION OF LABOR
Note that it is theoretically easy to treat labor as
we would any other classical input into
production such as tomatoes, steel, seeds, or
capital.
 In the course of your studies you might want to
think about this from time to time.
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LABOR
How mobile is labor?
 Do prevailing wages adjust to excess supply or
demand for labor?
 Can certain kinds of labor easily be discriminated
against?
 What important institutions influence labor
supply and/or labor demand decisions?
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FROM HERE WHERE?
Now that we have previewed some aspects of
micro theory we will explore methods used to
model demand and supply functions.
 What goes on behind the demand function?
 What goes on behind the supply function?
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FROM HERE…
Price determination might be a reflection of
optimal decision making by consumers and
producers.
 Micro theory can be used as a guide:
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Descriptive models of behavior
 Prescriptive models of behavior
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Ethical Models
 Optimal Models
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STEP ONE
 We
build are skills by first looking at the
demand function.
 We will need a few mathematical tools to
help us understand how the demand
function expresses optimal consumer
choice.
 Consumers choose among baskets of
commodities in order to maximize utility
subject to budgetary constraints.
STEP TWO
After we derive the demand function we will do
similar exercises for the firm – to discover how
the supply function represents maximal profit
decision making.
 The model is a bit asymmetrical, as we will see.
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STEPS THREE, FOUR, …
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Once we are familiar with the basics of supply &
demand
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What are industries?
What is meant by economic welfare?
When do markets work and when do markets fail?
How would we measure failure?
When is their a role for government?
CALCULUS
Derivatives measure the slopes of lines.
 For example, curves do not have slopes, but lines
tangent to curves do.
 Notice something about curves that have peaks
and troughs:
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At the peaks and the troughs, the lines tangent at
these points have zero slope.
FIRST ORDER CONDITIONS
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Finding where the derivatives are equal to zero
constitute the first order conditions for maxima
and/or minima of functions.
SECOND ORDER CONDITIONS
If we find a candidate for a maximum or a
minimum, how do we tell?
 SOC’s help us determine if we have found a max,
a min, or something else.
 Why are we doing this when we could just graph
it?
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Multiple dimensions
 Econometric specification
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CALCULUS
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Now watch this example…after the presentation
we will slow down and learn how to use the rules
of calculus. We will have many simple examples
and lots of practice problems.
F(X)
= X3 - .25X2 – 3X + 3
F’(X)
= 3X2 – .5X - 3
F’(X)
= 3X2 – .5X - 3
At x = 1.0868 f’(x) = 0
 At x = -0.9201 f’(x) = 0
 These are called the critical values of f(x).
 Note that at 1.0868 , f(x) reaches what we call a
local minimum.
 At -0.9201, f(x) reaches a local maximum.
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F’’(X)
= 6X - .5
At x=1.08, f’’(x) = 6.0279 which is a positive
number.
 At x=-0.92, f’’(x) = - 6.0279, which is a negative
number.
 These are examples of FOC and SOC, finding a
local min and a local max.
 Note f(x) has no global max or min.
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EXAMPLES
 f(x)
=k
 f(x) = ax
 f(x) = ax2 + bx + c
 f(x) = g(x)*h(x)
 f(x) = g(h(x))
 f(x) = g(x)/h(x)
 f(x) = ln(x)
 f(x) = ex
EXAMPLES
 f(x,y)
 Now we have two derivatives
 fx and fy which are called partial
 f(x,y) = axy + by2 + c
 fx
derivatives
= ay
 fy = ax + 2by
 FOC’s involve a simultaneous system of
equations to solve:
 fx
 fy
=0
=0
F(X,Y)
= 3X2 + 2Y2
F(X,Y)
= 3X2 + 2Y2
Here, fx = 6x and fy = 4y
 At the point (0,0) both of these equations are
equal to zero.
 Thus (0,0) is a critical value and we see that (0,0)
is associated with a minimum value of our
objective function
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F(X,Y)
= 3X2 – 2Y2
F(X,Y)
= 3X2 – 2Y2
For this function there is one critical value, again
at (x,y) = (0,0).
 But note that this is not associated with a max or
a min.
 It is called a saddle point.
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GREAT NEWS
In this class (and in other econ classes you will
take) the functions you deal with will be nicely
behaved.
 By nicely behaved we mean that we can easily
find critical values.
 And these critical values will be associated with
maximum or minimum values.
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FOREST FOR TREES
 Let’s
also remember something important.
We do not want to get bogged down in the
details of mathematics and forget why we
are doing calculus in the first place!
 At our level we want to come up with
models of prescriptive (optimal) behavior
and calculus is tool we use along the way.
 Always remember … narrative reasoning
is more convincing that equations.