范里安的微观经济学现代观点的摘要（英文版）：范里安中级微观摘要

Chapter 1 1
Chapter 1
The Market
This chapter was written so I would have something to talk about on the rst
day of class,I wanted to give students an idea of what economics was all about,
and what my lectures would be like,and yet not have anything that was really
critical for the course,(At Michigan,students are still shopping around on the
rst day,and a good number of them won’t necessarily be at the lecture.)
I chose to discuss a housing market since it gives a way to describe a number
of economic ideas in very simple language and gives a good guide to what lies
ahead,In this chapter I was deliberately looking for surprising results|analytic
insights that wouldn’t arise from \just thinking" about a problem,The two
most surprising results that I presented are the condominium example and the
tax example in Section 1.6,It is worth emphasizing in class just why these results
are true,and how they illustrate the power of economic modeling.
It also makes sense to describe their limitations,Suppose that every con-
dominium conversion involved knocking out the walls and creating two apart-
ments,Then what would happen to the price of apartments? Suppose that the
condominiums attracted suburbanites who wouldn’t otherwise consider renting
an apartment,In each of these cases,the price of remaining apartments would
rise when condominium conversion took place.
The point of a simple economic model of the sort considered here is to focus
our thoughts on what the relevant e ects are,not to come to a once-and-for-all
conclusion about the urban housing market,The real insight that is o ered by
these examples is that you have to consider both the supply and the demand
side of the apartment market when you analyze the impact of this particular
policy.
The only concept that the students seem to have trouble with in this chapter
is the idea of Pareto e ciency,I usually talk about the idea a little more than
is in the book and rephrase it a few times,But then I tell them not to worry
about it too much,since we’ll look at it in great detail later in the course.
The workbook problems here are pretty straightforward,The biggest problem
is getting the students to draw the true (discontinuous) demand curve,as in
Figure 1.1,rather than just to sketch in a downward-sloping curve as in Figure
1.2,This is a good time to emphasize to the students that when they are given
numbers describing a curve,they have to use the numbers|they can’t just sketch
in any old shape.
2 Chapter Highlights
The Market
A,Example of an economic model | the market for apartments
1,models are simpli cations of reality
2,for example,assume all apartments are identical
3,some are close to the university,others are far away
4,price of outer-ring apartments is exogenous | determined outside the
model
5,price of inner-ring apartments is endogenous | determined within the
model
B,Two principles of economics
1,optimization principle | people choose actions that are in their interest
2,equilibrium principle | people’s actions must eventually be consistent
with each other
C,Constructing the demand curve
1,line up the people by willingness-to-pay,See Figure 1.1.
2,for large numbers of people,this is essentially a smooth curve as in Figure
1.2.
D,Supply curve
1,depends on time frame
2,but we’ll look at the short run | when supply of apartments is xed.
E,Equilibrium
1,when demand equals supply
2,price that clears the market
F,Comparative statics
1,how does equilibrium adjust when economic conditions change?
2,\comparative" | compare two equilibria
3,\statics" | only look at equilibria,not at adjustment
4,example | increase in supply lowers price; see Figure 1.5.
5,example | create condos which are purchased by renters; no e ect on
price; see Figure 1.6.
G,Other ways to allocate apartments
1,discriminating monopolist
2,ordinary monopolist
3,rent control
H,Comparing di erent institutions
1,need a criterion to compare how e cient these di erent allocation methods
are.
2,an allocation is Pareto e cient if there is no way to make some group
of people better o without making someone else worse o,
3,if something is not Pareto e cient,then there is some way to make some
people better o without making someone else worse o,
4,if something is not Pareto e cient,then there is some kind of \waste" in
the system.
I,Checking e ciency of di erent methods
1,free market | e cient
2,discriminating monopolist | e cient
3,ordinary monopolist | not e cient
4,rent control | not e cient
Chapter 1 3
J,Equilibrium in long run
1,supply will change
2,can examine e ciency in this context as well
4 Chapter Highlights
Chapter 2
Budget Constraint
Most of the material here is pretty straightforward,Drive home the formula
for the slope of the budget line,emphasizing the derivation on page 23,Try
some di erent notation to make sure that they see the idea of the budget line,
and don’t just memorize the formulas,In the workbook,we use a number of
di erent choices of notation for precisely this reason,It is also worth pointing
out that the slope of a line depends on the (arbitrary) choice of which variable
is plotted on the vertical axis,It is surprising how often confusion arises on this
point.
Students sometimes have problems with the idea of a numeraire good,They
understand the algebra,but they don’t understand when it would be used,One
nice example is in foreign currency exchange,If you have English pounds and
American dollars,then you can measure the total wealth that you have in either
dollars or pounds by choosing one or the other of the two goods as numeraire.
In the workbook,students sometimes get thrown in exercises where one of
the goods has a negative price,so the budget line has a positive slope,This
comes from trying to memorize formulas and gures rather than thinking about
the problem,This is a good exercise to go over in order to warn students about
the dangers of rote learning!
Budget Constraint
A,Consumer theory,consumers choose the best bundles of goods they can
a ord.
1,this is virtually the entire theory in a nutshell
2,but this theory has many surprising consequences
B,Two parts to theory
1,\can a ord" | budget constraint
2,\best" | according to consumers’ preferences
Chapter 2 5
C,What do we want to do with the theory?
1,test it | see if it is adequate to describe consumer behavior
2,predict how behavior changes as economic environment changes
3,use observed behavior to estimate underlying values
a) cost-bene t analysis
b) predicting impact of some policy
D,Consumption bundle
1,(x
1;x
2
) | how much of each good is consumed
2,(p
1;p
2
) | prices of the two goods
3,m | money the consumer has to spend
4,budget constraint,p
1
x
1
+ p
2
x
2
m
5,all (x
1;x
2
) that satisfy this constraint make up the budget set of the
consumer,See Figure 2.1.
E,Two goods
1,theory works with more than two goods,but can’t draw pictures.
2,often think of good 2 (say) as a composite good,representing money to
spend on other goods.
3,budget constraint becomes p
1
x
1
+ x
2
m.
4,money spent on good 1 (p
1
x
1
) plus the money spent on good 2 (x
2
)has
to be less than or equal to the amount available (m).
F,Budget line
1,p
1
x
1
+ p
2
x
2
= m
2,also written as x
2
= m=p
2
(p
1
=p
2
)x
1
.
3,budget line has slope of?p
1
=p
2
and vertical intercept of m=p
2
.
4,set x
1
= 0 to nd vertical intercept (m=p
2
); set x
2
= 0 to nd horizontal
intercept (m=p
1
).
5,slope of budget line measures opportunity cost of good 1 | how much of
good 2 you must give up in order to consume more of good 1.
G,Changes in budget line
1,increasing m makes parallel shift out,See Figure 2.2.
2,increasing p
1
makes budget line steeper,See Figure 2.3.
3,increasing p
2
makes budget line flatter
4,just see how intercepts change
5,multiplying all prices by t is just like dividing income by t
6,multiplying all prices and income by t doesn’t change budget line
a) \a perfectly balanced inflation doesn’t change consumption possibili-
ties"
H,The numeraire
1,can arbitrarily assign one price a value of 1 and measure other price relative
to that
2,useful when measuring relative prices; e.g.,English pounds per dollar,1987
dollars versus 1974 dollars,etc.
I,Taxes,subsidies,and rationing
1,quantity tax | tax levied on units bought,p
1
+t
2,value tax | tax levied on dollars spent,p
1
+ p
1
.Alsoknownasad
valorem tax
3,subsidies | opposite of a tax
a) p
1
s
b) (1? )p
1
6 Chapter Highlights
4,lump sum tax or subsidy | amount of tax or subsidy is independent of
the consumer’s choices,Also called a head tax or a poll tax
5,rationing | can’t consume more than a certain amount of some good
J,Example | food stamps
1,before 1979 was an ad valorem subsidy on food
a) paid a certain amount of money to get food stamps which were worth
more than they cost
b) some rationing component | could only buy a maximum amount of
food stamps
2,after 1979 got a straight lump-sum grant of food coupons,Not the same
as a pure lump-sum grant since could only spend the coupons on food.
Chapter 3 7
Chapter 3
Preferences
This chapter is more abstract and therefore needs somewhat more motivation
than the previous chapters,It might be a good idea to talk about relations in
general before introducing the particular idea of preference relations,Try the
relations of \taller," and \heavier," and \taller and heavier." Point out that
\taller and heavier" isn’t a complete relation,while the other two are,This
general discussion can motivate the general idea of preference relations.
Make sure that the students learn the speci c examples of preferences such
as perfect substitutes,perfect complements,etc,They will use these examples
many,many times in the next few weeks!
When describing the ideas of perfect substitutes,emphasize that the de ning
characteristic is that the slope of the indi erence curves is constant,not that it
is?1,In the text,I always stick with the case where the slope is?1,but in
the workbook,we often treat the general case,The same warning goes with the
perfect complements case,I work out the symmetric case in the text and try to
get the students to do the asymmetric case in the workbook.
The de nition of the marginal rate of substitution is fraught with \sign
confusion." Should the MRSbe de ned as a negative or a positive number? I’ve
chosen to give the MRSits natural sign in the book,but I warn the students that
many economists tend to speak of the MRSin terms of absolute value,Example:
diminishing marginal rate of substitution refers to a situation where the absolute
value of the MRS decreases as we move along an indi erence curve,The actual
value of the MRS (a negative number) is increasing in this movement!
Students often begin to have problems with the workbook exercises here.
The rst confusion they have is that they get mixed up about the idea that
indi erence curves measure the directions where preferences are constant,and
instead draw lines that indicate the directions that preferences are increasing.
The second problem that they have is in knowing when to draw just arbitrary
curves that qualitatively depict some behavior or other,and when to draw exact
shapes.
Try asking your students to draw their indi erence curves between ve dollar
bills and one dollar bills,O er to trade with them based on what they draw,In
addition to getting them to think,this is a good way to supplement your faculty
salary.
8 Chapter Highlights
Preferences
A,Preferences are relationships between bundles.
1,if a consumer would choose bundle (x
1;x
2
)when(y
1;y
2
) is available,then
it is natural to say that bundle (x
1;x
2
) is preferred to (y
1;y
2
)bythis
consumer.
2,preferences have to do with the entire bundle of goods,not with individual
goods.
B,Notation
1,(x
1;x
2
) (y
1;y
2
) means the x-bundle is strictly preferred to the y-
bundle
2,(x
1;x
2
) (y
1;y
2
) means that the x-bundle is regarded as indi erent to
the y-bundle
3,(x
1;x
2
) (y
1;y
2
) means the x-bundle is at least as good as (preferred
to or indi erent to) the y-bundle
C,Assumptions about preferences
1,complete | any two bundles can be compared
2,reflexive | any bundle is at least as good as itself
3,transitive | if X Y and Y Z,thenX Z
a) transitivity necessary for theory of optimal choice
D,Indi erence curves
1,graph the set of bundles that are indi erent to some bundle,See Figure
3.1.
2,indi erence curves are like contour lines on a map
3,note that indi erence curves describing two distinct levels of preference
cannot cross,See Figure 3.2.
a) proof | use transitivity
E,Examples of preferences
1,perfect substitutes,Figure 3.3.
a) red pencils and blue pencils; pints and quarts
b) constant rate of trade-o between the two goods
2,perfect complements,Figure 3.4.
a) always consumed together
b) right shoes and left shoes; co ee and cream
3,bads,Figure 3.5.
4,neutrals,Figure 3.6.
5,satiation or bliss point Figure 3.7.
F,Well-behaved preferences
1,monotonicity | more of either good is better
a) implies indi erence curves have negative slope,Figure 3.9.
2,convexity | averages are preferred to extremes,Figure 3.10.
a) slope gets flatter as you move further to right
b) example of non-convex preferences
G,Marginal rate of substitution
1,slope of the indi erence curve
2,MRS= x
2
= x
1
along an indi erence curve,Figure 3.11.
3,sign problem | natural sign is negative,since indi erence curves will
generally have negative slope
4,measures how the consumer is willing to trade o consumption of good 1
for consumption of good 2,Figure 3.12.
Chapter 3 9
5,measures marginal willingness to pay (give up)
a) not the same as how much you have to pay
b) but how much you would be willing to pay
10 Chapter Highlights
Chapter 4
Utility
In this chapter,the level of abstraction kicks up another notch,Students often
have trouble with the idea of utility,It is sometimes hard for trained economists
to sympathize with them su ciently,since it seems like such an obvious notion
to us.
Here is a way to approach the subject,Suppose that we return to the idea of
the \heavier than" relation discussed in the last chapter,Think of having a big
balance scale with two trays,You can put someone on each side of the balance
scale and see which person is heavier,but you don’t have any standardized
weights,Nevertheless you have a way to determine whether x is heavier than y.
Now suppose that you decide to establish a scale,You get a bunch of
stones,check that they are all the same weight,and then measure the weight of
individuals in stones,It is clear that x is heavier than y if x’s weight in stones
is heavier than y’s weight in stones.
Somebody else might use di erent units of measurements|kilograms,pounds,
or whatever,It doesn’t make any di erence in terms of deciding who is heavier.
At this point it is easy to draw the analogy with utility|just as pounds give
a way to represent the \heavier than" order numerically,utility gives a way
to represent the preference order numerically,Just as the units of weight are
arbitrary,so are the units of utility.
This analogy can also be used to explore the concept of a positive monotonic
transformation,a concept that students have great trouble with,Tell them that
a monotonic transformation is just like changing units of measurement in the
weight example.
However,it is also important for students to understand that nonlinear
changes of units are possible,Here is a nice example to illustrate this,Suppose
that wood is always sold in piles shaped like cubes,Think of the relation \one
pile has more wood than another." Then you can represent this relation by
looking at the measure of the sides of the piles,the surface area of the piles,or
the volume of the piles,That is,x,x
2
,orx
3
gives exactly the same comparison
between the piles,Each of these numbers is a di erent representation of the
utility of a cube of wood.
Be sure to go over carefully the examples here,The Cobb-Douglas example
is an important one,since we use it so much in the workbook,Emphasize that
it is just a nice functional form that gives convenient expressions,Be sure to
Chapter 4 11
elaborate on the idea thatx
a
1
x
b
2
is the general form for Cobb-Douglas preferences,
but various monotonic transformations (e.g.,the log) can make it look quite
di erent,It’s a good idea to calculate the MRS for a few representations of
the Cobb-Douglas utility function in class so that people can see how to do
them and,more importantly,that the MRS doesn’t change as you change the
representation of utility.
The example at the end of the chapter,on commuting behavior,is a very
nice one,If you present it right,it will convince your students that utility is an
operational concept,Talk about how the same methods can be used in marketing
surveys,surveys of college admissions,etc.
The exercises in the workbook for this chapter are very important since they
drive home the ideas,A lot of times,students think that they understand some
point,but they don’t,and these exercises will point that out to them,It is
a good idea to let the students discover for themselves that a sure- re way to
tell whether one utility function represents the same preferences as another is to
compute the two marginal rate of substitution functions,If they don’t get this
idea on their own,you can pose it as a question and lead them to the answer.
Utility
A,Two ways of viewing utility
1,old way
a) measures how \satis ed" you are
1) not operational
2) many other problems
2,new way
a) summarizes preferences
b) a utility function assigns a number to each bundle of goods so that more
preferred bundles get higher numbers
c) that is,u(x
1;x
2
) >u(y
1;y
2
) if and only if (x
1;x
2
) (y
1;y
2
)
d) only the ordering of bundles counts,so this is a theory of ordinal
utility
e) advantages
1) operational
2) gives a complete theory of demand
B,Utility functions are not unique
1,if u(x
1;x
2
) is a utility function that represents some preferences,andf( )is
any increasing function,then f(u(x
1;x
2
)) represents the same preferences
2,why? Because u(x
1;x
2
) >u(y
1;y
2
)onlyiff(u(x
1;x
2
)) >f(u(y
1;y
2
))
3,so if u(x
1;x
2
) is a utility function then any positive monotonic transfor-
mation of it is also a utility function that represents the same preferences
C,Constructing a utility function
1,can do it mechanically using the indi erence curves,Figure 4.2.
2,can do it using the \meaning" of the preferences
D,Examples
1,utility to indi erence curves
a) easy | just plot all points where the utility is constant
2,indi erence curves to utility
3,examples
a) perfect substitutes | all that matters is total number of pencils,so
u(x
1;x
2
)=x
1
+x
2
does the trick
12 Chapter Highlights
1) can use any monotonic transformation of this as well,such as
log (x
1
+x
2
)
b) perfect complements | what matters is the minimum of the left and
right shoes you have,so u(x
1;x
2
)=minfx
1;x
2
gworks
c) quasilinear preferences | indi erence curves are vertically parallel.
Figure 4.4.
1) utility function has form u(x
1;x
2
)=v(x
1
)+x
2
d) Cobb-Douglas preferences,Figure 4.5.
1) utility has form u(x
1;x
2
)=x
b
1
x
c
2
2) convenient to take transformation f(u)=u
1
b+c
and write x
b
b+c
1
x
c
b+c
2
3) or x
a
1
x
1?a
2
,wherea = b=(b+c)
E,Marginal utility
1,extra utility from some extra consumption of one of the goods,holding the
other good xed
2,this is a derivative,but a special kind of derivative | a partial derivative
3,this just means that you look at the derivative of u(x
1;x
2
) keeping x
2
xed
| treating it like a constant
4,examples
a) if u(x
1;x
2
)=x
1
+ x
2
,thenMU
1
= @u=@x
1
=1
b) if u(x
1;x
2
)=x
a
1
x
1?a
2
,thenMU
1
= @u=@x
1
= ax
a?1
1
x
1?a
2
5,note that marginal utility depends on which utility function you choose to
represent preferences
a) if you multiply utility times 2,you multiply marginal utility times 2
b) thus it is not an operational concept
c) however,MUis closely related to MRS,which is an operational concept
6,relationship between MU and MRS
a) u(x
1;x
2
)=k,wherek is a constant,describes an indi erence curve
b) we want to measure slope of indi erence curve,the MRS
c) so consider a change (dx
1;dx
2
) that keeps utility constant,Then
MU
1
dx
1
+MU
2
dx
2
=0
@u
@x
1
dx
1
+
@u
@x
2
dx
2
=0
d) hence
dx
2
dx
1
=?
MU
1
MU
2
e) so we can compute MRS from knowing the utility function
F,Example
1,take a bus or take a car to work?
2,let x
1
be the time of taking a car,y
1
be the time of taking a bus,Let x
2
be cost of car,etc.
3,suppose utility function takes linear formU(x
1;:::;x
n
)=
1
x
1
+:::+
n
x
n
4,we can observe a number of choices and use statistical techniques to
estimate the parameters
i
that best describe choices
5,one study that did this could forecast the actual choice over 93% of the
time
6,once we have the utility function we can do many things with it:
a) calculate the marginal rate of substitution between two characteristics
1) how much money would the average consumer give up in order to
get a shorter travel time?
b) forecast consumer response to proposed changes
c) estimate whether proposed change is worthwhile in a bene t-cost sense
Chapter 5 13
Chapter 5
Choice
This is the chapter where we bring it all together,Make sure that students
understand the method of maximization and don’t just memorize the various
special cases,The problems in the workbook are designed to show the futility of
memorizing special cases,but often students try it anyway.
The material in Section 5.4 is very important|I introduce it by saying \Why
should you care that the MRS equals the price ratio?" The answer is that this
allows economists to determine something about peoples’ trade-o s by observing
market prices,Thus it allows for the possibility of bene t-cost analysis.
The material in Section 5.5 on choosing taxes is the rst big non-obvious
result from using consumer theory ideas,I go over it very carefully,to make
sure that students understand the result,and emphasize how this analysis
uses the techniques that we’ve developed,Pound home the idea that the
analytic techniques of microeconomics have a big payo |they allow us to answer
questions that we wouldn’t have been able to answer without these techniques.
If you are doing a calculus-based course,be sure to spend some time on the
appendix to this chapter,Emphasize that to solve a constrained maximization
problem,you must have two equations,One equation is the constraint,and one
equation is the optimization condition,I usually work a Cobb-Douglas and a
perfect complements problem to illustrate this,In the Cobb-Douglas case,the
optimization condition is that the MRS equals the price ratio,In the perfect
complements case,the optimization condition is that the consumer chooses a
bundle at the corner.
Choice
A,Optimal choice
1,move along the budget line until preferred set doesn’t cross the budget set.
Figure 5.1.
2,note that tangency occurs at optimal point | necessary condition for
optimum,In symbols,MRS=?price ratio =?p
1
=p
2
.
a) exception | kinky tastes,Figure 5.2.
b) exception | boundary optimum,Figure 5.3.
3,tangency is not su cient,Figure 5.4.
a) unless indi erence curves are convex.
14 Chapter Highlights
b) unless optimum is interior.
4,optimal choice is demanded bundle
a) as we vary prices and income,we get demand functions.
b) want to study how optimal choice | the demanded bundle { changes
as price and income change
B,Examples
1,perfect substitutes,x
1
= m=p
1
if p
1
<p
2; 0 otherwise,Figure 5.5.
2,perfect complements,x
1
= m=(p
1
+p
2
),Figure 5.6.
3,neutrals and bads,x
1
= m=p
1
.
4,discrete goods,Figure 5.7.
a) suppose good is either consumed or not
b) then compare (1;m?p
1
)with(0;m) and see which is better.
5,concave preferences,similar to perfect substitutes,Note that tangency
doesn’t work,Figure 5.8.
6,Cobb-Douglas preferences,x
1
= am=p
1
,Note constant budget shares,a =
budget share of good 1.
C,Estimating utility function
1,examine consumption data
2,see if you can \ t" a utility function to it
3,e.g.,if income shares are more or less constant,Cobb-Douglas does a good
job
4,can use the tted utility function as guide to policy decisions
5,in real life more complicated forms are used,but basic idea is the same
D,Implications of MRS condition
1,why do we care that MRS=?price ratio?
2,if everyone faces the same prices,then everyone has the same local trade-o
between the two goods,This is independent of income and tastes.
3,since everyone locally values the trade-o the same,we can make policy
judgments,Is it worth sacri cing one good to get more of the other? Prices
serve as a guide to relative marginal valuations.
E,Application | choosing a tax,Which is better,a commodity tax or an income
tax?
1,can show an income tax is always better in the sense that given any
commodity tax,there is an income tax that makes the consumer better
o,Figure 5.9.
2,outline of argument:
a) original budget constraint,p
1
x
1
+p
2
x
2
= m
b) budget constraint with tax,(p
1
+t)x
1
+p
2
x
2
= m
c) optimal choice with tax,(p
1
+t)x
1
+ p
2
x
2
= m
d) revenue raised is tx
1
e) income tax that raises same amount of revenue leads to budget con-
straint,p
1
x
1
+ p
2
x
2
= m?tx
1
1) this line has same slope as original budget line
2) also passes through (x
1;x
2
)
3) proof,p
1
x
1
+p
2
x
2
= m?tx
1
4) this means that (x
1;x
2
) is a ordable under the income tax,so the
optimal choice under the income tax must be even better than
(x
1;x
2
)
3,caveats
a) only applies for one consumer | for each consumer there is an income
tax that is better
Chapter 5 15
b) income is exogenous | if income responds to tax,problems
c) no supply response | only looked at demand side
F,Appendix | solving for the optimal choice
1,calculus problem | constrained maximization
2,max u(x
1;x
2
)s.t.p
1
x
1
+ p
2
x
2
= m
3,method 1,write down MRS= p
1
=p
2
and budget constraint and solve.
4,method 2,substitute from constraint into objective function and solve.
5,method 3,Lagrange’s method
a) write Lagrangian,L = u(x
1;x
2
)? (p
1
x
1
+p
2
x
2
m).
b) di erentiate with respect to x
1;x
2;,
c) solve equations.
6,example 1,Cobb-Douglas problem in book
7,example 2,quasilinear preferences
a) max u(x
1
)+x
2
s.t,p
1
x
1
+ x
2
= m
b) easiest to substitute,but works each way
16 Chapter Highlights
Chapter 6
Demand
This is a very important chapter,since it uni es all the material in the
previous chapter,It is also the chapter that separates the sheep from the goats.
If the student has been paying attention for the previous 5 chapters and has been
religiously doing the homework,then it is fairly easy to handle this chapter,Alas,
I have often found that students have developed a false sense of con dence after
seeing budget constraints,drift through the discussions of preference and utility,
and come crashing down to earth at Chapter 6.
So,the rst thing to do is to get them to review the previous chapters.
Emphasize how each chapter builds on the previous chapters,and how Chapter 6
represents a culmination of this building,In turn Chapter 6 is a foundation for
further analysis,and must be mastered in order to continue.
Part of the problem is that there is a large number of new concepts in this
chapter,o er curves,demand curves,Engel curves,inferior goods,Gi en goods,
etc,A list of these ideas along with their de nitions and page references is often
helpful just for getting the concepts down pat.
If you are doing a calculus-based course,the material in the appendix on
quasilinear preferences is quite important,We will refer to this treatment later
on when we discuss consumer’s surplus,so it is a good idea to go through it
carefully now.
Students usually have a rough time with the workbook problems,In part,I
think that this is due to the fact that we have now got a critical mass of ideas,
and that it has to percolate a bit before they can start brewing some new ideas.
A few words of encouragement help a lot here,as well as drawing links with the
earlier chapters,Most students will go back on their own and see what they
missed on rst reading,if you indicate that is a good thing to do,Remember:
the point of the workbook problems is to show the students what they don’t
understand,not to give them a pat on the back,The role of the professor is to
give them a pat on the back,or a nudge in the behind,whichever seems more
appropriate.
Demand
A,Demand functions | relate prices and income to choices
Chapter 6 17
B,How do choices change as economic environment changes?
1,changes in income
a) this is a parallel shift out of the budget line
b) increase in income increases demand | normal good,Figure 6.1.
c) increase in income decreases demand | inferior good,Figure 6.2.
d) as income changes,the optimal choice moves along the income expan-
sion path
e) the relationship between the optimal choice and income,with prices
xed,is called the Engel curve,Figure 6.3.
2,changes in price
a) this is a tilt or pivot of the budget line
b) decrease in price increases demand | ordinary good,Figure 6.9.
c) decrease in price decreases demand | Gi en good,Figure 6.10.
d) as price changes the optimal choice moves along the o er curve
e) the relationship between the optimal choice and a price,with income
and the other price xed,is called the demand curve
C,Examples
1,perfect substitutes,Figure 6.12.
2,perfect complements,Figure 6.13.
3,discrete good,Figure 6.14.
a) reservation price | price where consumer is just indi erent between
consuming next unit of good and not consuming it
b) u(0;m)=u(1;m?r
1
)
c) special case,quasilinear preferences
d) v(0) +m = v(1) +m?r
1
e) assume that v(0) = 0
f) then r
1
= v(1)
g) similarly,r
2
= v(2)?v(1)
h) reservation prices just measure marginal utilities
D,Substitutes and complements
1,increase in p
2
increases demand for x
1
| substitutes
2,increase in p
2
decreases demand for x
1
| complements
E,Inverse demand curve
1,usually think of demand curve as measuring quantity as a function of price
| but can also think of price as a function of quantity
2,this is the inverse demand curve
3,same relationship,just represented di erently
18 Chapter Highlights
Chapter 7
Revealed Preference
This is a big change of pace,and usually a welcome one,The basic idea of
revealed preference,as described in Section 7.1,is a very intuitive one,All I
want to do in this chapter is give the students the tools to express that intuition
algebraically.
I think that the material in Section 7.3,on recovering preferences,is very
exciting,Start out with the idea of indirect revealed preference,as depicted in
Figure 7.2,Point out that the optimization model allows us to predict how this
person would behave when faced with a choice between (x
1;x
2
)and(z
1;z
2
),even
though we have never observed the person when faced with this choice! This is a
big idea,and a very important one,Again,drive home how the economic model
of optimization allows us to make strong predictions about behavior.
Figure 7.3 is the natural extension of this line of reasoning,Given the
idea of revealed preference,and more importantly the idea of indirect revealed
preference,we can determine the shape of underlying indi erence curves from
looking at choice data,I motivate this in terms of bene t-cost issues,but you
could also choose to think about forecasting demand for products in a marketing
survey,or similar applications.
Once students understand the idea of revealed preference,they can usually
understand the Weak Axiom right away,However,they generally have di culty
in actually checking whether the Weak Axiom is satis ed by some real numbers.
I added Section 7.5 for this reason; it just outlines one systematic way to check
WARP,The students can omit this in their rst reading,but they might want
to come back to it when they start to do the exercises,If your students know a
little computer programming,you might ask them to think about how to write
a computer program to check WARP.
The same comments go for the treatment of the Strong Axiom and checking
SARP,This is probably overkill,but I found that students couldn’t really handle
problem 7.5 in the workbook without some guidance about how to systematically
check SARP,Speaking of the workbook,the problems in this section are really
fun,I am especially fond of 7.6 and 7.7,Problem 7.9 had some wrong numbers
in it in early printings of Workouts,so people with old books should be warned.
Finally,the material on index numbers is very worthwhile,Students here
about price indices and cost-of-living indices all the time,so it’s nice to describe
the theory that lies behind these ideas.
Chapter 7 19
Revealed Preference
A,Motivation
1,up until now we’ve started with preference and then described behavior
2,revealed preference is \working backwards" | start with behavior and
describe preferences
3,recovering preferences | how to use observed choices to \estimate" the
indi erence curves
B,Basic idea
1,if (x
1;x
2
) is chosen when (y
1;y
2
) is a ordable,then we know that (x
1;x
2
)
is at least as good as (y
1;y
2
)
2,in equations,if (x
1;x
2
) is chosen when prices are (p
1;p
2
)andp
1
x
1
+p
2
x
2
p
1
y
1
+p
2
y
2
,then(x
1;x
2
) (y
1;y
2
)
3,see Figure 7.1.
4,if p
1
x
1
+ p
2
x
2
p
1
y
1
+ p
2
y
2
,wesaythat(x
1;x
2
)isdirectly revealed
preferred to (y
1;y
2
)
5,if X is directly revealed preferred to Y,andY is directly revealed preferred
to Z (etc.),then we say that X is indirectly revealed preferred to Z.
See Figure 7.2.
6,the \chains" of revealed preference can give us a lot of information about
the preferences,See Figure 7.3.
7,the information revealed about tastes by choices can be used in formulating
economic policy
C,Weak Axiom of Revealed Preference
1,recovering preferences makes sense only if consumer is actually maximizing
2,what if we observed a case like Figure 7.4.
3,in this case X is revealed preferred to Y and Y is also revealed preferred
to X!
4,in symbols,we have (x
1;x
2
) purchased at prices (p
1;p
2
)and(y
1;y
2
)
purchased at prices (q
1;q
2
)andp
1
x
1
+p
2
x
2
>p
1
y
1
+p
2
y
2
andq
1
y
1
+q
2
y
2
>
q
1
x
1
+q
2
x
2
5,this kind of behavior is inconsistent with the optimizing model of consumer
choice
6,the Weak Axiom of Revealed Preference (WARP) rules out this kind of
behavior
7,WARP,if (x
1;x
2
) is directly revealed preferred to (y
1;y
2
),then (y
1;y
2
)
cannot be directly revealed preferred to (x
1;x
2
)
8,WARP,ifp
1
x
1
+p
2
x
2
p
1
y
1
+p
2
y
2
,then it must happen thatq
1
y
1
+q
2
y
2
q
1
x
1
+q
2
x
2
9,this condition can be checked by hand or by computer
D,Strong Axiom of Revealed Preference
1,WARP is only a necessary condition for behavior to be consistent with
utility maximization
2,Strong Axiom of Revealed Preference (SARP),if (x
1;x
2
) is directly or
indirectly revealed preferred to (y
1;y
2
),then (y
1;y
2
)cannotbedirectlyor
indirectly revealed preferred to (x
1;x
2
)
3,SARP is a necessary and su cient condition for utility maximization
4,this means that if the consumer is maximizing utility,then his behavior
must be consistent with SARP
5,furthermore if his observed behavior is consistent with SARP,then we can
always nd a utility function that explains the behavior of the consumer
as maximizing behavior.
20 Chapter Highlights
6,can also be tested by a computer
E,Index numbers
1,given consumption and prices in 2 years,base year b and some other year
t
2,how does consumption in year t compare with base year consumption?
3,general form of a consumption index:
w
1
x
t
1
+w
2
x
t
2
w
1
x
b
1
+w
2
x
b
2
4,natural to use prices as weights
5,get two indices depending on whether you use period t or period b prices
6,Paasche index uses period t (current period) weights:
p
t
1
x
t
1
+p
t
2
x
t
2
p
t
1
x
b
1
+p
t
2
x
b
2
7,Laspeyres index uses period b (base period) weights:
p
b
1
x
t
1
+p
b
2
x
t
2
p
b
1
x
b
1
+p
b
2
x
b
2
8,note connection with revealed preference,if Paasche index is greater than
1,then period t must be better than period b:
a)
p
t
1
x
t
1
+p
t
2
x
t
2
p
t
1
x
b
1
+p
t
2
x
b
2
> 1
b)
p
t
1
x
t
1
+p
t
2
x
t
2
>p
t
1
x
b
1
+ p
t
2
x
b
2
c) so period t is revealed preferred to period b
9,same sort of thing can be done with Laspeyres index | if Laspeyres index
is less than 1,consumer is worse o
Chapter 8 21
Chapter 8
Slutsky Equation
Most books talk about income and substitution e ects,but then they don’t
do anything with the ideas,My view is that you have to give the student enough
of an understanding of an idea to be able to compute with it; otherwise,why
bother?
The Slutsky decomposition is an analytical tool that allows us to understand
how demand changes when a price changes,It does this by breaking the total
change in demand up into smaller pieces,The sign of the overall e ect depends
on the sign of the pieces,but the sign of the pieces is easier to determine.
I have used the Slutsky de nition of substitution e ect in this chapter,This is
because it is much easier to compute examples using this de nition,The Hicksian
de nition is theoretically more elegant,but students can’t compute with it until
they have more advanced mathematical tools.
A large part of getting this material across is just convincing the students to
read the book,The change in income necessary to compensate for a change in
price is neither a di cult concept nor a di cult calculation,but it has to be
repeated a few times before the students grasp it.
One way to describe income and substitution e ects is to give an example
based on their own consumption patterns,Talk about a student who spends all
of her allowance on food and books,Suppose that the price of books drops in
half,but her parents nd out about it and cut her allowance,How much do they
cut her allowance if they want her to keep her old consumption level a ordable?
Once they grasp the idea of the substitution and income e ect,it isn’t hard
to put them together in Section 8.4,The next real hurdle is expressing the
Slutsky equation in terms of rates of change,as is done in Section 8.5,This
is the way that we usually refer to the Slutsky equation in later chapters,so it
is worthwhile going through the algebra so they can see where it comes from.
However,if you don’t want to go through the algebraic computations,just make
sure that they get the basic point,the change in demand can be decomposed
into a substitution e ect (always negative,i.e.,opposite the direction of price
change) and an income e ect (positive or negative depending on whether we
have a normal or inferior good).
I usually skip the Optional sections in this chapter,but they are there for
reference if needed,I like the tax rebate section,but it is a little sophisticated.
Emphasize the idea that even if you give the money from the tax back to the
22 Chapter Highlights
consumers,the demand for the good will go down and consumers will be left
worse o,
Slutsky Equation
A,We want a way to decompose the e ect of a price change into \simpler" pieces.
1,that’s what analysis is all about
2,break up into simple pieces to determine behavior of whole
B,Break up price change into a pivot and a shift | see Figure 8.2.
1,these are hypothetical changes
2,we can examine each change in isolation and look at sum of two changes
C,Change in demand due to pivot is the substitution e ect.
1,this measures how demand changes when we change prices,keeping
purchasing power xed
2,how much would a person demand if he had just enough money to consume
the original bundle?
3,this isolates the pure e ect from changing the relative prices
4,substitution e ect must be negative due to revealed preference.
a) \negative" means quantity moves opposite the direction of price
D,Change in demand due to shift is the income e ect.
1,increase income,keep prices xed
2,income e ect can increase or decrease demand depending on whether we
have a normal or inferior good
E,Total change in demand is substitution e ect plus the income e ect.
1,if good is normal good,the substitution e ect and the income e ect
reinforce each other
2,if good is inferior good,total e ect is ambiguous
3,see Figure 8.3.
F,Speci c examples
1,perfect complements | Figure 8.4.
2,perfect substitutes | Figure 8.5.
3,quasilinear | Figure 8.6.
G,Application | rebating a tax
1,put a tax on gasoline and return the revenues
2,original budget constraint,px
+y
= m
3,after tax budget constraint,(p+ t)x
0
+ y
0
= m+ tx
0
4,so consumption after tax satis es px
0
+ y
0
= m
5,so (x
0;y
0
) was a ordable originally and rejected in favor of (x;y
)
6,consumer must be worse o
H,Rates of change
1,can also express Slutsky e ect in terms of rates of change
2,takes the form
@x
@p
=
@x
s
@p
@x
@m
x
3,can interpret each part just as before
Chapter 9 23
Chapter 9
Buying and Selling
The idea of an endowment is an important one,and I wanted to devote a whole
chapter to it rather than give it the cursory treatment it gets in most books,It
is somewhat unnatural in a two-good context,so it is worth pointing out to
students that arti ciality and emphasizing that the concept of an endowment
does make perfectly good sense in a more general context.
Emphasize the statement in Section 9.3 that an increase in the value of the
endowment allows for greater consumption possibilities of both goods,You’ll be
happy you did this when you discuss present value! Be sure to explain why a
consumer would necessarily prefer an endowment with higher value,while she
may or may not prefer a consumption bundle with higher value.
The section on price changes is a very nice application of revealed preference
arguments,Students often appreciate this idea a lot more after seeing these
applications.
The Slutsky equation treatment in this chapter is quite neat,but a trifle
involved,Point out that in the original treatment of the Slutsky equation money
income didn’t change when prices changed|only the purchasing power of the
money changed,In this chapter,where consumers get their money from selling
their endowments,money income does change when purchasing power changes,
and this e ect has to be accounted for.
I have found that blowing up Figure 9.7 and carefully stepping through the
movements is a big help in seeing this point,Point out that if we take away
the budget line through point C,we have the standard diagram of the previous
chapter,The movement from D to C is the only new thing that has been added
in this chapter.
If you’ve got a group that is pretty comfortable with abstraction,the
treatment in the appendix to this chapter will be of interest,It gives an exact
derivation of the Slutsky equation in this case.
Section 9.7 gives a very short example of the Slutsky equation when an endow-
ment is present,Point out how the result comes solely from the maximization
hypothesis,and how hard it would be to gure this out without some analytic
tools,That’s the point of analytic tools like the Slutsky equation,they make this
kind of calculation mechanical so that you don’t have to reproduce a complicated
path of reasoning in each particular case.
24 Chapter Highlights
The last topic in the chapter is the analysis of labor supply,The rst thing
we do is manipulate the budget constraint so it ts into the framework studied
earlier,Emphasize that this is a common strategy for analysis,arrange the
problem at hand so that it looks like something we’ve seen before,Also,it is
useful to emphasize the interpretation of the endowment in this context,the
endowment is what you end up consuming if you don’t engage in any market
transactions.
Once the labor supply problem has been put in the standard framework,we
can apply all the tools that we have at our disposal,The rst one is the Slutsky
equation.InSection9.9Igothroughamistakenanalysis,andthencorrectitto
give the right analysis,I think that this is appropriate in this case,since so many
people get the labor supply analysis wrong,A backward-bending labor supply
curve is not a Gi en phenomenon,The supply curve of labor slopes backward
because the endowment of leisure is worth more when the wage rate rises,and
this can lead to an increased consumption of leisure due to the income e ect.
The overtime example is really a dandy illustration of substitution e ects.
I sometimes introduce the idea by considering the following paradox,if an
employer increases a flat wage by some amount,and pays a higher wage for all
hours worked,his employees could easily end up choosing to work less,But if the
employer pays the same increased wage as an overtime wage,the employees will
never choose to work less,and will likely choose to work more,Isn’t it paradoxical
that giving the workers more money (via the flat wage increase) results in less
labor forthcoming? Seen in terms of substitution e ects and revealed preference,
it all makes very good sense,but without those ideas,this common phenomenon
can seem very confusing.
Buying and Selling
A,Up until now,people have only had money to exchange for goods,But in
reality,people sell things they own (e.g.,labor) to acquire goods,Want to
model this idea.
B,Net and gross demands
1,endowment:(!
1;!
2
) | what you have before you enter the market.
2,gross demands:(x
1;x
2
) | what you end up consuming.
3,net demands:(x
1
!
1;x
2
!
2
) | what you actually buy (positive) and
sell (negative).
4,for economists gross demands are more important; for laypeople net
demands are more important.
C,Budget constraint
1,value of what you consume = value of what you sell.
2,p
1
x
1
+ p
2
x
2
= p
1
!
1
+ p
2
!
2
3,p
1
(x
1
!
1
)+p
2
(x
2
!
2
)=0
4,budget line depicted in Figure 9.1,Note endowment is always a ordable.
5,with two goods,the consumer is always a net demander of one good,a net
supplier of the other.
D,Comparative statics
1,changing the endowment
a) normal and inferior
b) increasing the value of the endowment makes the consumer better o,
Note that this is di erent from increasing the value of the consumption
bundle,Need access to market.
2,changing prices
Chapter 9 25
a) if the price of a good the consumer is selling goes down,and the
consumer decides to remain a seller,then welfare goes down,See Figure
9.3.
b) if the consumer is a net buyer of a good and the price decreases,then
the consumer will remain a net buyer,Figure 9.4.
c) etc.
3,o er curves and demand curves
a) o er curves | what consumer \o ers" to buy or sell
b) gross demand curve
c) net demand curves (and net supply curves)
E,Slutsky equation
1,when prices change,we now have three e ects
a) ordinary substitution e ect
b) ordinary income e ect
c) endowment income e ect | change in the value of the endowment
a ects demand.
2,three e ects shown in Figure 9.7.
3,the income e ect depends on the net demand.
4,Slutsky equation now takes the form
@x
1
@p
1
=
@x
s
1
@p
1
+(!
1
x
1
)
@x
1
@m
5,read through proof in appendix.
F,Labor supply
G,Two goods
1,consumption (C)
2,labor (L) | maximum amount you can work is
L
3,money (M)
H,Budget constraint for labor supply
1,pC = M + wL
2,de ne
C = M=p
3,pC +w(
L?L)=p
C +w
L
4,de ne leisure R =
L?L;note
R =
L
5,pC +wR = p
C + w
R = p
C +w
L
6,this is just like ordinary budget constraint
7,supply of labor is like demand for leisure
8,w=p is price of leisure
I,Comparative statics
1,apply Slutsky equation to demand for leisure to get
@R
@w
= substitution e ect + (
R?R) income e ect
2,increase in the wage rate has an ambiguous e ect on supply of labor.
Depends on how much labor is supplied already.
3,backward bending labor supply curve
J,Overtime
1,o er workers a higher straight wage,they may work less.
2,o er them a higher overtime wage,they must work at least as much.
3,overtime is a way to get at the substitution e ect.
26 Chapter Highlights
Chapter 10
Intertemporal Choice
This is one of my favorite topics,since it uses consumer theory in such
fundamental ways,and yet has many important and practical consequences.
The intertemporal budget constraint is pretty straightforward,I sometimes
draw the kinked shape that results from di erent borrowing and lending rates,
just to drive the point home,It is good to spell out the importance of convexity
and monotonicity for intertemporal preferences,Ask your students what savings
behavior would be exhibited by a person with convex intertemporal preferences.
The di erence between the present value and the future value formulation of
the budget constraint can be seen as a choice of numeraire.
The comparative statics is simply relabeled graphs we’ve seen before,but it
is still worth describing in detail as a concrete example.
I think that it is worth repeating the conclusion of Section 10.6 several times,
as students seem to have a hard time absorbing it,An investment that shifts
the endowment in a way that increases its present value is an investment that
every consumer must prefer (as long as they can borrow and lend at the same
interest rate),It is a good idea to express this point in several di erent ways.
One especially important way is to talk explicitly about investments as changes
in the endowment ( m
1; m
2
),and then point out that any investment with a
positive net present value is worthwhile.
Emphasize that present value is really a linear operation,despite appearances.
Given a table of present values,as Table 11.1,show how easy it is to calculate
present values.
The installment loan example is a very nice one,It is good to motivate it by
rst considering a person who borrows $1,000 and then pays back $1,200 a year
later,What rate of interest is he paying? Show that this rate can be found by
solving the equation
1000(1 +r) = 1200;
which can be written as
1000 =
1200
1+r
:
Chapter 10 27
It is then very natural to argue that the monthly rate of interest for the
installment loan is given by the i that solves the equation
1000 =
100
1+i
+
100
(1 +i)
2
+:::+
100
(1 +i)
12
There are (at least) two ways to compute the yearly rate,One way is to follow
the accountant’s convention (and the Truth in Lending Act) and use the formula
r =12i,Another,perhaps more sensible,way is to compound the monthly
returns and use the formula 1 + r =(1+i)
12
,I followed the accountant’s
convention in the gures reported in the text.
The workbook problems for this chapter are also quite worthwhile,Problem
11.1 is a nice example of present value analysis,using the perpetuity formulas.
Problem 11.6 illustrates the budget constraint with di erent borrowing and
lending rates.
Intertemporal Choice
A,Budget constraint
1,(m
1;m
2
) money in each time period is endowment
2,allow the consumer to borrow and lend at rate r
3,c
2
= m
2
+(1+r)(m
1
c
1
)
4,note that this works for both borrowing and lending,as long as it is at the
same interest rate
5,various forms of the budget constraint
a) (1 +r)c
1
+ c
2
=(1+r)m
1
+m
2
| future value
b) c
1
+c
2
=(1 +r)=m
1
+m
2
=(1 + r) | present value
c) choice of numeraire
d) see Figure 10.2.
6,preferences | convexity and monotonicity are very natural
B,Comparative statics
1,if consumer is initially a lender and interest rate increases,he remains a
lender,Figure 10.4.
2,a borrower is made worse o by an increase in the interest rate,Figure
10.5.
3,Slutsky allows us to look at the e ect of increasing the price of today’s
consumption (increasing the interest rate)
a) change in consumption today when interest rate increases = substitu-
tion e ect + (m
1
c
1
) income e ect
b) assuming normality,an increase in interest rate lowers current consump-
tion for a borrower,and has an ambiguous e ect for lender
c) provide intuition
C,Inflation
1,put in prices,p
1
=1andp
2
2,budget constraint takes the form
p
2
c
2
= m
2
+(1+r)(m
1
c
1
)
3,or
c
2
=
m
2
p
2
+
(1 +r)
p
2
(m
1
c
1
)
4,if is rate of inflation,then p
2
=(1+ )p
1
5,1 + =(1+r)=(1 + ) is the real interest rate
6,=(r? )=(1 + )or r?
28 Chapter Highlights
D,Present value | a closer look
1,future value and present value | what do they mean?
2,if the consumer can borrow and lend freely,then she would always prefer
a consumption pattern with a greater present value.
E,Present value works for any number of periods.
F,Use of present value
1,the one correct way to rank investment decisions
2,linear operation,so relatively easy to calculate
G,Bonds
1,coupon x,maturity date T,face value F
2,consols
3,the value of a console is given by PV = x=r
a) proof,x = r PV
H,Installment loans
1,borrow some money and pay it back over a period of time
2,what is the true rate of interest?
3,example,borrow $1,000 and pay back 12 equal installments of $100.
4,have to value a stream of payments of 1;000,?100,:::,?100.
5,turns out that the true interest rate is about 35%!
Chapter 11 29
Chapter 11
Asset Markets
This chapter ts in very nicely with the present value calculations in the last
chapter,The idea that all riskless assets should earn the same rate of return in
equilibrium is a very powerful idea,and generally receives inadequate treatment
in intermediate micro texts.
I especially like the arbitrage argument,and showing how it is equivalent to
all assets selling for their present values,The applications of the Hotelling oil
price model and the forest management model are quite compelling to students.
One interesting twist that you might point out in the forestry problem is that
the market value of the standing forest will always be its present value,and that
present value will grow at the rate of interest|like any other asset,However,
the value of the harvested forest will grow more rapidly than the interest rate
until we reach the optimal harvest time,and then grow less rapidly.
The problems in Workouts are quite practical in nature,and it is worth
pointing this out to students,Emphasize that present value calculations are the
meat and potatoes of investment analysis.
Asset Markets
A,Consider a world of perfect certainty,Then all assets must have the same
rate of return.
1,if one asset had a higher rate of return than another,who would buy the
asset with the lower return?
2,how do asset prices adjust? Answer,Riskless arbitrage.
a) two assets,Bond earns r,other asset costs p
0
now.
b) invest $1 in bond,get 1 +r dollars tomorrow.
c) invest p
0
x = 1 dollars in other asset,get p
1
x dollars tomorrow.
d) amounts must be equal,which says that 1 + r = p
1
=p
0
.
3,this is just another way to say present value.
a) p
0
= p
1
=(1 + r).
4,think about the process of adjustment.
B,Example from stock market
1,index futures and underlying assets that make up the futures.
2,no risk in investment,even though asset values are risky,because there is
a xed relationship between the two assets at the time of expiration.
30 Chapter Highlights
C,Adjustments for di erences in characteristics
1,liquidity and transactions cost
2,taxes
3,form of returns | consumption return and nancial return
D,Applications
1,depletable resource | price of oil
a) let p
t
= price of oil at time t
b) oil in the ground is like money in the bank,so p
t+1
=(1+r)p
t
c) demand equals supply over time
d) let T = time to exhaustion,D = demand per year,and S = available
supply,Hence T = S=D
e) let C = cost of next best alternative (e.g.,liqui ed coal)
f) arbitrage implies p
0
= C=(1 +r)
T
2,harvesting a forest
a) F(t)=valueofforestattimet
b) natural to think of this increasing rapidly at rst and then slowing down
c) harvest when rate of growth of forest = rate of interest,Figure 11.1.
E,This theory tells you relationships that have to hold between asset prices,
given the interest rate.
F,But what determines the interest rate?
1,answer,aggregate borrowing and lending behavior
2,or,consumption and investment choices over time
G,What do nancial institutions do?
1,adjust interest rate so that amount people want to borrow equals amount
they want to lend
2,change pattern of consumption possible over time,Example of college
student and retiree
3,example of entrepreneur and investors
Chapter 12 31
Chapter 12
Uncertainty
This chapter begins with the idea of contingent consumption and an insurance
market example,Make sure that you de ne \contingent" since a lot of students
don’t know the term,(The de nition is given in the book.) The emphasis in
this rst section is on the idea that exactly the same tools that we have used
earlier can be used to analyze choice under uncertainty,so it is worth talking
about what happens to the budget line when the price of insurance changes,etc.
The expected utility discussion is reasonably elementary,However,it is
often hard to motivate the expected utility hypothesis without seeing a lot of
applications,I put it in since some schools might want to have an elementary
treatment of the subject for use in other courses,such as nance courses.
The easiest application of expected utility theory that I could think of was the
result that expected utility maximizers facing actuarially fair insurance would
fully insure,In the Information chapter I talk about moral hazard and adverse
selection in insurance markets,and those might be fun ideas to touch on in class
discussion.
The last three sections on diversi cation,risk spreading,and the role of the
stock market are important economic ideas,I usually discuss these ideas in
verbal terms and skip the details of the expected utility material,This seems
like a reasonable compromise for a general purpose intermediate micro course.
Uncertainty
A,Contingent consumption
1,what consumption or wealth you will get in each possible outcome of some
random event.
2,example,rain or shine,car is wrecked or not,etc.
3,consumer cares about pattern of contingent consumption,U(c
1;c
2
).
4,market allows you to trade patterns of contingent consumption | insur-
ance market,Insurance premium is like a relative price for the di erent
kinds of consumption.
5,can use standard apparatus to analyze choice of contingent consumption.
32 Chapter Highlights
B,Utility functions
1,preferences over the consumption in di erent events depend on the prob-
abilities that the events will occur.
2,so u(c
1;c
2;
1;
2
) will be the general form of the utility function.
3,under certain plausible assumptions,utility can be written as being linear
in the probabilities,p
1
u(c
1
)+p
2
u(c
2
),That is,the utility of a pattern of
consumption is just the expected utility over the possible outcomes.
C,Risk aversion
1,shape of expected utility function describes attitudes towards risk.
2,draw utility of wealth and expected utility of gamble,Note that a person
prefers a sure thing to expected value,Figure 12.2.
3,diversi cation and risk sharing
D,Role of the stock market
1,aids in diversi cation and in risk sharing.
2,just as entrepreneur can rearrange his consumption patterns through time
by going public,he can also rearrange his consumption across states of
nature.
Chapter 13 33
Chapter 13
Risky Assets
The rst part of this chapter is just notation and review of the concepts of
mean and standard deviation,If your students have had some statistics,these
ideas should be pretty standard,If they haven’t had any statistics,then be sure
to get the basics down before proceeding.
The big idea here is in Figure 13.2,In mean-standard deviation space,the
\budget constraint" is a straight line,Again,all of the technical apparatus of
consumer theory can be brought to bear on analyzing this particular kind of
choice problem,Ask what happens to the \price of risk" when the risk-free
rate goes down,What do students think this will do to the budget line and
the portfolio choice? Don’t let them guess|make them give reasons for their
statements.
Section 13.2 is a little bit of a fudge,I do give the actual de nition of beta in
a footnote,but I don’t really go through the calculations for the Capital Asset
Pricing Model.
The idea of the risk-adjusted interest rate and the story of how returns adjust
is a nice one and should be accessible to most students who understood the case
of adjustment with certainty.
It might be worth pointing out that participants in the stock market take all
this stu very seriously,There are consulting services that sell their estimates
of beta for big bucks and use them as measures of risk all the time.
Risky Assets
A,Utility depends on mean and standard deviation of wealth.
1,utility = u(
w;
w
)
2,this form of utility function describes tastes.
B,Invest in a risky portfolio (with expected return r
m
) and a riskless asset (with
return r
f
)
1,suppose you invest a fraction x in the risky asset
2,expected return = xr
m
+(1?x)r
f
3,standard deviation of return = x
m
4,this relationship gives \budget line" as in Figure 13.2.
34 Chapter Highlights
C,At optimum we must have the price of risk equal to the slope of the budget
line,MRS=(r
m
r
f
)=
m
1,the observable value (r
m
r
f
)=
m
is the price of risk
2,can be used to value other investments,like any other price
D,Measuring the risk of a stock | depends on how it contributes to the risk of
the overall portfolio.
1,
i
= covariance of asset i with the market portfolio/standard deviation of
market portfolio
2,roughly speaking,
i
measures how sensitive a particular asset is to the
market as a whole
3,assets with negative betas are worth a lot,since they reduce risk
4,how returns adjust | plot the market line
E,Equilibrium
1,the risk-adjusted rates of return should be equalized
2,in equations:
r
i
i
(r
m
r
f
)=r
j
j
(r
m
r
f
)
3,suppose asset j is riskless; then
r
i
i
(r
m
r
f
)=r
f
4,this is called the Capital Asset Pricing Model (CAPM)
F,Examples of use of CAPM
1,how returns adjust | see Figure 13.4.
2,public utility rate of return choice
3,ranking mutual funds
4,investment analysis,public and private
Chapter 14 35
Chapter 14
Consumer’s Surplus
This chapter derives consumer’s surplus using the demand theory for discrete
goods that was developed earlier in Chapters 5 and 6,I review this material in
Section 14.1 just to be safe,Given that derivation,it is easy to work backwards
to get utility.
Later in the chapter I introduce the idea of compensating and equivalent
variation,In my treatment,I use the example of a tax,but another example
that is somewhat closer to home is the idea of cost-of-living indexes for various
places to live,Take an example of an executive in New York who is o ered a job
in Tucson,Relative prices di er drastically in these two locations,How much
money would the executive need at the Tucson prices to make him as well o
as he was in New York? How much money would his New York company have
to pay him to make him as well o in New York as he would be if he moved to
Tucson?
The example right before Section 14.9 shows that the compensating and the
equivalent variation are the same in the case of quasilinear utility,Finally the
appendix to this chapter gives a calculus treatment of consumer’s surplus,along
with some calculations for a few special demand functions and a numerical com-
parison of consumer’s surplus,compensating variation,and equivalent variation.
Consumer’s Surplus
A,Basic idea of consumer’s surplus
1,want a measure of how much a person is willing to pay for something,How
much a person is willing to sacri ce of one thing to get something else.
2,price measures marginal willingness to pay,so add up over all di erent
outputs to get total willingness to pay.
3,total bene t (or gross consumer’s surplus),net consumer’s surplus,change
in consumer’s surplus,See Figure 14.1.
36 Chapter Highlights
B,Discrete demand
1,remember that the reservation prices measure the \marginal utility"
2,r
1
= v(1)?v(0),r
2
= v(2)?v(1),r
3
= v(3)?v(2),etc.
3,hence,r
1
+r
2
+r
3
= v(3)?v(0) = v(3) (since v(0) = 0)
4,this is just the total area under the demand curve.
5,in general to get the \net" utility,or net consumer’s surplus,have to
subtract the amount that the consumer has to spend to get these bene ts
C,Continuous demand,Figure 14.2.
1,suppose utility has form v(x)+y
2,then inverse demand curve has form p(x)=v
0
(x)
3,by fundamental theorem of calculus:
v(x)?v(0) =
Z
x
0
v
0
(t)dt =
Z
x
0
p(t)dt
4,This is the generalization of discrete argument
D,Change in consumer’s surplus,Figure 14.3.
E,Producer’s surplus | area above supply curve,Change in producer’s surplus
1,see Figure 14.6.
2,intuitive interpretation,the sum of the marginal willingnesses to supply
F,This all works ne in the case of quasilinear utility,but what do you do in
general?
G,Compensating and equivalent variation,See Figure 14.4.
1,compensating,how much extra money would you need after a price change
to be as well o as you were before the price change?
2,equivalent,how much extra money would you need before the price change
to be just as well o as you would be after the price change?
3,in the case of quasilinear utility,these two numbers are just equal to the
change in consumer’s surplus.
4,in general,they are di erent,::but the change in consumer’s surplus is
usually a good approximation to them.
Chapter 15 37
Chapter 15
Market Demand
It would be logical to proceed directly to discussing the theory of the rm,but
I wanted to take a break from pure optimization analysis,and discuss instead
some ideas from equilibrium analysis,I think that this switch of gears helps
students to see where they are going and why all this stu is useful.
The most important idea in this chapter is elasticity,Elasticity was introduced
earlier in Chapter 6,but I never did anything much with it there,Here we can
really put it through its paces,The calculations here are all pretty standard,but
I’m more careful than usual to distinguish between elasticity and the absolute
value of elasticity.
If you use calculus,make sure that you compute elasticities for the linear and
log-linear cases.
I love the La er curve example in the appendix,Here are some totally trivial
elasticity calculations that give a major insight into a big policy issue,I really
push on this example in class to show people how what they have learned can
really help in making informed judgments about policy.
Market Demand
A,To get market demand,just add up individual demands.
1,add horizontally
2,properly account for zero demands; Figure 15.2.
B,Often think of market behaving like a single individual.
1,representative consumer model
2,not true in general,but reasonable assumption for this course
C,Inverse of aggregate demand curve measures the MRS for each individual.
D,Reservation price model
1,appropriate when one good comes in large discrete units
2,reservation price is price that just makes a person indi erent
3,de ned by u(0;m)=u(1;m?p
1
)
4,see Figure 15.3.
5,add up demand curves to get aggregate demand curve
38 Chapter Highlights
E,Elasticity
1,measures responsiveness of demand to price
2.
=
p
q
dq
dp
3,example for linear demand curve
a) for linear demand,q = a?bp,so =?bp=q =?bp=(a?bp)
b) note that =?1 when we are halfway down the demand curve
c) see Figure 15.4.
4,suppose demand takes form q = Ap
b
5,then elasticity is given by
=?
p
q
bAp
b?1
=
bAp
b
Ap
b
=?b
6,thus elasticity is constant along this demand curve
7,note that logq =logA?blogp
8,what does elasticity depend on? In general how many and how close
substitutes a good has.
F,How does revenue change when you change price?
1,R = pq,so R =(p +dp)(q + dq)?pq = pdq +qdp+ dpdq
2,last term is very small relative to others
3,dR=dp= q +pdq=dp
4,see Figure 15.5.
5,dR=dp> 0whenjej< 1
G,How does revenue change as you change quantity?
1,marginal revenue = MR= dR=dq = p +qdp=dq= p[1 + 1= ].
2,elastic,absolute value of elasticity greater than 1
3,inelastic,absolute value of elasticity less than 1
4,application,Monopolist never sets a price wherej j< 1 | because it could
always make more money by reducing output.
H,Marginal revenue curve
1,always the case that dR=dq = p+qdp=dq.
2,in case of linear (inverse) demand,p = a?bq,MR = dR=dq = p?bq =
(a?bq)?bq = a?2bq.
I,La er curve
1,how does tax revenue respond to changes in tax rates?
2,idea of La er curve,Figure 15.8.
3,theory is OK,but what do the magnitudes have to be?
4,model of labor market,Figure 15.9.
5,tax revenue = T = t wS(w(t)) where w(t)=(1?t) w
6,when is dT=dt< 0?
7,calculate derivative to nd that La er curve will have negative slope when
dS
dw
w
S
>
1?t
t
8,so if tax rate is,50,would need labor supply elasticity greater than 1 to
get La er e ect
9,very unlikely to see magnitude this large
Chapter 16 39
Chapter 16
Equilibrium
Some people have suggested that it would make more sense to save this
chapter until after deriving supply curves,but I still feel that it is in a better
position here,After all,the students have seen labor supply curves and net
supply curves earlier in the course,and it isn’t any shock to see demand and
supply treated together now.
The rst part of the chapter is pretty standard,although I go to extra pains
to be clear to emphasize the idea of the inverse demand and supply curves,I tell
the students that the inverse functions describe the same relationship,but just
from a di erent viewpoint.
The treatment of taxes is more thorough than is usually the case,I like
the idea of looking at taxation in several di erent ways,It is a good idea to
emphasize that there are really four di erent variables in a taxation problem:
the demand price p
d
,the supply price p
s
,the amount demanded q
d
,andthe
amount supplied q
s
,When confronted with a tax problem,the rst thing you
should do is write down the relationships between these four variables.
The most typical set of relationships is
p
d
= p
s
+t
q
d
= q
s
But other relationships are possible,For example,if a tax-in-kind is levied,
as in the King Kanuta problem in the workbook,then the amount demanded
will be di erent than the amount supplied,In fact the only systematic way to
work out the King Kanuta problem is to be very careful about writing down the
relationships among the four variables.
You should emphasize that the incidence of the tax doesn’t depend on the
legal requirements of who is responsible for paying the tax,The Social Security
tax is a really nice example for this,The Social Security tax is based on 15% of
the nominal wage,The employer \pays" half of the tax and the worker \pays"
the other half,But of course,this is a ction,Show the students how we could
rede ne the nominal wage so that the worker paid all the tax or the employer
paid all the tax,and leave the take-home pay of the worker unchanged.
This leads naturally to a discussion of the real incidence of a tax,the ideas
of \passing along a tax," and so on.
40 Chapter Highlights
I like to use the old red pencil/blue pencil example at this point,If red pencils
and blue pencils are perfect substitutes in consumption and production,what is
the impact of a tax on red pencils? There is a big output e ect|consumption
and production of red pencils would drop to zero,But what is the e ect on
consumer utility and producer pro ts? Zero|consumers and producers just
substitute to other activities,This leads naturally to the idea of measuring the
impact of a tax via consumer and producer surplus,as is done in Section 16.8.
The two examples that end the chapter,the market for loans and the food
subsidies,are really wonderful examples and deserve careful discussion,I like to
point out to the students how confused they would be in trying to understand
these examples without the analytic methods of economics.
Equilibrium
A,Supply curves | measure amount the supplier wants to supply at each price
1,review idea of net supply from Chapter 9
B,Equilibrium
1,competitive market | each agent takes prices as outside his or her control
a) many small agents
b) a few agents who think that the others keep xed prices
2,equilibrium price | that price where desired demand equals desired supply
a) D(p)=S(p)
3,special cases | Figure 16.1.
a) vertical supply | quantity determined by supply,price determined by
demand
b) horizontal supply | quantity determined by demand,price determined
by supply
4,an equivalent de nition of equilibrium,where inverse demand curve crosses
inverse supply curve
a) P
d
(q)=P
s
(q)
5,examples with linear curves
C,Comparative statics
1,shift each curve separately
2,shift both curves together
D,Taxes | nice example of comparative statics
1,demand price and supply price | di erent in case of taxes
2,p
d
= p
s
+t
3,equilibrium happens when D(p
d
)=S(p
s
)
4,put equations together:
a) D(p
s
+ t)=S(p
s
)
b) or D(p
d
)=S(p
d
t)
5,also can solve using inverse demands:
a) P
d
(q)=P
s
(q)+t
b) or P
d
(q)?t = P
s
(q)
6,see Figure 16.3,and Figure 16.4.
E,Passing along a tax | Figure 16.5.
1,flat supply curve
2,vertical supply curve
Chapter 16 41
F,Deadweight loss of a tax | Figure 16.7.
1,bene ts to consumers
2,bene ts to producers
3,value of lost output
G,Market for loans
1,tax system subsidizes borrowing,tax lending
2,with no tax,D(r
)=S(r
)
3,with tax,D((1?t)r
0
)=S((1?t)r
0
)
4,hence,(1?t)r
0
= r
,Quantity transacted is same
5,see Figure 16.8.
H,Food subsidies
1,buy up harvest and resell at half price.
2,before program,D(p
)+K = S
3,after program,D(^p=2) +K = S
4,so,^p =2p
.
5,subsidized mortgages | unless the housing stock changes,no e ect on
cost.
I,Pareto e ciency
1,e cient output is where demand equals supply
2,because that is where demand price equals supply price.
3,that is,the marginal willingness to buy equals the marginal willingness to
sell.
4,deadweight loss measures loss due to ine ciency.
42 Chapter Highlights
Chapter 17
Auctions
This is a fun chapter,since it brings in some real-life examples and non-
obvious points about a widely-used form of market,The classi cation is
straightforward,but it would be good to ask the students for examples of
common-value and private-value auctions,(If there is a resale market,the
distinction may be a bit blurred.) You might talk about online auctions like
eBay.
The bidding rules are pretty straightforward as well,The interesting part
is the section on auction design,which deserves some careful treatment,It
is useful to describe the source of ine ciency in the pro t-maximization case.
Essentially the pro t-maximizing monopoly seller restricts expected output,just
as the ordinary monopolist restricts actual output.
The Vickrey auction argument is very nice|a little bit abstract,but not too
hard to prove.
It is worth going over the bidding ring example in Chapter 24 here,just to
show how collusion can work.
Finally the Winner’s Curse is a nice story,I know one person who auctions
o a jar of pennies,which is a nice common-value auction,He always makes
money on the auction,a good example of the winner’s curse!
Auctions
A,Auctions are one of the oldest form of markets
1,500 BC in Babylon
2,1970s o shore oil
3,1990s FCC airwave auctions
4,various privatization projects
B,Classi cation of auctions
1,private-value auctions
2,common-value auctions
C,Bidding rules
1,English auction,reserve price,bid increment
2,Dutch auction
3,sealed-bid auction
4,Vickrey auction (philatelist auction,second-price auction)
Chapter 17 43
D,Auction design
1,special case of economic mechanism design
2,possible goals
a) Pareto e ciency
b) pro t maximization
3,Pareto e ciency in private value auction
a) person who values the good most highly gets it
b) otherwise would be Pareto improvement possible
4,Case 1,seller knows values v
1;:::;v
n
a) trivial answer,set price at highest value
b) this is Pareto e cient
5,Case 2,seller doesn’t know value
a) run English auction
b) person with highest value gets the good
c) Pareto e cient
d) pays price equal to second-highest value
6,pro t maximization in private-value auctions
a) depends on sellers’ beliefs about buyers’ values
b) example,2 bidders with values of either $10 or $100
c) assume equally likely so possibilities are (10,10),(10,100),(100,10),or
(100,100)
d) minimal bid increment of $1,flip a coin for ties
e) revenue will be (10,11,11,100)
f) expected revenue will be $33
g) is this the best the seller can do?
h) No! If he sets a reserve price of $100 he gets (0,100,100,100)
i) expected pro t is $75 which is much better
j) not Pareto e cient
7,Dutch auction,sealed-bid auction
a) might not be Pareto e cient
8,Vickrey auction
a) if everyone reveals true value will be e cient
b) but will they want to tell the truth?
c) Yes! Look at special case of two buyers
d) payo = Prob(b
1
b
2
)[v
1
b
2
]
e) if v
1
>b
2
,want to make probability = 1
f) if v
1
<b
2
,want to make probability = 0
g) it pays to tell the truth (in this case)
h) note that this is essentially the same outcome as English auction
E,Problems with auctions
1,susceptible to collusion (bidding rings)
2,dropping out (Australian satellite-TV licenses)
F,Winner’s curse
1,common value auction
2,assume that each person bids estimated value
3,then most optimistic bidder wins
4,but this is almost certainly an overestimate of value
5,optimal strategy is to adjust bid downward
6,amount that you adjust down depends on number of other bidders
44 Chapter Highlights
Chapter 18
Technology
Here we start our discussion of rm behavior,This chapter discusses the
concepts that economists use to describe technologies,Almost all of the material
here is quite straightforward,especially given all of the exposure that the students
have had to indi erence curves,utility functions,etc.
Since students are by now quite familiar with Cobb-Douglas utility functions,
you should be sure to emphasize that monotonic transformations are no longer
warranted,since now the value of the production function represents some real,
physical amount of output,Of course,you could choose to measure the output
in di erent units,in which case the parameters of the production function would
change,But given the units of measurement,we don’t have any choice about
how to measure production.
The new ideas are the ideas of the short and long runs,and the idea of returns
to scale,These ideas will show up several times in the next few chapters,so the
initial discussion is rather brief,In the workbook we give several examples of
technologies and ask about their return-to-scale properties,It’s a good idea to
work one or two examples to show the students what is going on.
Technology
A,Need a way to describe the technological constraints facing a rm
1,what patterns of inputs and outputs are feasible?
B,Inputs
1,factors of production
2,classi cations,labor,land,raw materials,capital
3,usually try to measure in flows
4,nancial capital vs,physical capital
Chapter 18 45
C,Describing technological constraints
1,production set | combinations of inputs and outputs that are feasible
patterns of production
2,production function | upper boundary of production set
3,see Figure 18.1.
4,isoquants | all combinations of inputs that produce a constant level of
output
5,isoquants (constant output) are just like indi erence curves (constant
utility)
D,Examples of isoquants
1,xed proportions | one man,one shovel
2,perfect substitutes | pencils
3,Cobb-Douglas | y = Ax
a
1
x
b
2
4,can’t take monotonic transformations any more!
E,Well-behaved technologies
1,monotonic | more inputs produce more output
2,convex | averages produce more than extremes
F,Marginal product
1,MP
1
is how much extra output you get from increasing the input of good
1
2,holding good 2 xed
3,MP
1
= @f(x
1;x
2
)=@x
1
G,Technical rate of substitution
1,like the marginal rate of substitution
2,given by the ratio of marginal products
3.
TRS=
dx
2
dx
1
=?
@f=@x
1
@f=@x
2
H,Diminishing marginal product
1,more and more of a single input produces more output,but at a decreasing
rate,See Figure 18.5.
2,law of diminishing returns
I,Diminishing technical rate of substitution
1,equivalent to convexity
2,note di erence between diminishing MP and diminishing TRS
J,Long run and short run
1,All factors varied | long run
2,Some factors xed | short run
K,Returns to scale
1,constant returns | baseline case
2,increasing returns
3,decreasing returns
46 Chapter Highlights
Chapter 19
Profit Maximization
I start out the chapter with a careful de nition of pro ts,you must value
each output and input at its market price,whether or not the good is actually
sold on a market,This is because the market price measures the price at which
you could sell the input,and thus measures the true opportunity cost of using
the factor in this production process rather than in some other use.
I give some commonplace examples of this idea,but more examples won’t
hurt,It’s good to get this idea across carefully now,since it will make it much
easier to discuss the idea of zero long-run pro ts when it comes up,This idea
is usually a stumbling block for students,and a careful examination about just
what it is that goes into the de nition of economic pro ts helps a lot in getting
the point across.
The material on stock market value is something that is left out of most texts,
but since we have had a careful discussion of asset markets,we can draw the link
between maximizing pro ts and maximizing stock market value.
The rest of the material in the chapter is fairly standard,The one novel
feature is the revealed pro tability approach to rm behavior,This section,
Section 18.10,shows how you can use the fact that the rm is maximizing pro ts
to derive comparative statics conclusions,If you have treated revealed preference
in consumption carefully,students should have no trouble with this approach.
Pro t Maximization
A,Pro ts de ned to be revenues minus costs
1,value each output and input at its market price | even if it is not sold on
amarket.
2,it could be sold,so using it in production rather than somewhere else is
an opportunity cost.
3,measure in terms of flows,In general,maximize present value of flow of
pro ts.
Chapter 19 47
B,Stock market value
1,in world of certainty,stock market value equals present value of stream of
pro ts
2,so maximizing stock market value is the same as maximizing present value
of pro ts
3,uncertainty | more complicated,but still works
C,Short-run and long-run maximization
1,xed factors | plant and equipment
2,quasi- xed factors | can be eliminated if operate at zero output (adver-
tising,lights,heat,etc.)
D,Short-run pro t maximization,Figure 19.1.
1,max pf(x)?wx
2,pf
0
(x
)?w =0
3,in words,the value of the marginal product equals wage rate
4,comparative statics,change w and p and see how x and f(x)respond
E,Long-run pro t maximization
1,p@f=@x
1
= w
1
,p@f=@x
2
= w
2
F,Pro t maximization and returns to scale
1,constant returns to scale implies pro ts are zero
a) note that this doesn’t mean that economic factors aren’t all appropri-
ately rewarded
b) use examples
2,increasing returns to scale implies competitive model doesn’t make sense
G,revealed pro tability
1,simple,rigorous way to do comparative statics
2,observe two choices,at time t and time s
3,(p
t;w
t;y
t;x
t
)and(p
s;w
s;y
s;x
s
)
4,if rm is pro t maximizing,then must have
p
t
y
t
w
t
x
t
p
t
y
s
w
t
x
s
p
s
y
s
w
s
x
s
p
s
y
t
w
s
x
t
5,write these equations as
p
t
y
t
w
t
x
t
p
t
y
s
w
t
x
s
p
s
y
t
+w
s
x
t
p
s
y
s
+ w
s
x
s
6,add these two inequalities:
(p
t
p
s
)y
t
(w
t
w
s
)x
t
(p
t
p
s
)y
s
(w
t
w
s
)x
s
7,rearrange:
(p
t
p
s
)(y
t
y
s
)?(w
t
w
s
)(x
t
x
s
) 0
8,or
p y? w x 0
9,implications for changing output and factor prices
48 Chapter Highlights
Chapter 20
Cost Minimization
The treatment in this chapter is pretty standard,except for the material on
revealed cost minimization,However,by now the students have seen this kind
of material three times,so they shouldn’t have much di culty with it.
It is worthwhile emphasizing the di erence between the unconditional factor
demand functions of Chapter 18 and the conditional factor demand functions of
Chapter 19,Here we are looking at the best input choice holding the physical
level of output xed,In Chapter 18 we looked for the best input choice holding
the price of output xed,where the level of output is adjusted to its most
pro table level.
The material on returns to scale and the cost function is important to get
across,as we will refer in future chapters to cases of increasing average cost,
decreasing average cost,etc,It is important to be able to link these ideas to the
returns-to-scale ideas discussed in earlier chapters.
The material in Sections 19.4 and 19.5 lays the groundwork for ideas that
will be further explored in the next chapter,Both sections are just exploring
various de nitions,Section 19.4 will be used in discussing the shapes of short-
run and long-run cost curves,Section 19.5 will be used to distinguish between
two di erent concepts of xed costs in the short and long runs.
Cost Minimization
A,Cost minimization problem
1,minimize cost to produce some given level of output:
min
x
1;x
2
w
1
x
1
+ w
2
x
2
s.t,f(x
1;x
2
)=y
2,geometric solution,slope of isoquant equals slope of isocost curve,Figure
20.1.
3,equation is,w
1
=w
2
= MP
1
=MP
2
4,optimal choices of factors are the conditional factor demand functions
5,optimal cost is the cost function
6,examples
Chapter 20 49
a) if f(x
1;x
2
)=x
1
+ x
2
,thenc(w
1;w
2;y)=minfw
1;w
2
gy
b) if f(x
1;x
2
)=minfx
1;x
2
g,thenc(w
1;w
2;y)=(w
1
+w
2
)y
c) can calculate other answers using calculus
B,Revealed cost minimization
1,suppose we hold output xed and observe choices at di erent factor prices.
2,when prices are (w
s
1;w
s
2
),choice is (x
s
1;x
s
2
),and when prices are (w
t
1;w
t
2
),
choice is (x
t
1;x
t
2
).
3,if choices minimize cost,then we must have
w
t
1
x
t
1
+ w
t
2
x
t
2
w
t
1
x
s
1
+ w
t
1
x
s
2
w
s
1
x
s
1
+w
s
1
x
s
2
w
s
1
x
t
1
+w
s
2
x
t
2
4,this is the Weak Axiom of Cost Minimization (WACM)
5,what does it imply about rm behavior?
6,multiply the second equation by?1andget
w
t
1
x
t
1
+ w
t
2
x
t
2
w
t
1
x
s
1
+ w
t
1
x
s
2
w
s
1
x
t
1
w
s
1
x
t
2
w
s
1
x
s
1
w
s
2
x
s
2
7,add these two inequalites:
(w
t
1
w
s
1
)(x
t
1
x
s
1
)+(w
t
2
w
s
2
)(x
t
1
x
s
1
) 0
w
1
x
1
+ w
2
x
2
0
8,roughly speaking,\factor demands move opposite to changes in factor
prices"
9,in particular,factor demand curves must slope downward.
C,Returns to scale and the cost function
1,increasing returns to scale implies decreasing AC
2,constant returns implies constant AC
3,decreasing returns implies increasing AC
D,Long-run and short-run costs
1,long run,all inputs variable
2,short run,some inputs xed
E,Fixed and quasi- xed costs
1,xed,must be paid,whatever the output level
2,quasi- xed,only paid when output is positive (heating,lighting,etc.)
50 Chapter Highlights
Chapter 21
Cost Curves
Now we get to the standard meat and potatoes of undergraduate microeco-
nomics,The rst section lays out the rationale behind U-shaped average cost
curves,To me the most natural rationale is constant xed costs and increasing
average variable costs.
The link between marginal costs and variable costs is left out of a lot of books,
but is important for understanding producer’s surplus.
I am very keen on the cost function c(y)=y
2
+ 1,and use it in a lot of the
examples,Be sure to go over its derivation and show how it gives rise to the
various cost curves.
The material on how to get the long-run cost curve from the short-run cost
curve is pretty straightforward,It may be a little easier to rst do Section 20.5,
and then draw in a lot of extra short-run curves to get to the diagram in Figure
20.7.
Cost Curves
A,Family of cost curves
1,total cost,c(y)=c
v
(y)+F
2.
c(y)
y
=
c
v
(y)
y
+
F
y
AC = AVC +AFC
3,see Figure 21.1.
4,marginal cost is the change in cost due to change in output c
0
(y)=
dc(y)=dy = dc
v
(y)=dy
a) marginal cost equals AVC at zero units of output
b) goes through minimum point of AC and AVC,Figure 21.2.
1)
d
dy
c(y)
y
=
yc
0
(y)?c(y)
y
2
2) this is negative (for example) when c
0
(y) <c(y)=y
Chapter 21 51
c) fundamental theorem of calculus implies that
c
v
(y)=
Z
y
0
c
0
(t)dt
d) geometrically,the area under the marginal cost curve gives the total
variable costs,Figure 21.3.
e) intuitively,the maginal cost curve measures the cost of each additional
unit,so adding up the MCs gives the variable cost
B,Example,c(y)=y
2
+1
1,AC = y +1=y
2,AVC = y
3,MC=2y
4,Figure 21.4.
C,Long-run cost from short-run cost
1,average costs,Figure 21.8.
2,marginal costs,Figure 21.9.
52 Chapter Highlights
Chapter 22
Firm Supply
After all that material on technology and optimization problems,it is fun to
get back to the behavior of \real" economic units,I devote a fair amount of
time to laying out the idea of a purely competitive market,It is important to
distinguish between the de nition of a competitive market and the rationale for
that de nition,The de nition is that it is a market where rms take the market
price as being given,independent of the actions of any particular rm,The usual
rationale for this assumption is that each rm is a negligible part of the market.
However,it is also important to emphasize that even markets with a middling
number of rms may act in a reasonably competitive fashion,For example,if
each rm believes that the other rms will keep their prices xed no matter what
price it charges,we have a model where each rm faces a demand curve for its
product that is essentially flat,This idea|the distinction between the market
demand curve and the demand curve facing a rm|is an important one to get
across,Economists often talk about a quantity-setting rm or a price-setting
rm,but these ideas are really rather unnatural,Real rms set both variables.
But a rm in a highly competitive market has no real choice about what price
to set|it has to meet the price at which everyone else is selling if it wants to
make any sales at all,For a competitive rm,the only real choice variable is
how much it wants to sell at the going market price.
Firm Supply
A,Firms face two sorts of constraints
1,technological constraints | summarize in cost function
2,market constraints | how will consumers and other rms react to a given
rm’s choice?
B,Pure competition
1,formally | takes market price as given,outside of any particular rm’s
control
2,example,many small price takers
3,demand curve facing a competitive rm | Figure 22.1.
Chapter 22 53
C,Supply decision of competitive rm
1,max
y
py?c(y)
2,rst-order condition,p = c
0
(y)
3,price equals marginal cost determines supply as function of price
4,second-order condition,?c
00
(y) 0,or c
0
(y) 0.
5,only upward-sloping part of marginal cost curve matters
6,is it pro table to operate at all?
a) compare py?c
v
(y)?F with?F
b) pro ts from operating will be greater when p>c
v
(y)=y
c) operate when price covers average variable costs
D,So supply curve is the upward-sloping part of MC curve that lies above the
AVC curve
1,see Figure 22.3.
E,Inverse supply curve
1,p = c
0
(y) measures the marginal cost curve directly
F,Example,c(y)=y
2
+1
1,p =2y gives the (inverse) supply curve
2,is p AVC?
a) yes,since 2y y for all y 0
3,see Figure 22.7.
G,Producer’s surplus
1,producer’s surplus is de ned to be py?c
v
(y)
2,since c
v
(y) = area under marginal cost curve
3,producer’s surplus is also the area above the marginal cost curve
4,we can also use the \rectangle" for part of PS and the \area above MC"
for the rest
5,see Figure 22.5.
H,Long-run supply | use long-run MC,In long run,price must be greater
than AC
I,Special case | constant average cost (CRS),flat supply curve
1,see Figure 22.10.
54 Chapter Highlights
Chapter 23
Industry Supply
The treatment of industry supply in the case of free entry given in this chapter
is more satisfactory than that one usually sees,I simply draw the supply curves
for di erent numbers of rms and look for the lowest intersection that allows
for nonnegative pro ts,After drawing a few examples of this sort,students are
quite ready to believe that the equilibrium price can never get very far above
minimum average cost,This naturally leads to the standard approximation of
taking the supply curve of a competitive industry as being flat at price equals
minimum average cost.
The idea that long-run pro ts are zero in Sections 22.4 and 22.5 is a very
important one,and often misunderstood,Be sure to emphasize the exact sense
in which it is true.
The other big idea in this chapter is the idea of economic rent,I like to
express the relationship between the two ideas this way:
Long-run pro ts in competitive industries are always zero,If there are
no barriers to entry,then entry competes pro ts away to zero,If there
are speci c factors that prevent entry,then competition to acquire those
factors forces pro ts to zero,In a sense,it is always the attempt to enter
an industry that forces pro ts to zero,new rms either enter an industry
by adding rms to the industry or by buying out existing rms,The rst
form of entry increases supply and decreases prices; the second form of
entry doesn’t a ect supply,but simply pushes up the factor prices and
costs,But either way,pro ts get driven to zero.
I like the discussion of economic rent and the politics of rent quite a bit,One
great example of rent seeking is to discuss the social costs of theft,It’s not the
transfer of property that represents a social loss; it’s all the expense that one
hastogototo prevent theft that represents the social loss,The true social cost
of theft is not the lost TVs,but the cost of the locks on the doors! If students
appreciate the insight in this sentence,they are well on their way to becoming
real economists,(If they don’t appreciate the insight,they’ll just think you’re
nuts.)
Finally,the treatment of energy policy in Section 22.10 is a lot of fun,The
students really begin to appreciate why marginal cost is important after they see
this example.
Chapter 23 55
Industry Supply
A,Short-run industry supply
1,sum of the MC curves
2,equilibrium in short run
a) look for point where D(p)=S(p)
b) can then measure pro ts of rms
c) see Figure 23.2.
B,Long-run industry supply
1,change to long-run technology
2,entry and exit by rms
a) look at curves with di erent number of rms
b) nd lowest curve consistent with nonnegative pro ts
c) see Figure 23.3.
C,Long-run supply curve
1,exact | see Figure 23.4.
2,approximate | flat at p = minimum AC
3,like replication argument
D,Taxation in long and short runs
1,see Figure 23.6.
2,in industry with entry and exit
3,part of tax is borne by each side
4,long run | all borne by consumers
E,Meaning of zero pro ts
1,pure economic pro t means anyone can get it
2,a mature industry may show accounting pro ts,but economic pro ts are
probably zero
F,Economic rent
1,what if some factors are scarce in the long run?
a) licenses | liquor,taxicab
b) raw materials,land,etc.
2,xed from viewpoint of industry,variable from viewpoint of rm
3,in this case,industry can only support a certain number of rms
4,whatever factor is preventing entry earns rents
a) always the possibility of entry that drives pro ts to zero
b) if pro ts are being made,rms enter industry by
1) bringing in new resources
2) bidding up prices of existing resources
5,see Figure 23.7.
6,discount flow of rents to get asset value
7,politics of rent
a) rents are a pure surplus payment
b) but people compete for those rents
c) taxicab licenses | current holders want very much to prevent entry
d) subsidies and rents | incidence of subsidy falls on the rents
1) tobacco subsidies
2) farm policy in general
e) rent seeking
56 Chapter Highlights
G,Energy policy
1,two-tiered oil pricing
2,price controls
3,entitlement program
Chapter 24 57
Chapter 24
Monopoly
This chapter discusses the theory of monopoly and compares it with that of
competition,The big idea here is the ine ciency of monopoly,The rst way
to drive it home is to use the fundamental de nition of Pareto improvement:
whenever price exceeds marginal cost,there must be a whole set of transactions
that are Pareto improving,The second way is to add up the consumer and
producer surpluses to measure the deadweight loss of monopoly.
The example of an optimal patent life is a nice way to illustrate why society
might want to allow certain kinds of monopolies,I often talk about the current
hot topic of software manufacturers wanting to protect the \look and feel" of
their software.
Monopoly
A,Pro t maximization
1,max r(y)?c(y) implies r
0
(y)=c
0
(y)
2,max p(y)y?c(y) implies p(y)+p
0
(y)y = c
0
(y)
3,can also write this as
p(y)
1+
dp
dy
y
p
= c
0
(y)
4,or p(y)[1 + 1= ]=c
0
(y)
5,linear case
a) in case of linear demand,p = a?by,marginal revenue is given by
MR= a?2by
b) see Figure 24.1.
6,constant elasticity,q = Ap
a) in this case,MR= p[1 + 1= ]
b) so,optimal condition is p[1 + 1= ]=c
0
(y)
c) markup on marginal cost
d) see Figure 24.2.
B,Taxes
1,linear case | price goes up by half of tax,Figure 24.3.
2,log case | price goes up by more than tax,since price is a markup on MC
58 Chapter Highlights
C,Ine ciency of monopoly
1,Pareto e cient means no way to make some group better o without
hurting some other group
2,Pareto ine cient means that there is some way to make some group better
o without hurting some other group
3,monopoly is Pareto ine cient since P>MC
4,measure of the deadweight loss | value of lost output
5,see Figure 24.5.
D,Patents
1,sometimes we want to pay this cost of ine ciency
2,patents,trade-o of innovation against monopoly losses
E,Natural monopoly
1,public utilities (gas,electricity,telephone) are often thought of as natural
monopolies
2,occurs when p = mc is unpro table | decreasing AC
3,Figure 24.6.
4,often occurs when xed costs are big and marginal costs are small
5,how to handle
a) government operates and covers de cit from general revenues
b) regulates pricing behavior so that price = AC
F,Cause of monopoly
1,MES large relative to size of market
2,collusion
3,law (oranges,sports,etc.)
4,trademarks,copyrights,brand names,etc.
Chapter 25 59
Chapter 25
Monopoly Behavior
This chapter is concerned with price discrimination,product di erentiation,
monopolistic competition,and the like.
Price discrimination is a great topic for discussion,It is good to bring up
examples of price discrimination from the students’ lives,A local movie theater
here o ers discounts on Tuesday nights,Local bars have happy hours,The
electricity company charges nonlinear prices for electricity service,There are
many more examples of this sort of thing.
In the fourth edition I have described rst-,second- and third-degree price
discrimination in a more systematic way,The second-degree analysis is quite
interesting,I think,since it uses only consumers’ surplus analysis.
The sections on bundling and on two-part tari s are also quite interesting.
There are hundreds of examples of bundling you might discuss,Two-part tari s
are also quite common and have the bonus of serving as a good example of
rst-degree price discrimination,You might want to talk about the e ciency
implications of two-part tari s.
Finally,the Hotelling boardwalk example is very useful,In the text I empha-
size the point that the example can lead to extreme product di erentiation,as
well as no di erentiation,even in the case of two players.
Monopoly Behavior
A,Price discrimination
1,rst degree | perfect price discrimination
a) gives Pareto e cient output
b) same as take-it-or-leave-it o er
c) producer gets all surplus
2,second degree | nonlinear pricing
a) two demand curves
b) would like to charge each full surplus
c) but have to charge bigger one less to ensure self-selection
d) but then want to reduce the amount o ered to smaller consumer
3,third degree | most common
60 Chapter Highlights
a)
max p
1
(y
1
)y
1
+p
2
(y
2
)y
2
c(y
1
+ y
2
)
b) gives us the rst-order conditions
p
1
+ p
0
1
(y
1
)y
1
= c
0
(y
1
+ y
2
)
p
2
+ p
0
2
(y
2
)y
2
= c
0
(y
1
+ y
2
)
c) or
p
1
1?
1
j
1
j
= MC
p
2
1?
1
j
2
j
= MC
d) result,if p
1
>p
2
,thenj
1
j<j
2
j
e) more elastic users pay lower prices
B,Two-part tari s
1,what happens if everyone is the same?
2,entrance fee = full surplus
3,usage fee = marginal cost
C,Bundling
1,type A,wtp $120 for word processor,$100 for spreadsheet
2,type B,wtp $100 for word processor,$120 for spreadsheet
3,no bundling pro ts = $400
4,bundling pro ts =$440
5,reduce dispersion of wtp
D,Monopolistic competition
1,rare to see pure monopoly
2,product di erentiation { so some market power
3,free entry
4,result | excess capacity theorem
a) see Figure 25.3.
b) (but is it really?)
5,location model of product di erentiation
a) ice cream vendors on the boardwalk
b) socially optimal to locate at 1=4and3=4
c) but this is \unstable"
d) only stable con guration is for both to locate at middle
e) is there too much conformity in di erentiated markets?
Chapter 26 61
Chapter 26
Factor Markets
I added this chapter in order to discuss some of the problems with imperfect
competition in factor markets,There are three topics,a monopolist’s demand
for a factor,monopsony,and vertically integrated monopolies.
The monopolist’s demand is a snap if the students know a little calculus,If
they don’t,you have to talk your way through it,I’m not sure that this topic
really deserves much emphasis if the students don’t have the math to handle it.
The section on monopsony is pretty standard; the minimum wage example is
useful,You might talk some about the situation in professional sports,to show
students that there are real-life examples of monopsonies.
I’m very fond of the integrated monopoly example,The fact that the
integrated monopoly has a lower price is surprising,It shows that in antitrust,
sometimes the cure is worse than the disease!
Factor Markets
A,Monopoly in output market
1,marginal product,MP
x
2,marginal revenue,MR
y
3,marginal revenue product,MRP
x
4,value of the marginal product,pMP
x
a) MRP = p
h
1?
1
j j
i
b) note that this is less than value of MP
B,Monopoly/monoposony in input market
1,market power by demander of factor
2,maximize pf(x)?w(x)x
3,get MR= MC,but with particular form
4,now MC= w
1+
1
5,linear example,Figure 26.2.
6,minimum wage
62 Chapter Highlights
C,Upstream and downstream monopoly
1,one monopolist produces a factor that he sells to another monopolist
2,suppose that one unit of the input produces one unit of output in
downstream monopolist
3,each monopolist wants to mark up its output price over marginal cost
4,results in a double markup
5,if rms integrated,would only have a single markup
6,price would go down
Chapter 27 63
Chapter 27
Oligopoly
This chapter is a serious attempt to convey some of the standard models
of strategic interaction to intermediate microeconomics students,This is an
ambitious goal,but with some motivation it can be done,I have pursued a
middle ground in this chapter between the traditional approach to oligopoly and
the more modern game theoretic approach.
I’ve departed from the standard order of discussing things here since I think
that it is much clearer the way I do it.
I start with a little classi cation scheme,rms can choose prices or quantities,
and they can move simultaneously or sequentially,This gives us four cases
to analyse,You might discuss other strategic variables at this point,product
di erentiation,investment decisions,entry,etc.
I proceed to analyse the case of quantity leadership|the Stackelberg model.
Here you should emphasize the importance of thinking strategically,putting
yourself in the shoes of the other guy and thinking about how he will react to
your choices,Once that insight is there,it is fairly straightforward to do the
analysis.
The next case to look at is the case of price leadership,The logic is just the
same,and the calculations are even easier.
Then we move to simultaneous quantity setting|the Cournot/Nash model.
I have been careful to phrase the concept of a Cournot equilibrium as an
equilibrium in beliefs as well as actions|each rm is maximizing given its beliefs
about the other rm’s choices,and each rm nds that its beliefs are con rmed
in equilibrium,I nd that it is very useful to calculate out an equilibrium
example,so that students can see the richness of the idea involved,The graphical
treatment is also very helpful.
Section 26.7,on adjustment to equilibrium,is a little bit of a cheat,This is
not really consistent with a thoroughgoing game theoretic analysis,but I put it
in anyway since the students seem to like it,It shows in a graphic way how an
apparently sensible adjustment process can lead to the Cournot equilibrium.
Section 26.8,on many rms,is a very nice illustration of what the idea of a
\demand curve facing a rm" looks like,The idea that a Cournot equilibrium
approaches the competitive equilibrium as market shares go to zero is a useful
one,and the calculations in this section motivate this idea quite powerfully.
64 Chapter Highlights
Next,I treat simultaneous price setting|the Bertrand model,I like the
interpretation of \bidding" for the consumers,There are a number of real-world
examples where forcing rms to make sealed bids results in much lower prices.
The logic behind this is essentially that of Bertrand competition,In Ann Arbor,
the local coursepack providers quote you a 5-cents-a-page price for copying,but
the sealed bids usually end up under 2.5 cents.
Section 26.10 on collusion is also very important,I usually motivate this
using OPEC as an example,Each rm negotiates to set a quota that maximizes
overall cartel pro ts,::and then each rm goes home and tries to cheat on the
cartel,It is worth pointing out that equation 26.6 implies that the smaller rm
1’s output is,relative to rm 2,the more incentive rm 2 has to cheat on the
cartel agreement,This is true since
1
y
1
=?
p
Y
y
2
:
If the output of rm 2 is large,then
1
= y
1
will be large.
In Figure 26.5 it is useful to point out that the reason that we get a whole
range of outputs that maximize industry pro ts is that we have assumed that
marginal costs are identical|in fact,we have assumed that they are zero for both
rms,If the marginal costs were di erent,we would most likely get a unique
cartel solution.
Oligopoly
A,Oligopoly is the study of the interaction of a small number of rms
1,duopoly is simplest case
2,unlikely to have a general solution; depends on market structure and
speci c details of how rms interact
B,Classi cation of theories
1,non-collusive
a) sequential moves
1) quantity setting | Stackelberg
2) price setting | price leader
b) simultaneous moves
1) quantity setting | Cournot
2) price setting | Bertrand
2,collusive
C,Stackelberg behavior
1,asymmetry | one rm,quantity leader,gets to set quantity rst
2,maximize pro ts,given the reaction behavior of the other rm
3,take into response that the other rm will follow my lead
4,analyze in reverse
5,rm 2
a) max
y
2
P(y
1
+y
2
)y
2
c(y
2
)
b) FOC,P(y
1
+ y
2
)+P
0
(y
1
+y
2
)y
2
= c
0
(y
2
)
c) solution gives reaction function,f
2
(y
1
)
d) see Figure 27.1
6,rm 1
a) max
y
1
P(y
1
+f
2
(y
1
))y
1
c(y
1
)
b) FOC,P(y
1
+ f
2
(y
1
)) + P
0
(y
1
+ f
2
(y
1
))y
1
= c
0
(y
1
)
c) see Figure 27.2
7,graphical solution in Figure 27.4.
Chapter 27 65
D,Price-setting behavior
1,leader sets price,follower takes it as given
2,given p
1
,rm 2 supplies S
2
(p
1
)
3,if demand is D(p),this leaves D(p
1
)?S
2
(p
1
) for leader
4,hence leader wants to maximizep
1
y
1
c(y
1
) such that y
1
= D(p
1
)?S
2
(p
1
)
5,leader faces \residual demand curve"
E,Cournot equilibrium | simultaneous quantity setting
1,each rm makes a choice of output,given its forecast of the other rm’s
output
2,let y
1
be the output choice of rm 1 and y
e
2
be rm 1’s beliefs about rm
2’s output choice
3,maximization problem max
y
1
p(y
1
+y
e
2
)y
1
c(y
1
)
4,let Y = y
1
+ y
e
2
5,rst-order condition is
p(Y)+p
0
(Y )y
1
= c
0
(y
1
)
6,this gives rm 1’s reaction curve | how it chooses output given its beliefs
about rm 2’s output
7,see Figure 27.1.
8,look for Cournot equilibrium | where each rm nds its expectations
con rmed in equilibrium
9,so y
1
= y
e
1
and y
2
= y
e
2
F,Example of Cournot
1,assume zero costs
2,linear demand function p(Y)=a?bY
3,pro t function,[a?b(y
1
+ y
2
)]y
1
= ay
1
by
2
1
by
1
y
2
4,derive reaction curve
a) maximize pro ts
b) a?2by
1
by
2
=0
c) calculate to get y
1
=(a?by
2
)=2b
d) do same sort of thing to get reaction curve for other rm
5,look for intersection of reaction curves
G,Bertrand { simultaneous price setting
1,consider case with constant identical marginal cost
2,if rm 1 thinks that other rm will set p
2
,what should it set?
3,if I think p
2
is greater than my MC,setp
1
slightly smaller than p
2
4,I get all the customers and make positive pro ts
5,only consistent (equilibrium) beliefs are p
1
= p
2
= MC
H,Collusion
1,rms get together to maximize joint pro ts
2,marginal impact on joint pro ts from selling output of either rm must be
the same
3,maxp(y
1
+y
2
)[y
1
+ y
2
]?c(y
1
)?c(y
2
)
4,P(y
1
+ y
2
)+P
0
(y
1
+y
2
)[y
1
+ y
2
]=c
0
(y
1
)=c
0
(y
2
)
5,note instability | if rm 1 believes rm 2 will keep its output xed,it will
always pay it to increase its own output
6,problems with OPEC
7,if it doesn’t believe other rm will keep its output xed,it will cheat rst!
66 Chapter Highlights
Chapter 28
Game Theory
This is a fun chapter,Students like it a lot,and faculty usually enjoy teaching
it,Game theory is hot stu in economics these days,and this chapter tries to
convey some of the reasons why.
The rst two equilibrium concepts,that of a dominant strategy equilibrium
and of a Nash equilibrium,are reasonably easy to convey,The idea of a Nash
equilibrium in mixed strategies is a little harder,Here’s an example that will
motivate the idea.
Consider the game of baseball,The pitcher has two strategies,pitch high or
pitch low,Likewise,the batter has two strategies,swing high or swing low,If
the batter connects,he gets a payo of 1 and the pitcher gets zero,If the batter
misses,the pitcher gets a payo of 1.
What are the Nash equilibria in this game? If the pitcher always pitches
high,the batter will always swing high,and if the pitcher always pitches low,
then the batter will always swing low,It is clear from this observation|and
from observing baseball games|that the equilibrium strategy must involved a
mixed strategy,The pitcher will flip a coin and decide whether to pitch high or
low,and the batter flips a coin to decide whether to swing high or low,The
batter will connect 50% of the time,Here students are very willing to accept
that the optimal strategy must involve randomization.
If you really want to get them buzzing,you can talk about the following
paradox,If the batter really believes that the pitcher will really randomize 50{
50,then he might as well swing high all the time,But of course,once the pitcher
detects this departure from randomizing,he will modify his own behavior to
exploit the batter’s sloppiness,This example drives home the important point
that what keeps the players at the Nash equilibrium is the desire to avoid being
psyched out by their opponents.
Most students have heard of the prisoners’ dilemma by now,but they haven’t
seen the analysis of the repeated game,The reason why the repeated game
is di erent from the one-shot game is that in the repeated game,the strategy
choice at time t can depend on the entire history of the game up until t.Thus
choices at time t?1 may have some influence on choices at time t,This opens
the possibility of tit-for-tat and other strategies that can allow for cooperative
solutions.
Chapter 28 67
The analysis of the sequential games,and especially the game of entry
deterrence,is a very interesting topic,Students really get excited about this
kind of analysis since they think that it will help them be better managers.
(Well,who knows,maybe it will!)
It is fun to describe Schelling’s game of the kidnapper with cold feet|this has
a plot line very similar to the movie Nasty People,A kidnapper grabs a victim
and then gets cold feet,The problem is that if he releases his victim,the rational
strategy for the victim is to go to the police and identify the kidnapper,The
problem with this sequential game is that the victim has no way to precommit
to staying away from the police.
Schelling’s solution is characteristically inventive,he suggests that the victim
allow the kidnapper to photograph him in some unspeakably disgusting act.
This gives the kidnapper a threat|if the victim ever exposes the kidnapper,the
kidnapper can release the photo,The students think that this game is great
fun,You can ask them to suggest various \unspeakably disgusting acts" that
the victim might suggest.
Game Theory
A,Game theory studies strategic interaction,developed by von Neumann and
Morgenstern around 1950
B,How to depict payo s of game from di erent strategies
1,two players
2,two strategies
3,example
Row
Column
Left Right
Top 1;2 0;1
Bottom 2;1 1;0
a) this depicts a dominant strategy
b) each person has a strategy that is best no matter what the other person
does
c) nice when it happens,but doesn’t happen that often
C,Nash equilibrium
1,what if there is no dominant strategy?
2,in this case,look for strategy that is best if the other player plays his best
strategy
3,note the \circularity" of de nition
4,appropriate when you are playing against a \rational" opponent
5,each person is playing the best given his expectations about the other
person’s play and expectations are actually con rmed
6,example:
Row
Column
Left Right
Top 2;1 0;0
Bottom 0;0 1;2
a) note (top,left) is Nash; (bottom,right) is also Nash
68 Chapter Highlights
7,Nash equilibrium in pure strategies may not exist.
Row
Column
Left Right
Top 0;0 0;?1
Bottom 1;0?1;3
8,but if allow mixed strategies (and people only care about expected payo ),
then Nash equilibrium will always exist
D,Prisoners’ dilemma
1,2 prisoners,each may confess (and implicate other) or deny
2,gives payo matrix
Row
Column
Left Right
Top?3;?3 0;?6
Bottom?6;0?1;?1
3,note that (confess,confess) is unique dominant strategy equilibrium,but
(deny,deny) is Pareto e cient
4,example,cheating in a cartel
5,example,agreeing to get rid of spies
6,problem | no way to communicate and make binding agreements
E,Repeated games
1,if game is repeated with same players,then there may be ways to enforce
a better solution to prisoners’ dilemma
2,suppose PD is repeated 10 times and people know it
a) then backward induction says it is a dominant strategy to cheat every
round
3,suppose that PD is repeated an inde nite number of times
a) then may pay to cooperate
4,Axelrod’s experiment,tit-for-tat
F,Example { enforcing cartel and price wars
G,Sequential game | time of choices matters
H,Example:
Row
Column
Left Right
Top 1;9 1;9
Bottom 0;0 2;1
1,(top,left) and (bottom,right) are both Nash equilibria
2,but in extensive form (top,left) is not reasonable,Figure 27.6.
3,to solve game,start at end and work backward
4,(top,left) is not an equilibrium,since the choice of \top" is not a credible
choice
I,Example,entry deterrence
1,stay out and ght
2,excess capacity to prevent entry | change payo s
3,see Figure 27.7.
4,strategic ine ciency
Chapter 29 69
Chapter 29
Exchange
This chapter starts out with a relatively standard treatment of trade in an
Edgeworth box,This leads naturally to the idea of Pareto e cient allocations
as the outcome of a voluntary trading process,Given the many possibilities
that can result from unstructured voluntary trade,I then turn to examining a
particular mechanism for trade,the competitive market mechanism.
It is important to emphasize that if there are really only two players,the
market mechanism isn’t very plausible,We assume that our two players take
prices as given; this is sensible only in a model with many players,One way
out of this problem is to suppose that there are one hundred A players and one
hundred B players,and that the Edgeworth box depicts the bundle that each
type has,If there are two hundred small consumers in the Edgeworth box,then
there is no problem with them behaving competitively.
The rest of the treatment here is fairly standard,The reductio ad absurdum
proof in 28.10 throws a few students|they’ve generally forgotten any logic
they’ve learned by the time they get to college,So if you want to go over
this proof,you should remind them of the logic that it uses.
The main problem with presenting the two welfare theorems is that the
students don’t have any other examples of resource allocation mechanisms with
which to compare the Walrasian market,That’s why I like the monopoly in the
Edgeworth box example,A standard monopolist in the Edgeworth box gives an
example of a market-based resource allocation system that results in a Pareto
ine cient allocation,A perfectly discriminating monopolist gives an example
of a market-based resource allocation scheme other than pure competition that
results in Pareto e ciency,These two examples help to illustrate the richness of
the idea of Pareto e ciency,as well as some of its limitations.
The implications of the rst and second welfare theorems are profound,but it
is sometimes hard to convey that profundity,It helps people to see the various
aspects of these ideas if they can discuss them a little.
Exchange
A,Partial equilbrium | theory of single market
70 Chapter Highlights
B,General equilibrium | interactions among many markets
1,complements and substitutes
2,prices a ect income,::but income a ects prices
C,We do pure exchange rst,then production
D,Edgeworth box
1,Figure 29.1.
2,allocation
3,feasible allocation
4,consumption bundles
5,initial endowment
6,nal allocation
E,Trade
1,move to Pareto preferred point
2,keep going until no more mutally preferred trades
F,Pareto e cient allocations
1,where trade stops | no mutual improvement possible
2,Pareto e cient | no way to make both people better o
3,indi erence curves must be tangent
4,Pareto set,or contract curve | locus of all PE points
G,Market trade
1,speci c way to trade | using price system
2,gross demands and net demands; Figure 29.3.
3,market equilibrium | where supply equals demand
4,see Figure 29.4.
H,Algebra
1,only one of the markets needs to clear
2,Walras’s law,if each individual satis es his or her budget constraint,then
the market as a whole must satisfy its budget constraint
3,existence of equilibrium?
I,E ciency
1,does the market exhaust all the gains from trade?
2,is the market outcome e cient?
3,First Theorem of Welfare Economics | yes
4,is any e cient allocation a market equilbrium?
5,Second Theorem of Welfare Economics | yes,if things are appropriately
convex
6,see Figure 29.8.
J,Meaning of First Welfare Theorem
1,implicit assumptions | no externalities
2,competitive behavior
3,existence
4,shows that there is a general mechanism that will achieve e cient outcomes
5,can decentralize decisions
Chapter 29 71
K,Meaning of Second Welfare Theorem
1,prices play allocative and distributive role
2,use market for allocative role and income redistribution for distributive
role
3,but problems in production economy
a) how to measure endowments?
b) how to redistribute endowments?
72 Chapter Highlights
Chapter 30
Production
In this chapter I describe a general equilibrium model of production,the
classical Robinson Crusoe economy,I usually start my lecture by apologizing for
the two-good,one-person nature of this example,since this is a context where a
two-good treatment seems quite unnatural,On the other hand,there isn’t much
way to avoid this unnatural discussion and still stick to a graphical treatment.
The fundamental idea is that the price system serves as a way to decentralize
resource allocation problems,Robinson,the consumer,only has to know the
public prices,his own income,and his own tastes,Robinson,the producer,only
has to know the prices,The consumer doesn’t have to know anything about
what is technologically feasible,and the rm doesn’t have to know anything
about tastes,All of the relevant information about tastes and technology end
up being summarized in the equilibrium prices.
This decentralization role of the price system isn’t very interesting in the
one- or two-person economy,but if there are thousands of people,it can be
extremely important,Thus it is important to understand those cases where the
price system works well as a decentralization device and those cases where it
works poorly.
In this chapter,the e cacy of the price system depends on the nature of the
technology|everything works out just dandy if there are decreasing or constant
returns to scale,but if there are increasing returns to scale,it all breaks down.
It is a good idea to compare the problems that arise with increasing-returns-to-
scale technology discussed here with the problems that arise with the decreasing-
average-costs technology discussed in the chapter on monopoly,These are just
two di erent ways of depicting the same phenomenon|marginal cost pricing is
not viable since it results in negative pro ts.
In Section 29.10 I describe the basic idea of comparative advantage,This is a
very important idea in economics,but unless students take international trade,
they probably won’t see it after the standard treatment in their principles course.
Chapter 30 73
Production
A,Want to study production in a general equilibrium context
1,two-good model is somewhat arti cial
2,but necessary for a graphical treatment
B,Robinson Crusoe economy
1,Robinson is both consumer and producer
2,consumes leisure and coconuts
3,can make leisure-consumption choice directly as in Figure 29.1.
4,or can make it indirectly via the market
C,Crusoe,Inc,| the rm’s choices
1,rm looks at prices and chooses a pro t-maximizing plan
2,generates some pro ts
,See Figure 29.2.
D,Robinson the consumer
1,Robinson collects pro ts as nonlabor income
2,looks at price and wage and decides how much to work
3,chooses optimal consumption point,See Figure 29.3.
E,In equilibrium,demand equals supply
1,demand for labor equals supply of labor
2,demand for consumption equals supply of consumption
F,Decentralization
1,each \agent" in the economy only has to look at the prices and make his
own decisions
2,the consumer doesn’t have to know anything about the production problem
3,the producer doesn’t have to know anything about the consumer’s problem
4,all information is conveyed in prices
5,in a one-person economy,this is silly
6,but in a many-person economy,there can be great savings
G,Di erent kinds of technologies
1,constant returns to scale | zero pro ts
2,decreasing returns to scale | positive pro ts
3,increasing returns to scale | competitive markets don’t work,Natural
monopoly problem
H,Welfare theorems
1,First welfare theorem | competitive markets are Pareto e cient
2,Second welfare theorem | any Pareto e cient outcome can be achieved
by competitive markets
I,Production possibilities
1,if there is more than one good,we can illustrate the production set,Figure
29.7.
2,if there is more than one way to produce output,producers can exploit
comparative advantage,Figure 29.8.
3,production possibilities and the Edgeworth box,Figure 29.9.
74 Chapter Highlights
Chapter 31
Welfare
I like to describe the aggregation of preference issues in terms of manipulation.
Majority voting is bad because the outcome can depend on the order in which
the vote is taken and this can lead to agenda manipulation,Rank-order voting
is bad because introducing a new alternative can change the outcome of the
process,which creates another way to manipulate the political process,Arrow’s
theorem can be interpreted to say that there is no way to avoid such manipulation
possibilities.
However,that being said,we typically resort to looking at simple ways
to aggregate preferences through the use of welfare functions,The essential
point to get across here is the connection between Pareto e ciency and welfare
maximization,every welfare maximum is e cient,Furthermore,subject to the
usual convexity conditions,every e cient allocation is a welfare maximum for
some welfare function.
The fair allocation stu is fun,Students like it,since it addresses problems
of equity in a nice way,I sometimes talk about other methods of fair division,
such as one person cuts and the other chooses,etc.
Welfare
A,Incorporate distributional considerations into the analysis
B,Need some way to compare individual preferences or utilities
C,Aggregation of preferences
1,majority voting
2,paradox of voting; see Table 31.1
3,rank order voting
4,dependence of irrelevant alternatives; see Table 31.2
D,Arrow’s impossibility theorem
E,Social welfare fuctions
1,add together utilities in some way
2,classical utilitarian:
P
n
i=1
u
i
3,weighted sum of utilities:
P
n
i=1
a
i
u
i
4,minimax,minfu
1;:::;u
n
g
Chapter 31 75
F,Maximizing welfare
1,every welfare maximum is Pareto e cient,Figure 31.1.
2,every Pareto e cient allocation is welfare maximum (if utility possibilities
set is convex)
G,Fair allocations
1,generalized the idea of symmetric treatment
2,if u
i
(x
j
) >u
i
(x
i
),then we say that i envies j
3,typically will be possible to nd allocations that are envy-free and e cient
4,proof,start out with equal division and let people trade using a competitive
market
5,end up with equal incomes; if someone envies someone else,then they
couldn’t have purchased the best bundle they could a ord
76 Chapter Highlights
Chapter 32
Externalities
I really like the smokers and nonsmokers example in the Edgeworth box.
I think that it gets the main points about externalities across very simply.
Students sometimes get confused about the vertical axis,Emphasize that this is
the total amount of smoke in the apartment,not how much each person smokes.
Only one person generates the smoke|but both people have to consume it.
This presentation shows how special it is when there is a unique optimal level
of the externality,Essentially that only occurs when preferences are quasilinear,
as shown in Figure 31.2,By the way,Figure 31.2 is a great optical illusion; the
Pareto e cient allocations form a horizontal line,although it looks as though
the line slants from right to left.
Quasilinear preferences make a lot of sense in the production context; after
all,pro t functions are quasilinear,I treat the standard Pigouvian tax in Section
31.4,but the deeper idea in that section is the idea that the e cient outcome
is independent of the assignment of property rights,Students resist the idea
that a polluter could have the right to pollute,and its victim would have to buy
back clean water from it,But if they understand that idea,they will understand
externalities a lot better.
Section 31.5 is an important one too,since it shows that if there is a productive
externality involving only a few rms,then there is a natural market signal
to internalize the externality,There was a wonderful example of this on the
TV show L.A,Law a few weeks ago,A water company was polluting the
groundwater of a neighboring trailer park,The nasty executive from the water
company said that it was reasonable for the water company to make a million-
dollar damage settlement every few years since it would cost $30 million to clean
up their technology,This provided a lot of drama on the TV,but it was terrible
economics,The sensible thing to do was for the water company to buy up
the trailer park|certain to cost a lot less than one million dollars|and evict
the tenants,This way they could internalize the externality,and make everyone
better o,Unfortunately,the L.A,lawyers didn’t suggest this to the waterworks.
Perhaps they thought that they would lose their fees.
Chapter 32 77
Externalities
A,Consumption externality occurs when an agent cares directly about another
agent’s consumption or production of some good
1,playing loud music
2,smoking a cheap cigar
B,Production externality occurs when a rm’s production function depends on
choices of another rm or consumer
1,apple orchard and honeybees
2,pollution
C,Example,smokers and nonsmokers
1,two roommates who consume smoke and money; one likes smoke,the other
doesn’t
2,depict preferences
3,depict endowment
a) each has $100
b) but what is initial endowment of smoke?
c) endowment depends on legal system | just like rights to private
property
d) right to clean air
e) right to smoke
f) Pareto e cient amounts of smoke and money
g) contract curve; how to trade
h) Figure 32.1.
i) price mechanism generates a \price of smoke"
j) problems arise because property rights are poorly determined.
4,under some conditions,the amount of smoke is independent of the assign-
ment of property rights,Figure 32.2.
D,Production externalities
1,S,a steel rm and F,a shery
2,steel,max
s
p
s
s?c
s
(s;x)
3,shery,max
f
p
f
f?c
f
(f;x)
4,FOC for steel mill:
p
s
=
@c
s
@s
0=
@c
s
@x
5,FOC for shery:
p
f
=
@c
f
(f;x)
@f
E,E cient solution
1,merge and maximize joint pro ts
2,internalize the externality
3.
max
s;f
p
s
s+p
f
f?c
s
(s;x)?c
f
(f;x)
4,get p
s
= @c
s
=@s,p
f
= @c
f
=@f and
0=
@c
s
@x
+
@c
f
@x
= marginal social cost
5,joint rm takes interaction into account
78 Chapter Highlights
6,private costs and social costs
7,how to get rms to recognize social cost
a) Pigouvian tax | set price of pollution to equal social cost
b) market pollution rights
c) assign property rights and let rms bargain over amount of pollution
8,market solution to externalities
a) either rm has incentive to buy out the other and internalize the
externality
b) since pro ts from coordination are greater than pro ts without
c) sometimes works with consumption externalities
Chapter 33 79
Chapter 33
Law
This chapter describe three topics in law and economics,Lots of undergrad-
uate economics majors aspire to be lawyers,so this chapter gives them a chance
to see a little bit of law,The rst topic is standard crime and punishment a la
Gary Becker,The second topic is a brief survey of some issues in tort liability
law,The nal topic is a cute examination of treble damages in antitrust.
It is probably a good idea to stress to the students that these are all very
simple models,A lot more work has been done in these areas in order to make
the models more realistic.
Law
A,survey three topics in law and economics
B,crime and punishment
1,some crimes appear to be motivated by economic considerations
2,so economics may be able to say something about how to influence criminal
acts
3,for example,what form should punishments take?
a) criminal presumably trades o bene ts and costs
b) if costs are all xed costs,shoplifting will be all or nothing
c) so we want \punishment to t the crime"
d) that is,provide marginal deterrence
4,likelihood and degree of punishment
a) punishment depends on probability of apprehension and severity of
punishment when caught
b) cost to state is increasing in probability since it costs more to catch a
large fraction of the cases of a crime
c) so makes sense to have a low probability of being caught and a high
cost when caught
d) in this sense the punishment (when caught) should be more costly than
the crime
e) for example,have a large ne for littering because it is hard to enforce
5,quali cation
a) judge or jury might not impose large ne
b) criminals may misperceive probability of being caught
80 Chapter Highlights
c) severe punishments can lead to greater crime
d) \you may as well hang for a cow as for a sheep"
C,liability law
1,in tort liability law one party injures another
a) how should injury be discouraged?
b) how should victim be compensated?
2,one party alone causes accident
a) x = amount of care taken by injurer
b) c
i
(x) = cost to injurer of care taken
c) L(x) = losses imposed on victim
d) social objective is to minimize c
i
(x)+L(x)
e) forms of liability law
1) no liability,ine cient amount of care
2) strict liability,internalize the externality|e cient level of care
3) negligence rule,results in e cient level of care if the level of due
care is set appropriately
3,both parties cause accident
a) y = care taken by victim
b) c
v
(y) = cost to victim of care
c) L(x;y) = loss incurred by victim
d) liability rules
1) strict liability,too little care by victims
2) strict division of losses,too little care by both
3) negligence rule,e cient care by both parties is a Nash equilibrium
4) strict liability with defense of contributory negligence,if law sets due
care correctly,e cient care is Nash equilibrium
5) imposing costs of accident on both injurer and victim also leads to
e cient outcome
D,treble damages in antitrust law
1,cartel maximizes pro ts (p?c)x(p)
2,expected damages paid to customers will be
D(x)= γ(p?c)x
where = probability of award,γ = 3 (or whatever)
3,objective function of the rm now becomes
max
p
[1? γ](p?c)x(p)
4,this is pure pro ts tax,so behavior of cartel doesn’t change care,(if the
cartel actually forms)
5,above discussion assumes consumer behavior is constant
a) what if consumers \seek to be damaged"?
b) consumers want to
max
x
u(x)+m?px+D(x)
c) leads to
max
x
u(x)+m?[p? γ(p?c)]x
d) e ective price facing consumer is ^p = p? γ(p?c)
Chapter 33 81
e) cartel’s problem now becomes
max
p
[1? γ](p?c)x(^p)
f) this is the same as
max
^p
(^p?c)x(^p)
g) the e ective price to the consumers doesn’t change!
h) the nominal price goes up|since cartel expects to pay some damages
i) consumers are willing to pay higher price since they expect to recover
some damages
82 Chapter Highlights
Chapter 34
Information Technology
There’s so much discussion these days about the Internet,the information
economy,and the information society that I thought it would be fun to try to
get some of these ideas into the classroom,What’s remarkable is how poorly
informed most of the commentators are about basic economics|not to mention
some of the research work that has been done on network economics,intellectual
property,and the like,In this chapter I try to provide some simple illustrations
of the way that simple application of intermediate microeconomics can lead to
signi cant insight,Consult Carl Shapiro and Hal R,Varian,Information Rules:
A Strategic Guide to the Network Economy,Harvard Business School Press,1999,
for lots of stories to spice up your lecture.
I start with a discussion of switching costs and lock-in,The major point
here is that in a competitive market,companies invest in getting their customers
locked in,but the pro t from doing so gets competed down to zero.
Next I describe some ideas in network economics,This analysis (which is more
than 25 years old) is a very nice way to look at all sorts of network phenomena.
Once your students understand the basic idea you might have them come up
with other examples of networks,An interesting set of examples arises where
there are two goods involved in the network,video tapes and video players,
or computers and software,You don’t want a computer unless there’s software
available,and you don’t want the software unless the computer is available,This
is a slight generalization of the model presented in the book,and it is fun to work
it out.
The next two topics in this chapter have to do with intellectual property,The
rst is a simple model of rights management that illustrates the tradeo between
value and sales,more liberal terms and conditions lead to higher values,but lower
sales,The trick is to balance these two e ects so as to maximize pro t.
The nal model is a nice little model of sharing,The nal result says,basically,
that producers make more money by allowing a product to be shared if it is
cheaper to share a single copy that it is to produce multiple copies,This is a
little surprising at rst,but on reflection it makes a lot of sense,Again,it is
useful to discuss examples,video rentals,library books,interlibrary loan,rental
skis,rental cars,etc.
Chapter 34 83
Information Technology
A,Systems competition
1,info tech components are complements
2,worry about complementers as much as competitors
B,Lock-in
1,cost of switching
2,when very large,we have lock-in
3,e.g.,switching ISPs
C,Example of switching ISPs
1,c = cost of providing service
2,p = price of service
3,if no switching costs,p = c
4,now add switching cost of s
5,allow seller to discount rst period by d
a) consumer switches if
(p?d)+
p
r
+ s>p+
p
r
b) implies d = s,which means supplier covers switching costs
6,competition forces pro t to zero
(p?s)?c+
p?c
r
=0
a) implies
p = c+
r
1+r
s
b) interpretation,ISP invests in discount,earns back premium over cost
in subsequent periods
D,Network externalities occur when the value of a good to one consumer depends
on how many other consumers purchase it.
1,examples,fax machines,modems,Internet connections,:::
E,Model,think of 1000 people who have willingness to pay ofv =1;2;3;:::;1000.
1,so number of people with willingness to pay greater or equal to p is 1000?p.
2,this is,in fact,the demand curve for the good.
F,But now suppose that the value of a fax machine is vn,wheren is the number
of people who purchase a fax.
1,if the price is p,then the marginal person satis es
p =^vn:
2,everyone with value greater than this person buys the fax machine,so
n = 1000?^v:
3,putting these two equations together gives us
p = n(1000?n):
4,note the peculiar shape of this demand curve!
84 Chapter Highlights
G,Suppose the fax machines are produced at a constant marginal cost of c.
1,there will then be 3 levels of output where demand equals supply.
2,note that the middle equilibrium is unstable; if costs decrease over time,
then system may reach critical mass."
3,examples,Adobe,Internet.
H,Rights management
1,o ering more liberal terms and conditions increases value,decreases sales
2,baseline case
a) y = amount consumed
b) p(y)=inversedemand
c) max
y
p(y)y
3,more liberal terms and conditions
a) Y = y with >1
b) P(Y)= p(Y)with >1
c)
max
Y
p(Y)
Y
d)
max
Y
p(Y )Y
4,conclusions
a) same amount consumed
b) less produced
c) pro ts goes up if >,down if inequality reversed
I,Sharing intellectual property
1,examples of sharing.
2,monopoly pro t maximization,p(y)y?cy?F gives output ^y.
3,What if good is shared amongk users? If y copies produced,x = kx copies
used,so marginal WTP isp(x),Inconvenience of sharing gives us marginal
wtp of p(x)?t.
4,What about demand by group? It is k[p(ky)?t].
5,willingness to pay goes up due due to k in front,down due to k in argument.
J,pro t maximization:
max
y
k[p(ky)?t]y?cy?F:
K,rearrange:
max
x
p(x)x?
c
k
+ t
x?F:
L,Marginal cost in this problem is (c=k+t),How does this compare to marginal
cost in original problem?
1,Pro ts will be larger when rental is possible when
c
k
+ t<c:
Or,
k
k +1
t<c:
a) If k is large,this reduces to t<c.
2,Interpretation,is it cheaper to produce an extra copy or have an existing
copy shared among more consumers?
Chapter 35 85
Chapter 35
Public Goods
I start by introducing the basic idea of a public good|a good that lacks
exclusion in consumption,The standard textbook treatment leaps right into
the Samuelson conditions,but I think that it makes much more sense to look
at the public provision of a discrete good,I derive the optimality condition in
this context,namely that the sum of the reservation prices exceeds the cost of
the good,Once students are armed with this example,the Samuelson case is a
relatively easy extension.
I then turn to a discussion of free riding and relate it to the prisoners’ dilemma.
The example there is a little forced,but it gets the point across,if each person
makes his decision about the public good independently,there may be inadequate
provision of the public good,It is fun to talk about other kinds of free riding;
e.g.,who cleans up the living room?
I next look at the classical Samuelson conditions for e ciency when the public
good can be provided at di erent levels of output,I treat the free rider problem
in Section 33.6,Figure 33.2 is really quite a nice diagram and repays careful
study.
The next topic for discussion is how to \solve" the public goods problem.
Students have been taught democratic ideals in high school civics classes,so
it might come as a shock to them that voting isn’t that good a mechanism
for making decisions about public goods,Here it is worthwhile to give some
examples where one person cares a lot about something and would be willing
to compensate others,but voting won’t be able to reach the Pareto e cient
decision,You might talk about ways that real-life political processes get around
this problem|e.g.,logrolling|but that may tend to confuse them unless they’ve
had some political science.
Finally I discuss the Clarke tax|a way to really \solve" the public goods
problem,at least for a special case,The best way to get students to understand
the Clarke tax is to actually have them use it,One faculty member I know had
his class use a Clarke tax procedure to determine the date of the midterm exam.
This is certainly a public goods problem,and the students really understood what
was going on when they actually participated,But even if you can’t determine
the provision of a real public good,like the date of the midterm,it is still of
interest to run through a numerical example,such as the one given in the book.
86 Chapter Highlights
Public Goods
A,Public goods involve a particular kind of externality | where the same
amount of the good has to be available to everyone.
B,Examples,national defense,street lights,roads,etc,| same amount must
be provided to all.
C,But people can value the public good in di erent ways.
D,Private goods
1,each person consumes di erent amount,but values it the same (at the
margin).
E,Public goods
1,each person consumes the same amount,but values it di erently.
F,Two questions about public goods
1,what is the optimal amount of a public good?
2,how well do various social institutions work in providing the optimal
amount of a public good?
G,Example,a TV for two roommates,Roommate i will contribute g
i
0
towards the purchase,TV will be purchased if g
1
+ g
2
C:
1,consider the reservation prices r
1
and r
2
,These measure maximum
willingness-to-pay for TV by each person.
2,suppose that we can nd (g
1;g
2
) such thatr
1
g
1
,r
2
g
2
andg
1
+g
2
C.
3,then clearly it is a good idea to provide the TV.
4,so,if r
1
+ r
2
C,then we can nd g
1
and g
2
that cover costs and should
provide the TV.
5,if r
1
+r
2
<C,then shouldn’t provide the TV.
6,condition for e ciency is that the sum of the willingnesses to pay must
exceed the cost of provision.
7,in case of divisible good (e.g.,how much to spend on TV),the optimum
occurs when the sum of the marginal willingness-to-pay equals marginal
cost.
a) if sum of MRSs exceeds marginal cost,can make everyone better o
by increasing the amount of public good.
b) if sum of MRSs is less than marginal cost,then should reduce the
amount of the public good.
H,Example of divisible good
1,two people each contributes g
i
to a TV,Person i gets utilityu
i
(g
1
+g
2
)?g
i
.
2,e cient alloction maximizes sum of utilities:
max u
1
(g
1
+ g
2
)+u
2
(g
1
+ g
2
)+?g
1
g
2
:
3,FOC:
u
0
1
(g
1
+g
2
)+u
0
2
(g
1
+g
2
)=1:
4,this determines the optimal amount of the public good,G
= g
1
+g
2
:
5,if there were n people,the condition would be
n
X
i=1
u
0
i
(G
)=1:
Chapter 35 87
I,Consider various social institutions to provide the public good.
1,voluntary contributions
a) person 1 will contribute until u
0
1
(g
1
+g
2
)=1.
b) person 2 will contribute until u
0
2
(g
1
+g
2
)=1.
c) person who has higher willingness to pay will contribute the entire
amount.
d) other person free rides | contributes zero.
2,majority voting
a) assume that there are n>2 people.
b) suppose that each person pays 1=n of the public good if it is provided.
c) if G units of the public good are provided,then person i gets bene t
u
i
(G)?
1
n
G:
d) person i will vote for an increase in the amount of the public good if
u
0
i
(G) >
1
n
:
e) if a majority of the people vote for an increase in the public good,then
we get a small increase.
f) so the amount of the public good is determined by the condition that
the median voter is happy with the current amount.
1) median voter means half the voters want more,half the voters want
less.
2) if m is the median voter,then want
u
0
m
(G)=
1
n
:
g) in general,this won’t be the optimal amount of the public good.
h) think of case where some voters really want a lot more of the public
good and would be willing to compensate those who don’t want more.
i) voting doesn’t take into account intensity of preference.
3,Clarke-Groves tax
a) in order to get an e cient amount of the public good,each person must
face the social costs of his decision.
b) there are ways of \bidding" for public good that do this.
88 Chapter Highlights
Chapter 36
Information
The students really like this material on information economics,but you have
to work at it to really get the ideas across.
The rst topic is the famous lemon’s market,I found it easy to get the idea
across,but the logic needs emphasizing,That’s why I go through the quality
choice model in the next section,The rst part of this model is basically the
same idea,but in a di erent context,I then summarize the fundamental idea|
the idea of adverse selection,Here it is fun to discuss other examples of adverse
selection.
The next topic is that of moral hazard,Again,it is useful to discuss other
examples to make sure the students have the idea straight.
The third topic is signaling,The Spence educational signaling model is a
wonderful example for college students,In particular,be sure to discuss the
\sheepskin e ect" example given in the text,It seems that the diploma must
carry signaling value,over and above the actual learning that it represents; your
class may want to discuss just what a diploma signals.
Finally,I discuss the topic of incentives,The basic thing to get across here
is the equivalence of all the compensation schemes in the presence of symmetric
information,The idea that sharecropping can be an e cient incentive scheme
when information is imperfect is a nice insight that deserves emphasis.
Information
A,Up until now,we have assumed complete information | consumers and rms
know the quality of the goods they buy and sell
B,But in real life,information may often be incomplete
C,Then people have to infer quality from price or other signals
D,Firms may supply such signals intentionally or inadvertently
1,used cars | why are you selling it?
2,warranties | signal of quality
Chapter 36 89
E,Model of used-car market
1,50 lemons for sale,50 plums
2,buyers willing to pay $2,400 for plum,$1,200 for lemon
3,sellers will sell plum for $2,000 and lemon for $1,000
4,full information solution
a) plum sells for price between $2,400 and $2,000
b) lemon sells for price between $1,200 and $1,000
5,incomplete information solution
a) can’t tell if car is a plum or a lemon
b) estimate quality by looking at average quality of cars on the market
c) suppose all cars were o ered for sale
d) then the willingness to pay for a car would be
1
2
2;400 +
1
2
1;200 = 1;800:
e) at this price,the owners of plums wouldn’t sell
f) only owners of lemons would sell
g) but then the maximum that buyers would be willing to pay would be
$1,200!
h) only equilibrium is for lemons to get o ered on market,and price to be
between $1,000 and $1,200
i) the bad cars have \driven out" the good cars
j) there is an externality between the good and bad cars
F,Quality choice
1,in the lemons model,quality is exogenous; what if quality is endogenous?
2,umbrella market
a) consumers are willing to pay $14 for a high-quality umbrella,$8 for a
low-quality umbrella
b) if a fraction q are high quality,willing to pay
p =14q+8(1?q):
c) suppose it costs $11.50 to produce high quality and $11 to produce low
quality
d) then if there are many rms,and each thinks that it will have a
negligible e ect on the price,each will choose to produce a low-quality
umbrella
e) but the amount that people are willing to pay for a low-quality umbrella
($8) exceeds the cost of production ($11)
f) the possibility of production of a low-quality good has destroyed the
market!
3,Adverse selection
a) consider insurance market
b) people who need insurance the most are more likely to buy it
c) rates based on average experience over population will not necessarily
cover costs
d) high-risk consumers can drive out low-risk consumers
e) mandatory insurance can make people better o on average
90 Chapter Highlights
G,Signaling
1,we have seen that when quality in market is mixed,the bad quality can
drive out the good
2,incentive for rms to identify high-quality goods by sending a signal to the
consumers
3,example,a warranty
4,high-quality producers can a ord to o er a warranty,low-quality producers
can’t
5,in equilibrium a warranty can di erentiate the two qualities
6,example|signaling by educational choice
a) two kinds of workers,able and unable
b) able have MP of a
2
,unable have an MP of a
1
,anda
2
>a
1
.
c) if rm can observe quality of worker,each type gets paid its MP
d) if can’t observe quality,must pay wage equal to average of MPs
e) suppose that there is some signal that they can acquire that will indicate
which type they are
f) for example,suppose that workers can choose education level
g) more able workers have cheaper costs of acquiring education (not
necessarily dollar costs)
h) then can have an equilibrium where able workers acquire education,to
distinguish themselves from unable workers
i) even though the education doesn’t change their MP
j) socially wasteful investment | only use is to distinguish one group from
another