Public Finance
Chapter3
Tools of Normative Analysis
CHENG Beinan PH.D
Contents





Welfare Economics
The First Fundamental Theorem
The Second Fundamental Theorem
Market Failure
Buying into Welfare Economics
§1. Welfare Economics
 Definition
 Branch of economic theory concerned
with the social desirability of alternative
economic states.
 Usage
 Distinguish two circumstances
 Markets can perform well
 Markets fail to be desirable
 Standard to judge the desirability
 Pareto Efficient: An allocation of resources such
that no person can be made better off without
making another person worse off.
 Pareto Improvement: An reallocation of
resources that makes at least one person better
off without making anyone else worse off.
 Conditions
 Pure economy exchange
 Production economy
§1.1 Pure Economy Exchange
 How to get the desirable condition in
the pure economy exchange?
 Tools:
 Edgeworth Box & Indifference Curve
 Procedure:
 Pareto improvement from any starting
point→ Pareto efficient points→ Contract
Curve
 Result in the math equation
Edgeworth Box
A device used to depict the
distribution of goods in a two
good- two person world.
y
0’
Fig leaves per year
r
v
u
0
Adam
Eve
w
s
x
Apples per year
Edgeworth Box
Back
Indifference curves in Edgeworth Box
r
Eve
0’
E1
Fig leaves per year
E2
E3
A3
A2
A1
s
0
Adam
Apples per year
Edgeworth Box
§1.1 Pure Economy Exchange
 How to get the desirable condition in
the pure economy exchange?
 Tools
 Edgeworth Box & Indifference Curve
 Procedure
 Pareto improvement from any starting
point→ Pareto efficient points→ Contract
Curve
 Result in the math equation
Procedure to get the desirable condition
in the pure economy exchange
 Pareto improvement from any
starting point→ Pareto efficient
points;
 Pareto improvement for Adam
 Pareto improvement for Eve
 Pareto improvement for both
 Pareto improvement from other
starting point→ Pareto efficient
points;
 Pareto efficient points → Contract
Curve
Making Adam better off without Eve
becoming worse off
Eve
0’
r
Fig leaves per year
Eg
g
h
A Pareto
Efficient
Allocation
p
Ag
Ag
Ag
s
0
Adam
Apples per year
Edgeworth Box
Making Eve better off without Adam
becoming worse off
Eve
0’
r
Fig leaves per year
Eg
g
p
Ep1
p1
A Pareto
Efficient
Allocation
Ag
s
0
Adam
Apples per year
Edgeworth Box
Making both Adam and Even better off
0’
r
Eg
Fig leaves per year
Eve
g
• Pareto efficient
• Pareto improvement
Ep2
p
p2
p1
Ap2
Ag
s
0
Adam
Apples per year
Edgeworth Box
Starting from a different initial point
Eve
0’
r
Fig leaves per year
Eg
g
k
p4
Ep2
p
p3
p2
p1
Ap2
Ag
s
0
Adam
Apples per year
Edgeworth Box
The Contract Curve
Eve
0’
r
Fig leaves per year
Eg
g
The
contract
curve
p4
Ep2
p
p3
p2
p1
Ap2
Ag
s
0
Adam
Apples per year
Edgeworth Box
Back
§1.1 Pure Economy Exchange
 How to get the desirable condition in
the pure economy exchange?
 Tools
 Edgeworth Box & Indifference Curve
 Procedure
 Pareto improvement from any starting
point→ Pareto efficient points→ Contract
Curve
 Result in the math equation
Pareto Efficiency in Consumption
Eve
Adam
MRSaf
=
MRSaf
§1. Welfare Economics
 Definition
 Branch of economic theory concerned with the
social desirability of alternative economic states.
 Standard to judge the desirability
 Pareto Efficient
 Pareto Improvement
 Conditions
 Pure economy exchange
 Production economy
§1.2 Production Economy
 How to get the desirable condition in
production economy?
 Tools:
 Production Possibilities Curve
 Marginal rate of transformation
 Marginal Cost
 Result in the math equation
Fig leaves per year
Production Possibilities Curve
A graph that shows the maximum quantity
of one output that can be produced, given
the amount of the other output.
C
│Slope│ =
marginal rate of
transformation
w
y
0
C
x
z
Apples per year
§1.2 Production Economy
 How to get the desirable condition in
production economy?
 Tools:
 Production Possibilities Curve
 Marginal rate of transformation
 Marginal Cost
 Result in the math equation
Definition
 Marginal rate of transformation:
 The rate at which the economy can
transform one good into another good; it
is the slope of the Production Possibilities
frontier.
 Marginal Cost:
 The incremental cost of producing one
more unit of output.
Marginal Rate of Transformation
 MRTaf = Marginal rate of
transformation of
apples for fig leaves
 MRTaf = MCa/MCf
§1.2 Production Economy
 How to get the desirable condition in
production economy?
 Tools:
 Production Possibilities Curve
 Marginal rate of transformation
 Marginal Cost
 Result in the math equation
Efficiency Conditions with
Variable Production
Adam
Eve
MRTaf = MRSaf = MRSaf
Adam
Eve
MCa/MCf = MRSaf = MRSaf
Q4
 Many controversial issues in public finance
concern when a central authority should allow
markets to work and when it should intervene.
Generally we think of the government as the
central authority, but it could be a university as
well. For example, according to Princeton
University's student newspaper, the Daily
Princetonian (April 16, 2007), there was "a
flourishing market of graduation ticket buyers
and sellers on [the Internet]." However, the
dean of students shut down the market,
arguing that "[s]elling tickets undermines that
spirit of community, and undermines the sense
of class unity that seniors have worked hard to
create."
 To analyze this policy, assume that a typical
senior's utility depends only on two
commodities, graduation tickets and a
composite of all other goods. Assume there are
two students, Angelo and Bahn, each of whom
starts out with three tickets. However, Angelo
is "rich" and has twice the amount of all other
goods as Bahn. For simplicity, you may assume
that graduation tickets are infinitely divisible.
 a. Draw an Edgeworth Box showing the initial
allocation, assuming conventionally shaped
indifference curves for both students.
 b. Using the Edgeworth Box, explain how the
ban on selling tickets can lead to an inefficient
outcome.
 c. Using the Edgeworth Box, represent a
situation in which the ban on selling tickets
does not reduce efficiency for these two
students.
Q12
 Consider an economy with two people, Victoria
and Albert, and two commodities, tea and
crumpets. Currently, Victoria and Albert would
both be willing to substitute two cups of tea for
one crumpet. Further, if the economy were to
produce one less cup of tea, the resources
released from tea production could be used to
produce three more crumpets. Is the allocation
of resources in this economy Pareto efficient?
If not, should there be more tea or more
crumpets?
Q13
 Suppose that Hannah's utility function is UH =
3T + 4C and Jose's utility function is UJ = 4T +
3C, where T is pounds of tea per year and C is
pounds of coffee per year. Suppose there are
fixed amounts of 28 pounds of coffee per year
and 21 pounds of tea per year. Suppose also
that the initial allocation is 15 pounds of coffee
to Hannah (leaving 13 pounds to Jose) and 10
pounds of tea to Hannah (leaving 11 pounds of
tea to Jose).
 a. What do the utility functions say about the
marginal rates of substitution of coffee for tea?
 b. Draw the Edgeworth Box showing
indifference curves and initial allocation.
 c. Draw the contract curve on the Edgeworth
Box. Explain why it looks different from the
contract curves depicted in the text.
 d. Is the initial allocation of coffee and tea
Pareto efficient?
Contents





Welfare Economics
The First Fundamental Theorem
The Second Fundamental Theorem
Market Failure
Buying into Welfare Economics
§2.The First Fundamental Theorem
 1st Theorem:
 If (1) competition is perfect; (2) market
exists; then Pareto efficient allocation of
resources emerges.
 Simple Proof:
 Efficiency in Consumption
 Efficiency Conditions with Variable
Production
Consumption Efficiency in Perfect
Competition
MRS
MRS
Adam
af
Eve
af


Q fAdam
QaAdam
Q
Eve
f
Eve
a
Q
Pa 
 
Pf 
Adam
Eve

MRS

MRS

af
af
Pa



Pf

Adam
a
Adam
f
P

P
Eve
a
Eve
f
P

P
§2.The First Fundamental Theorem
 1st Theorem:
 If (1) competition is perfect; (2) market
exists; then Pareto efficient allocation of
resources emerges.
 Simple Proof:
 Efficiency in Consumption
 Efficiency Conditions with Variable
Production
Production Efficiency in Perfect
Competition


Pa  MCa

Pa

Adam
Eve
Pf  MC f
 MRSaf  MRS af
  MRTaf 
Pf

MCa 
MRTaf 
MC f 
Q3
 Certain market transactions, such as selling
one's kidneys, seem morally repugnant to
many people. At a conference discussion on
what makes certain transactions morally
repugnant, a professor of psychology said,
"The problem is not that economists are
unreasonable people, it's that they're evil
people. ... They work in a different moral
universe." The psychologist argued that the
burden of proof should be "on someone who
wants to include a transaction in the
marketplace." Contract this view with the view
inherent in the First Fundamental Theorem of
Welfare Economics.
Contents
 Welfare Economics
 The First Fundamental Theorem
 The Second Fundamental
Theorem
 Market Failure
 Buying into Welfare Economics
§3. Fairness & 2nd Theorem
 The inferrer of 1st Theorem:
 Markets do well→ Small government
 Protect property rights
 Law and order, court system, national
defense
 Problem:
 Is Pareto efficiency enough?
 Pareto efficiency by itself is not enough to
rank alternative allocations of resources.
Efficiency versus Equity
Eve
0’
Fig leaves per year
r
p3
p5
q
s
0
Adam
Apples per year
Edgeworth Box
 Tools to get 2nd Theorem:
 Utility Possibilities Curve
 Definition
 Contract Curve→ Utility Possibilities Curve
 Social Welfare Function
 Definition
 W = F (UAdam, UEve)
 Social Welfare Function → Social
indifference curve
Adam’s utility
Utility Possibilities Curve
U
p3
p5
q
U
Eve’s utility
Definitions
 Utility Possibilities Curve: A graph
showing the maximum amount of one
person’s utility given each level of
utility attained by the other person.
 Social Welfare Function: A function
reflecting society’s views on how the
utilities of its members affect the
well-being of society as a whole.
 Tools to get 2nd Theorem:
 Utility Possibilities Curve
 Definition
 Contract Curve→ Utility Possibilities Curve
 Social Welfare Function
 Definition
 W = F (UAdam, UEve)
 Social Welfare Function → Social
indifference curve
Definitions
 Utility Possibilities Curve: A graph
showing the maximum amount of one
person’s utility given each level of
utility attained by the other person.
 Social Welfare Function: A function
reflecting society’s views on how the
utilities of its members affect the
well-being of society as a whole.
Adam’s utility
Social Indifference Curve
W = F(UAdam, UEve)
Increasing
social
welfare
Eve’s utility
Adam’s utility
Maximizing Social Welfare
i
iii
ii
Eve’s utility
 Basic conclusion:
 Even if perfect economy can generates a
Pareto efficient allocation of resources,
government intervention may be
necessary to achieve a “fair” distribution
of utility.
 How to balance efficiency & fairness?
 Metaphor
 2nd Theorem
 Tim Harford (2006, pp. 73-74)
 If your goal is to have all the sprinters cross the
line together, you could just change the rules of
the race, ordering the fast runners to slow down
and everyone to hold hands as they crossed the
line. A waste of talent. Or you could move some
starting blocks forward and some back, so that
although each sprinter was running as fast as he
could … the fastest had to cover enough extra
ground that he would end up breaking the tape
neck-and-neck with the slowest.
 2nd Theorem
 Society can attain any Pareto efficient
allocation of resources by making a
suitable assignment of initial
endowments and then letting people
freely trade with each other as in our
Edgeworth Box Model.
 Explanation: by redistribution income
suitably and then getting out of the way
and letting markets work, the
government can attain any point on the
utility possibilities frontier.
Q2
 In his commencement address at Wesleyan
University in 2008, then-Senator Barack
Obama told the students that "our individual
salvation depends on collective salvation." Is
this view consistent with the social welfare
function defined in Equation (3.10)?
Q5
 Recently, the California Insurance
Commissioner proposed a regulation that
would reduce the ability of insurers to use
geographic location in determining automobile
insurance rates. The change would raise the
insurance rates of rural and suburban
residents, and lower the rates of urban
residents. Is such a policy efficient? Is it likely
to improve social welfare?
Q6
 Imagine a simple economy with only tow
people, Augustus and Livia.
 a. Let the social welfare function be W = UL +
UA, where UL and UA are the utilities of Livia
and Augustus, respectively. Graph the social
indifference curves. How would you describe
the relative importance assigned to their
respective well-being?
 b. Repeat part a when: W = UL + 2UA,
 c. Assume that the utility possibility curve is as
follows. Graphically show how the optimal
solution differs between the welfare functions
given in parts a and b.
Q9
 Your airplane crashes in the Pacific Ocean. You
Land on a desert island with one other
passenger. A box containing 100 little bags of
peanuts also washes up on the island. The
peanuts are the only thing to eat.
 In this economy with two people, one
commodity, and no production, represent that
possible allocations in a diagram, and explain
why every allocation is Pareto efficient. Is
every allocation fair?
Q10
 [This problem is for readers who know some
calculus.] Suppose that there are only two
people in society, Mark and Judy, who must
split a fixed amount of income of $ 300. Mark’s
utility function is UM and his income is IM.
Judy’s utility function is UJ and her income is IJ.
Suppose that:
 UM = 100 ×IM 1/2 and UJ = 200 ×IJ1/2
 Let the social welfare function be: W = UM + UJ
 What distribution of the total income between
Mark and Judy maximizes social welfare?
Q11
 Suppose that Tang and Wilson must split a fixed 400
pounds of food between them. Tang's utility function is
UT = sqrt (F1) and Wilson's utility function is UW = 1/2
sqrt (F2), where F1 and F2 are pounds of food to Tang
and Wilson, respectively.
 a. How much utility will Tang and Wilson receive if the
food is distributed evenly between them?
 b. If the social welfare function is UT + UW, then what
distribution of food between Tang and Wilson maximizes
social welfare?
 c. If social welfare is maximized if they each obtain the
same level of utility, then what is the distribution of food
between Tang and Wilson that maximizes social welfare?
Contents





Welfare Economics
The First Fundamental Theorem
The Second Fundamental Theorem
Market Failure
Buying into Welfare Economics
§4. Market Failure
 Market Power
 Monopoly
 Oligopoly
 Nonexistence of Markets
 Asymmetric information
 Externality
 Public good
Definitions
 Monopoly: A market with only one
seller of a good.
 Asymmetric Information: A situation
in which one party engaged in an
economic transaction has better
information about the good or service
traded than the other party.
§4. Market Failure
 Market Power
 Monopoly
 Oligopoly
 Nonexistence of Markets
 Asymmetric information
 Externality
 Public good
Definitions
 Externality: An activity of one entity
affects the welfare of another entity
in a way that is outside the market.
 Public Good: A good that is nonrival
and nonexcludable in consumption.
Q1
 In which of the following markets do you
expect efficient outcomes? Why?
a. Hurricane insurance for beach houses
b. Medical care
c. Stack market
d. MP3 players
e. Loans for students who wish to attend
college
 f. Housing





Q8
 In each case listed below, can you
rationalize the government policy on the
basis of welfare economics?
 a. In Los Angeles, the police respond to
127,000 burglar alarm calls per year. There
is no charge. (97 percent of the alarms are
false.)
 b. Legislation passed in 2008 provides some
families that cannot meet their mortgage
payments with government-subsidized
mortgages.
 c. The federal government regulates cherry
frozen fruit pies, requiring that at least 25
percent of each pie by weight contain
cherries and that no more than 15 percent
of the cherries be blemished. There are no
such regulations for apple, blueberry, or
peach frozen pies.
 d. Legislation passed in 2008 guarantees
American sugar producers 85 percent of the
domestic sugar market.
 e. The National Energy Policy Act requires
that all new toilets flush with only 1.6
gallons of water. Most American homes have
toilets that consume 5.5 to 7 gallons per
flush.
 f. The United States currently provides a 51
cent per gallon subsidy for ethanol.
Contents





Welfare Economics
The First Fundamental Theorem
The Second Fundamental Theorem
Market Failure
Buying into Welfare Economics
§5.Buying into Welfare Economics
 The problems of welfare economics
 Individualistic outlook
 People’s utilities vs. other social goals
 People’s utilities be problematic
 merit goods
 Results orientation
 The process might be more important
 Advantage
 Coherent framework for analyzing policy
 Government activities involves with
reallocation, and need to be compared with
alternatives.
 The framework to analyze
 Will it have desirable distributional
consequences?
 Will it enhance efficiency?
 Can it be done at a reasonable cost?
Q7
 In recent years, a number of states
have instituted taxes on patrons of nude
and topless dace bars. Such taxes are
known as “sin taxes,” because they
target behavior that is believed to be
sinful. How do sin taxes relate to the
notion of merit goods?
Q14
 Indicate whether each of the following
statements is true, false, or uncertain,
and justify your answer.
 a. If everyone has the same marginal rate
of substitution, then the allocation of
resources is Pareto efficient.
 b. If the allocation of resources is Pareto
efficient, then everyone has the same
marginal rate of substitution.
 c. A policy change increases social welfare
if, and only if, it represents a Pareto
improvement.
 d. A reallocation from a point within the
utility possibilities curve to a point on the
utility possibilities curve results in a Pareto
improvement.