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Chapter 2 Fundamentals of Welfare Economics

- -In order to evaluate government policies, we

need a starting point - -Welfare Economics the branch of economic

theory concerned with the social desirability of

alternate economic states and policies

Chapter 2 Fundamentals of Welfare Economics

- Welfare Economics
- First Fundamental Theorem of Welfare Economics
- Second Fundamental Theorem of Welfare Economics

Theory - Starting Point Pure Exchange Economy

- We start with a simple model
- 2 people
- 2 goods, each of fixed quantity
- Determine good allocation
- The important results of this simple, 2-person

model hold in more real-world cases of many

people and many commodities

Pure Exchange Economy Example

- Two people Maka and Susan
- Two goods Food (f) Video Games (V)
- We put Maka on the origin, with the y-axis

representing food and the x axis representing

video games - If we connect a flipped graph of Susans goods,

we get an EDGEWORTH BOX, where y is all the food

available and x is all the video games

Makas Goods Graph

Ou is Makas food, and Ox is Makas Video Games

u

Food

O

x

Video Games

Maka

Edgeworth Box

Susan

y

O

Ow is Susans food, and Oy is Susans Video

Games

r

Total food in the market is Or(Os) and total

Video Games is Os (Or)

u

Food

w

Each point in the Edgeworth Box represents one

possible good allocation

O

s

x

Video Games

Maka

Edgeworth and utility

- We can then add INDIFFERENCE curves to Makas

graph (each curve indicating all combinations of

goods with the same utility) - Curves farther from O have a greater utility
- (For a review of indifference curves, refer to

Intermediate Microeconomics) - We can then superimpose Susans utility curves
- Curves farther from O have a greater utility

Makas Utility Curves

Makas utility is greatest at M3

Food

M3

M2

M1

O

Video Games

Maka

Edgeworth Box and Utility

Susan

O

Susan has the highest utility at S3

r

S1

A

S2

At point A, Maka has utility of M3 and Susan has

Utility of S2

S3

Food

M3

M2

M1

O

s

Video Games

Maka

Edgeworth Box and Utility

Susan

O

If consumption is at A, Maka has utility M1 while

Susan has utility S3

r

A

B

S3

By moving to point B and then point C, Makas

utility increases while Susans remains constant

C

Food

M3

M2

M1

O

s

Video Games

Maka

Pareto Efficiency

Susan

O

Point C, where the indifference curves barely

touch is called PARETO EFFICIENT, as one person

cant be made better off without harming the

other.

r

S3

C

Food

M3

M2

M1

O

s

Video Games

Maka

Pareto Efficiency

- When an allocation is NOT pareto efficient, it is

wasteful (at least one person could be made

better off) - Pareto efficiency evaluates the desirability of

an allocation - A PARETO IMPROVEMENT makes one person better off

without making anyone else worth off (like the

move from A to C) - However, there may be more than one pareto

improvement

Pareto Efficiency

Susan

O

If we start at point A -C is a pareto

improvement that makes Maka better off -D is a

pareto improvement that makes Susan better off -E

is a pareto improvement that makes both better off

r

A

S3

C

S4

Food

S5

E

M3

M2

D

M1

O

s

Video Games

Maka

The Contract Curve

- Assuming all possible starting points, we can

find all possible pareto efficient points and

join them to create a CONTRACT CURVE - All along the contract curve, opposing

indifferent curves are TANGENT to each other - Since the slope of the indifference curve is the

willingness to trade, or MARGINAL RATE OF

SUBSTITUTION (x for y) (MRSxy), along this

contract curve

Pareto Efficiency Condition

The Contract Curve

Susan

O

r

Food

O

s

Video Games

Maka

MATH House and Chase

- Assume that house and Chase have the following

utilities and MRS for books and coffee

The Pareto Efficiency Condition therefore becomes

MATH House and Chase

- If there are 10 books, and 4 cups of coffee, then

the contract curve is expressed as

If House has 6 books, a pareto efficient

allocation would be

MATH House and Chase

- Therefore, House would have 6 books and 2.4 cups

of coffee, and Chase would have 4 (10-6) books

and 1.6 (4-2.4) cups of coffee, for utilities of

Theory - Starting PointEconomy with production

- A production economy can be analyzed using the

PRODUCTION POSSIBILITIES CURVE/FRONTIER - The PPC shows all combinations of 2 goods that

can be produced using available inputs - The slope of the PPC shows how much of one good

must be sacrificed to produce more of the other

good, or MARGINAL RATE OF TRANSFORMATION (x for

y) (MRTxy) - Note that although the slope is negative, the

negative is assumed and rarely shown in simple

calculations

Production Possibilities Curve

Here the MRTSpr is equal to (7-5)/(2-1)-2, or

two robots must be given up for an extra pizza.

10

9

8

The marginal cost of the 3rd pizza, or MCp2

robots

7

6

The marginal cost of the 6th and 7th robots, or

MCr1 pizza

Robots

5

4

Therefore, MRTxyMCx/MCy

3

2

Therefore, MRTpr2/12

1

1

2

3

4

5

6

7

8

Pizzas

Efficiency and Production

- If production is possible in an economy, the

Pareto efficiency condition becomes

- Assume MRTpr3/4 and MRSpr2/4.
- -Therefore Maka could get 3 more robots by

transforming 4 pizzas - -BUT Maka only needs to get 2 robots for 4 pizzas

to maintain utility - -Therefore his utility increases from the extra

robot, Pareto efficiency isnt achieved

Efficiency Production Example

- From the PPC, we know that

- We can therefore reinterpret Pareto efficiency

as

Theory - First Fundamental Theorem Of Welfare

Economics

- IF
- All consumers and producers act as perfect

competitors (no one has market power) - and
- 2) A market exists for each and every commodity
- Then
- Resource allocation is Pareto Efficient

First Fundamental Theorem of Welfare Economics

Origins

- From microeconomic consumer theory, we know that

- Since prices are the same for all people

- Therefore economic theory gives us the first part

of Pareto efficiency

First Fundamental Theorem of Welfare Economics

Origins

- From basic economic theory, a perfect competitive

firm produces where PMC, therefore

- But we know that MRT is the ratio of MCs,

therefore

First Fundamental Theorem of Welfare Economics

Origins

- Again from microeconomic consumer theory, this

changes to

- Which satisfies the second requirement of Pareto

Efficiency - Therefore, we can expand Pareto Efficiency to

imply that

Efficiency?Fairness

- If Pareto Efficiency was the only concern,

competitive markets automatically achieve it and

there would be very little need for government - Government would exist to protect property rights
- Laws, Courts, and National Defense
- But Pareto Efficiency doesnt consider

distribution. One person could get all societys

resources while everyone else starves. This

isnt typically socially optimal.

Fairness

Susan

O

r

Points A and B are Pareto efficient, but either

Susan or Maka get almost all societys resources

B

C

Food

A

Many would argue C is better for society, even

though it is not Pareto efficient

O

s

Video Games

Maka

Fairness

- For each utility level of one person, there is a

maximum utility of the other - Graphing each utility against the other gives us

the UTILITY POSSIBILITIES CURVE - Just as typical utility is a function of goods

consumed Uf(x,y), societal utility can be seen

as a function of individual utilities Wf(U1,U2) - This is referred to as the SOCIAL WELFARE

FUNCTION, and can produce SOCIAL INDIFFERENCE

CURVES

Utility Possibilities Curve

All points on the curve are Pareto efficient,

while all points below the curve are not. Any

point above the curve is unobtainable

B

Makas Utility

C

A

O

Susans Utility

Maka

Typical Social Indifference Curves

An indifference curve farther from the origin

represents a higher level of social welfare.

Makas Utility

O

Susans Utility

Maka

Fairness

- If we superimpose social indifference curves on

top of the utilities possibilities curve, we can

find the Pareto efficient point that maximizes

social welfare - This leads us to the SECOND FUNDAMENTAL THEOREM

OF WELFARE ECONOMICS

Maximizing Social Welfare

ii is preferred to i, even though ii is not

Pareto efficient

i

ii

The highest possible social welfare, iii, is

Pareto efficient

Makas Utility

iii

O

Susans Utility

Maka

Second Fundamental Theorem of Welfare Economics

- The SECOND FUNDAMENTAL THEOREM OF WELFARE

ECONOMICS states that society can attain any

Pareto efficient allocation of resources by

making a suitable assignments of original

endowments, and then letting people trade - -Roughly, by redistributing income, society can

pick the starting point in the Edgeworth box,

therefore obtaining a desired point on the

Utility Possibility Frontier

Second Fundamental Theorem of Welfare Economics

Susan

O

r

Starting Point

Goal

Food

O

s

Video Games

Maka

Why Income Redistribution?

- Why achieve equity through income redistribution

instead of taxes/penalties and subsidies/incentive

s? - Taxes and penalties punish income-enhancing

behavior, encouraging people to work less. - Subsidies and incentives give an incentive to

stay in a negative state to keep receiving

subsidies and incentives. - Lump sum transfers have the least distortion.

Why Is Government so Big?

- Government has to ensure property laws are

protected. (1st Theorem) - Government has to redistribute income to achieve

equity. (2nd Theorem) - Often the assumptions of the First Welfare

Theorem do not hold (Chapter 3)

Welfare Economics Limitations

- We Assume Government exists to maximize the

utility of its citizens. - Government could aim to Be a global power,

achieve cultural goals, achieve religious goals,

etc. - Pluswhat if people want to sit on the couch all

day, watching the Biggest Loser? - Should the government support this activity?

Merit Goods

- Merit Good commodities that should be provided

even if society - doesnt want them ie police/fluorine in water
- And/Or
- b) is unwilling to cover their cost in the free

market - ie Canadian Broadcast Corporation (CBC)

Welfare Economics Evaluation

- -Welfare Economics is concerned with RESULTS, not

PROCESS - -is the HOW important?
- -contract law?
- -Old Testament law?
- -Lottery?
- -Free-for-all wrestling match?

Welfare Economics Evaluation

- Welfare Economics asks 3 questions of every

government action - Will it have desirable distributional

consequences? - Will it enhance efficiency?
- Is the cost reasonable?
- -Although these questions may be difficult to

answer, they provide direction, and if they are

all no, the government shouldnt interfere