Public Economics

Chikako YamauchiAssistant Professor, GRIPS

Lecture 3

Rosen, Ch. 3 Tools of Normative Analysis

What Should Government Do?

1. Should income taxes be cut?2. Do we need to subsidize the purchase of

medicine for the elderly?3. Should we increase value-added tax to

cover social security payments?4. Should we introduce national health

insurance?

Welfare Economics Need systematic framework to assess the

desirability of various government actions. Welfare economics provides criteria to analyze the

social desirability of alternative economic states. Distinguishes cases when private markets work

well from cases where government intervention may be warranted.

Relies heavily on basic microeconomic tools, particularly indifference curves.

Pure Exchange EconomyEconomy with 2 people (Adam & Eve) 2 commodities (Apples & Figs)

Fixed supply of commodities (ignore production; but changing production levels would modify the box dimensions)

Question: How should the 2 commodities be allocated?

An Edgeworth Box depicts the distribution of goods between the two people.

Pure Exchange EconomyFig 3.1: Adam gets Ox while Eve gets Oy

Each point represents an allocation between Adam and Eve.

At point v, Adams allocation of apples is Ox, and of figs is Ou. Eve consumes Oyof apples, and Ow of figs

Pure Exchange EconomyFig 3.1: Adam gets Ox while Eve gets Oy

Adams consumption of apples and figs increases as we move this way

Eves consumption of apples and figs increases as we move this way

Each point fully exhausts the resources on the island. Adam consumes what Eve doesnt.

Fig 3.2: A3 is better than A2, A2 is better than A1

Assume that Adam and Eve each has conventionally shaped indifference curves

Adams utility is higher for bundles toward the northeast in the Edgeworth Box

Adam would get even higher utility by moving further to the northeast, outside of the Edgeworth Box. Can he do that?

Fig 3.2: A3 is better than A2, A2 is better than A1

NO! Adam is constrained by the resources available in the island

Similarly, Eves utility is higher for bundles toward the southwest in the Edgeworth Box

Eves indifference curves therefore are flipped around. Her utility is higher on E3 compared E2 or E1

Figure 3.3: initial point gSuppose we are at g, some arbitrary point in the Edgeworth Box.Is it possible to reallocate apples and figs between Adam and Eve to make Adam better off, while Eve is made no worse off?

Fig. 3.3: point g < point h < point pAllocation h is one possibility. We are moving along Eves indifference curve, so her utility remains unchanged. Adams utility clearly increases.

At g, Adam is willing to give up many figs for an apple, but Eve will give up an apple for only a little fig. Thus, a trading opportunity exists.

Fig. 3.3: no way to make A better-off without making Eve worse off

Clearly, other allocations achieve this same goal, such as allocation p.

Once we reach allocation p, we cannot raise Adams utility any more, while keeping Eves utility unchanged.

Pure Exchange Economy An allocation is Pareto efficient if the only

way to make one person better off is to make another person worse off. Often used as the standard for evaluating

desirability of an allocation of resources. Pareto inefficient allocations are wasteful.

A Pareto improvement is a reallocation of resources that makes one person better off without making anyone else worse off.

Many allocations are Pareto efficientAllocations p, p1 and p2 are all Pareto efficient.

For Adam, p1

Contract Curve In fact, there is a whole set of Pareto efficient

points in the Edgeworth Box= contract curve

Contract curve is the locus of all the Pareto efficient points

Mathematical Characterization of Pareto Efficiency

Each of the Pareto efficient points is where an indifference curve of Adam is tangent to an indifference curve of Eve.

Mathematically, the slopes of Adams and Eves indifference curves are equal.

The (absolute value of) slope of the indifference curve indicates the rate at which the individual is willing to trade one good for another, know as the marginal rate of substitution (MRS).

Pareto efficiency requires: Adam Eveaf afMRS MRS

Production Economy In pure exchange economy, assumed

supplies of commodities were fixed. Now consider scenario where quantities

can change.

Production Possibilities Curve The production

possibilities curveshows the maximum quantity of figs that can be produced with any given quantity of apples, given the scarcity of the resources in the economy.

Production Economy For apple production to be increased, fig

production must necessarily fall. The marginal rate of transformation (MRT) of

apples for figs (MRTaf) shows the rate at which the economy can transform apples to fig leafs.

It is the absolute value of the slope of the production possibilities curve.

The marginal rate of transformation can be written in terms of marginal costs: a

aff

MC wyMRTMC xz

Efficiency with Variable Inputs With variable production, efficiency requires:

If this were not the case, it is possible to make one person better off with an adjustment of production. Rewriting in terms of marginal costs, we then have:

Adam Eveaf af afMRT MRS MRS

Adam Eveaaf af

f

MC MRS MRSMC

Paretoimprovementwithproduction

E0 E0

E

OAdam OAdam

OEve

OeveMRS

MRSMRT

MRT

MRSisnotequaltoMRT MRS=MRT

Paretoimprovementwithproduction

E0

E

E0

E

WhathappenedtoAdam WhathappenedtoEve

First Fundamental Theorem of Public Economics

Assume that 1. All producers and consumers act as perfect competitors (e.g.,

no market power) 2. A market exists for each and every commodity

Under these assumptions, the first fundamental theorem of welfare economics states that a Pareto efficient allocation will emerge.

Implication: Competitive economy automatically allocates resources efficiently, without central planning. (Adam Smiths invisible hand)

Conclusion: Free enterprise systems are amazingly productive.

First Fundamental Theorem of Public Economics

Intuition behind proof Price-taking consumers maximize utility by doing:

for i = Adam, Eve

This implies: Price-taking producers maximize profits by doing:

for k = a (apple), f (fig) This implies

Therefore,

i aaf

f

PMRSP

aa afff

P MC MRSP MC

k kMC P

Adam Eveaf afMRS MRS

Adam Eveaf af afMRS MRS MRT

Pareto efficient allocation conditions

Pareto efficient points do not necessarily allocate A&F equally [Fig 3.7a]

p5 *q *

If society values equal distribution more than efficiency, q might be better.

While the First Fund. Thm. says a competitive system will lead to P.E. allocation, there is no reason to think that this point maximizes social welfare

Pareto efficiency does not ensure fairness. Both p4 & p5 are Pareto efficient, but very unequal. Is q better than p5?

Utility possibilities curve shows well-being of A&E on PE points [Fig 3.10]

From the contract curve in the Edgeworth Box, we could graph the relationship between Adams and Eves utilities, on the utility possibilities curve.

Utility possibility curve shows a collection of Pareto efficient points, but different allocations of utility

The frontier of the utility possibilities curve is, by definition, attainable. Similar to a budget constraint.

How do we choose the best point?

Social welfare function

Could postulate a social welfare function, which embodies societys views on the relative well-being of Adam and Eve:

Could then maximize societys preferences, or demonstrate that some Pareto-inefficient bundles are preferred to some other Pareto-efficient ones.

,Adam EveW F U U

(i) Pareto efficient(ii)Not Pareto efficient, but preferred

to (i). This means that society values a more equal distribution of income, even if it is not efficient

(iii) Efficient and produces greatest total utility for society

Social welfare function [Fig 3.12]

Second Fundamental Theorem of Public Economics

The second fundamental theorem of welfare economics states that society can attain any Pareto-efficient allocation of resources by making a suitable assignment of initial endowments and then allowing free trade.

No adjustments to prices needed

(this statement is based on the assumption that government can reallocate endowments. Problems arise if the only available mechanisms for doing so, such as taxes, themselves induce inefficiencies)

Role of the Government The 2nd theorem suggests that, if society values

more than just efficiency, then government action may be needed to create fairness in the distribution of goods and resources

The 2nd theorem suggests that governmental intervention is not necessary as long as the two assumptions hold Consumers and producers are price takers There is a market for every good Government action may be needed when these two

assumptions do not hold

Market Failure 1: Market Power A firm that has the power to set prices (not a price-taker)

can raise prices above MC by supplying less output than perfect competition would produce

This will violate one of the P.E. conditions

The market will have imperfect competition Examples:

monopoly (one firm in a market) oligopoly (a few firms in a market) differentiated market (many firms in a market, but their products

are perceived to be of different quality) Shoes by Nikes and Adidas are different from shoes sold at

supermarkets

aa

ff

P MCP MC

Market Failure 2: Markets May Not Exist for Certain Goods

Public goods: once provided, everyone can consume without pay, or nonrival and nonexcludable in consumption People try to free-ride. So the market mechanism may not have a way to

force people to reveal their preferences for the good to be produced E.g., national defense, lighthouses, parks

Goods that have externality: a persons behavior affects another, and his private marginal costs do not match social marginal costs E.g., even if your roommate smokes in your room (consuming clean air

in the room), he only pays for his cigar, not for clean air in the room Insurance:

asymmetric information (buyer has information that is not available to seller, or vice versa) can lead to adverse selection (buyers only buy insurance for job loss when it is likely to happen) and moral hazard (not work hard once insured)

P.E. conditions do not hold ,k kMC P i aaff

PMRSP

Controversies surrounding the Welfare Economics Framework

Social welfare function assumes that there is an agreedgoal, and it is to maximize peoples utilities However a society could have different goals: increase the

power of the state, glorify God, etc. The framework is based on the assumption that people

know whats good for them. If people have ill-formed or corrupt preferences, then trying to maximize this utility is irrelevant merit goods: goods which ought to be provided, even if people

do not demand them, such as fine arts --- disguised value judgment?

The framework focuses on results, not processes through which the allocation of resources is made But how about whether people can freely enter contracts, and

whether public processes are democratic?

Advantages of the Welfare Economics Framework

It provides a coherent framework for assessing public policy through evaluating allocationswhich result from alternative policies

It impels us to ask three key questions in order to judge whether intervention is needed

Will it have desirable distributional consequences? Will it enhance economic efficiency? Can it be done at a reasonable cost?

Asking the right questions provides an invaluable structure for the decision-making process