Public Finance, 2nd Edition

GOVERNMENT EXPENDITURE THEORY AND MARKET FAILURE

The Fundamental Theorems of Welfare Economics

Since legitimacy for government intervention is deWned in terms of market

failure, the natural question to ask is ``In what sense do markets fail?'' To

determine the answer, let's begin with the problem of achieving an eYcient

allocation of resources.

The market system is entirely neutral with respect to society's well being,

of course. Nonetheless, if conditions are right, competitive markets generate

an eYcient allocation of resources. The problem for a market economy is that

the conditions or assumptions underlying a perfectly functioning market

system are far too strong. They typically do not hold in practice, and when

they do not a public policy can be described that is pareto superior to the free-

market allocation of resources. That is, the public policy can reallocate

resources so as to make at least one consumer better oV without making

any other consumer worse oV. This principle underlies all normative policy

prescriptions concerned with the allocation of resources.

To determine the subject matter of normative public sector theory, then,

consider the assumptions that would allow a market economy to achieve a

pareto-optimal allocation of resources. These ``best'' assumptions fall into

two distinct groups: a set of market assumptions about the structure of

individual markets within the market economy and a set of technical assump-

tions about consumers' preferences and production technologies.

The market assumptions are necessary to assure that all markets are

perfectly competitive, so that each economic agent is a price taker and acts on

full information. This is the case if four assumptions hold:

a. There are large numbers of buyers and sellers in each market.

b. There is no product diVerentiation within each market.

c. All buyers and sellers in each market have access to all relevant market

information.

d. There are no barriers to entry or exit in markets.

The technical assumptions are required to assure that both consumption

and production activities are ``well behaved,'' so that perfectly competitive

markets do generate a pareto-optimal allocation of resources. Consider the

following set of technical assumptions:

1. Preferences are convex.

2. Consumption possibilities form a convex set.

3. No consumer is satiated.

4. Some consumer is not satiated.

5. Preferences are continuous.

6. Individual utility is a function of one's own consumption and own

factor supplies.

14 GOVERNMENT EXPENDITURE THEORY AND MARKET FAILURE

7. An individual Wrm's production possibilities depend only upon its

own inputs and outputs.

8. Aggregate production possibilities are convex.

Assumptions 6 and 7 rule out the possibility of externalities in either

consumption or production. Assumptions 1, 2, and 5 on individual prefer-

ences are satisWed by the standard assumptions of consumer theory, that

utility functions are quasi concave, continuous, and twice diVerentiable.

Assumptions 3 or 4 are commonly employed in economic analysis. Assump-

tion 8 on aggregate production possibilities implies constant or increasing

opportunity costs and is satisWed if all individual Wrms' production functions

are continuous, twice diVerentiable, and exhibit either decreasing or constant

returns to scale. Assumption 8 rules out signiWcant increasing returns to

scale production, which would imply decreasing opportunity costs, or a

production-possibilities frontier convex to the origin.

Gerard Debreu has shown that:

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a. If assumptions 1, 2, 3, 6, and 7 hold, then a competitive equilibrium is

a pareto optimum.

b. If assumptions 1, 2, 4, 5, 6, 7, and 8 hold, then a pareto optimum can

be achieved by a competitive equilibrium with the appropriate distribution of

income.

Results (a) and (b) are the two fundamental theorems of welfare economics.

Debreu's fundamental theorems of welfare economics have the following

implication for public policy. If the four market assumptions hold so that all

markets are perfectly competitive, and the combination of technical assump-

tions speciWed under (a) or (b) of the fundamental theorems of welfare

economics hold as well, then the government sector would not be required

to make any decisions regarding the allocation of resources. Indeed, it would

not be permitted to do so, according to the normative ground rules.

The Distribution of Income

If all the appropriate market and technical assumptions hold, would there be

anything at all for the government to do? The answer is yes, because of

societie's concern for end-results equity. A perfectly functioning market

system can assure an eYcient allocation of resources. Perfect competition

also satisWes the process equity norm of equality of opportunity and is likely

to ensure a high degree of social mobility. But, even a perfectly functioning

market economy cannot guarantee that the distribution of the goods and

services will be socially acceptable. As noted above, the market takes the

ownership of resources as a given at any point in time. If society deems

4

G. Debreu, The Theory of Value: An Axiomatic Analysis of Economic Equilibrium, Wiley,

New York, 1959, chap. 6.

1. INTRODUCTION TO NORMATIVE PUBLIC SECTOR THEORY 15