Public Finance, 2nd Edition

social welfare function as the objective function, in essence simply adding the

assumption of asymmetric information to existing models. This strategy

makes sense for studying the other-things-equal implications of asymmetric

information. At the same time, however, it implicitly condones the incentive

to exploit private information as natural and socially acceptable behavior.

Is this sensible as a basis for normative policy analysis? If not, what should

the social objective function be? The foundations of normative theory,

always vulnerable at best, become shaky indeed in the face of private infor-

mation.

Private information can greatly complicate the quest for end-results

equity, so let us begin with the distribution question.

LUMP-SUM REDISTRIBUTIONS AND PRIVATE INFORMATION

In a Wrst-best environment, with perfect information, the government should

transfer one good or factor lump-sum to satisfy the interpersonal equity

conditions for a social welfare maximum. Presumably high-ability, high-

income people would be taxed and low-ability, low-income people would

receive transfers.

Lump-sum redistributions on the basis of ability could raise serious

objections, however. Suppose, as is commonly assumed, that everyone has

the same tastes and the social welfare function is equal weighted in the sense

that everyone has the same social marginal utility at the same commodity

bundle. People diVer only in their abilities. Under these assumptions, the

optimal lump-sum redistributions may violate Feldstein's vertical equity

principle of no reversals. The high-ability individuals, who are clearly better

oV before the redistributions, may be worse oV at the social welfare optimum

after the redistributions. The following simple example illustrates the possi-

bility of reversals.

2

Suppose there are two types of people: high-ability people (H) who

receive a wage W

H

and low-ability people (L) who receive a wage

W

L

,W

H

> W

L

. The two types of people have identical utility functions

deWned over a composite commodity, C, and labor, L, with L measured

negatively. Assume further that utility is separable in consumption and

labor:

U(C, L)  f(C)  g(L) (15:1)

with L measured negatively. Markets are competitive, consistent with a Wrst-

best environment, and P

C

 1, the numeraire.

2

The example is taken from J. Stiglitz, ``Pareto EYcient and Optimal Taxation and

the New New Welfare Economics,'' in A. Auerbach and M. Feldstein, Eds., Handbook of

Public Economics, Vol II, Elsevier Sciences Publishers B.V. (North-Holland), Amsterdam,

1987, chap. 15.

15. TAXATION UNDER ASYMMETRIC INFORMATION 487

. Pareto optimality: The two types of people equate their marginal rates of

substitution between consumption and leisure to their wages, as required

for pareto optimality:

g

L

H

f

C

H

 W

H

;

g

L

L

f

C

L

 W

L

(15:2)

. Interpersonal equity: Assuming that the good C is redistributed lump-sum,

the redistribution equalizes the social marginal utility of consumption

across the two types of people (and within each type):

qW

qU

H

f

C

H



qW

qU

L

f

C

L

(15:3)

With an equal-weighted social welfare function and the same tastes, Eq.

(15.3) implies and f

C

H

 f

C

L

and C

H

 C

L

at the social welfare optimum.

But equal consumption, coupled with the pareto-optimal condition, Eq.

(15.2), implies g

L

H

> g

L

L

. The marginal disutility of work is greater for the

high-ability types; they work harder. Therefore, the high-ability people have

the same level of consumption as the low-ability people and work harder at

the social welfare optimum. They are worse oV after the lump-sum redistri-

butions, in violation of Feldstein's no-reversals principle.

The reversal solution is guaranteed in this example because of the separ-

ability assumption. It may not happen with more general, nonseparable

utility, but it could, as illustrated in Fig. 15.1. A and A

0

are the equilibria

for each high-ability person before and after the lump-sum tax, and B and B

0

are the corresponding equilibria for each low-ability person before and after

the lump-sum transfer. A reversal is more likely the larger the redistributions

required to satisfy the interpersonal equity conditions.

Almost everyone would object to a tax-transfer policy that leads to utility

reversals. Therefore, although taxes and transfers based on ability are lump-

sum and Wrst-best optimal, high-ability people have a strong incentive to hide

their ability from the government. Assume they can do so. Given this incen-

tive, a natural modeling strategy is to assume that the government can at best

know people's incomes but not the separate components of their incomes,

their wages or their hours worked. The wage is an index of ability, and

knowing the hours worked, given income, would reveal the wage. But

income is endogenous, so that taxes and transfers of income cannot be

lump sum. Thus, the incentive and the means to hide ability force the

government into a second-best trade-oV between equity and eYciency, in

which the equity gains of redistributing income must be balanced against the

eYciency losses of both taxing and transferring the income. The redistribu-

tions of income must also guard against the possibility of reversals; if

not, high-income, high-ability people have an incentive to represent them-

selves as low-ability people who have high incomes because they work extra

hard.

488 LUMP-SUM REDISTRIBUTIONS AND PRIVATE INFORMATION