Public Finance, 2nd Edition

four times his income. This may appear to be a large gain, but it is made under

the extreme assumption of the richest person having inWnite income. The

minimum economy-wide budget share is likely to be much more than 1/4 as

large as the maximum budget share of the worst-oV individual. Also, this is

the limit of gain for the worst-oV individual, not the average poor person.

Sah conducts a number of simple exercises to get some feeling for the

amount of redistribution that is likely though commodity taxes and subsidies.

The variations include optimal taxation with a Rawlsian social welfare

function; CES utility functions with varying degrees of elasticity of substitu-

tion, from Cobb±Douglas to Leontief; two classes of people with diV erent

preferences; uniform preferences with an arbitrary number of classes; wide

diVerences in the range of incomes from richest to poorest; and one experi-

ment using actual data for the U.K. and the linear expenditure system. The

exercises almost always produce very modest proportional gains in the real

income of the worst-oV individual(s), usually less than 1.5 and often much

less. Sah concludes that not much redistribution is likely to be possible

through commodity taxes and subsidies.

The only caveat is if the rich consume some goods that the poor do not

consume and vice versa. Then indirect taxes and subsidies can be targeted to

the rich and poor just as income taxes can, with much greater redistributional

impact. The only natural limitation on the amount of redistribution is the size

of the tax base on the items consumed exclusively by the rich. For instance,

how much revenue can the government raise from a tax on yachts?

6

OPTIMAL TAXATION, PRIVATE INFORMATION, AND

SELF-SELECTION CONSTRAINTS

Suppose society decides that it has to resort to direct taxes on income to

achieve the redistributional bite that it wants from its tax system. It then has

to confront the two problems with income taxes mentioned above. One is the

trade-oV between the distributional gains and the eYciency losses of taxing

endogenous income. The other is the potential of violating Feldstein's verti-

cal equity principle of no reversals. This section focuses on the second

6

The analysis in this section should not leave the impression that commodity taxes

necessarily avoid problems of imperfect information. The diversion of goods to black markets

in an eVort to escape taxation is always a potential problem, especially in low-income countries.

John McLaren has recently published an analysis of optimal commodity taxes when evasion

through black markets is possible. His model generates a number of interesting conclusions. One

of the more compelling is that the government might want to tax just one good rather than used a

broader based sales tax to save on enforcement costs. This is exactly what many of the poorer

developing economies choose to do when they begin to levy taxes. Later on in this chapter we

present an analysis of tax evasion under an income tax. Space limitations prevent a presentation

of McLaren's model as well, but interested readers should consult J. McLaren, ``Black Markets

and Optimal Evadable Taxation,'' Economic Journal, May 1998.

15. TAXATION UNDER ASYMMETRIC INFORMATION 493