Public Finance, 2nd Edition

implies raising the tax on the good relatively more complementary (less

substitutable) with leisureÐfor example, raising t

j

if, roughly speaking,

M

1j

< M

1k

and vice versa. The only other possibility in a three-good world

is for one of the goods to be a Slutsky substitute for leisure (say, M

1k

> 0)

while the other is neither a substitute nor a complement (M

1j

 0). In this

case, the tax should be increased on the good for which the cross-price

derivative is zero, since it is relatively more complementary with leisure.

(Both goods cannot be Slutsky complements, since

P

3

k1

q

k

M

1k

 0 from

homogeneity of the compensated demand functions and M

11

< 0.)

Note, Wnally, that the Corlett±Hague analysis applies, strictly speaking,

only for small changes in taxes. Using the homogeneity conditions to obtain

expressions in terms of M

1k

and M

1j

requires evaluating all demand relation-

ships (M

k

,M

jk

, etc.) at the original proportional tax prices. The larger the tax

changes, the more inaccurate this evaluation becomes. There are no longer

any simple relationships between M

1k

and

P

ik; j

t

i

M

ik

or between M

1j

and

P

ik, j

t

i

M

ij

.

REFERENCES

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Journal of Public Economics, Vol. 1, 1972.

Atkinson, A., and Stiglitz, J., ``The Design of Tax Structure: Direct vs. Indirect Taxation,''

Journal of Public Economics, July / August 1976.

Baumol W., and Bradford, D., ``Optimal Departures from Marginal Cost Pricing,'' American

Economic Review, June 1970.

Besley, T., and Jewitt, I., ``Uniform Taxation and Consumer Preferences,'' Journal of Public

Economics, September 1995.

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Browning, E., ``The Excess Burden of Excise vs. Income Taxes: A SimpliWed Comparison,''

Public Finance, 3, 1975.

Browning, E., ``The Marginal Cost of Public Funds,'' Journal of Political Economy, April 1976.

Corlett, W., and Hague, D., ``Complementarity and the Excess Burden of Taxation,'' Review of

Economic Studies, Vol. 21(1), No. 54, 1953±1954.

Diamond, P. A., and McFadden, D., ``Some Uses of the Expenditure Function in Public

Finance,'' Journal of Public Economics, Vol. 3, 1974.

Diamond, P. A., and Mirrlees, J., ``Optimal Taxation and Public Production'' (2 parts; Part 1:

`Production EYciency,' Part II: `Tax Rules'), American Economic Review, March, June

1971.

Dixit, A., ``Welfare EVects of Tax and Price Changes,'' Journal of Public Economics, February

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