Public Finance, 2nd Edition

Equation (14.88) is the fundamental equation for evaluating tax changes

in a many-consumer economy with CRS general production technology. By

inspection, the supply responses (qY/qp) aVect the change in social welfare.

Equation (14.88) can also be compared directly with the results from a

one-consumer equivalent economy. Equation (14.17), reproduced here as Eq.

(14.89), calculated the change in loss as:

dL  (t

0

)M

ij



E

1

qY

qp

dt (14:89)

The second term in Eq. (14.88) is very close to Eq. (14.89) but not identical.

A trivial diVerence is the minus sign, resulting from the fact that dW dL.

More importantly, the demand derivatives (qX/qq) in Eq. (14.89) are

the compensated Slutsky terms, not the actual demand derivatives, reXecting

the fact that Eq. (14.89) derives from a conceptual compensation experi-

ment that is not particularly meaningful in a many-person environment. In

practical applications, however, it may prove useful to think of the change

in social welfare resulting from any change in tax rates as a linear combin-

ation of social welfare considerations and dead-weight eY ciency loss, with

the former embodied in the Wrst term of Eq. (14.88) and the latter in the

second term. This interpretation maintains the dichotomy between equity

and eYciency that exists in Wrst-best analysis, but it can only be viewed here

as a rough ``interpretative'' approximation. Whether it is useful or not

depends on the particular problem under consideration. We saw, for

example, that equity and eYciency terms are tightly intertwined in the

many-person optimal commodity tax rules. But it could be more

compelling for simple tax change problems, such as in the Corlett and

Hague analysis. The welfare eVects of such changes can be evaluated directly

by Eq. (14.88),

26

once the equal-revenue pattern of tax changes, d

~

t, has been

determined.

REFERENCES

Atkinson, A., ``How Progressive Should Income Tax Be?,'' in M. Parkin, Ed., Essays in Modern

Economics, Longman Group, Ltd., London, 1973.

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

Journal of Public Economics, July/August 1976.

Balcer, Y., GarWnkel, I., Krynski, K., and Sadka, E., ``Income Redistribution and the Structure

of Indirect Taxation,'' in E. Helpman, A. Razin, and E. Sadka, Eds., Social Policy Evalu-

ation: An Economic Perspective, Academic Press, New York, 1983.

Boadway, R., ``Cost±BeneWt Rules and General Equilibrium,'' Review of Economic Studies, June

1975.

26

Alternatively, Eq. (14.85) with nonconstant returns to scale production. In this case, the

vector of income changes d

~

I

h

would have to be speciWed and incorporated into the total

diVerential of the market clearance equations, Eq. (14.83).

482 REFERENCES

Broadway, R., ``Integrating Equity and EYciency in Applied Welfare Economics,'' Quarterly

Journal of Economics, November 1976.

Bradford, D., and Rosen, H., ``The Optimal Taxation of Commodities and Income,'' American

Economic Association Papers and Proceedings, May 1976.

Diamond, P. A., ``A Many Person Ramsey Tax Rule,'' Journal of Public Economics, February

1975.

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

1975.

Dixit, A., and Munk, K., ``Welfare EVects of Tax and Price Changes: A Correction,'' Journal of

Public Economics, August 1977.

Fair, R., ``The Optimal Distribution of Income,'' Quarterly Journal of Economics, November

1971.

Feldstein, M., ``Distributional Equity and the Optimal Structure of Public Prices,'' American

Economic Review, March 1972.

Green, J., ``Two Models of Optimal Pricing and Taxation,'' Oxford Economic Papers, November

1975.

Guesnerie, R., ``On the Direction of Tax Reform,'' Journal of Public Economics, April 1977.

Guesnerie, R., ``Financing Public Goods with Commodity Taxes: A Tax Reform Viewpoint,''

Econometrica, March 1979.

Harris, R., and Wildasin, D., ``An Alternative Approach to Aggregate Surplus Analysis,''

Journal of Public Economics, April 1985.

Hartwick, J., ``Optimal Price Discrimination,'' Journal of Public Economics, February 1978.

Hatta, T., ``A Theory of Piecemeal Policy Recommendations,'' Review of Economic Studies,

February 1977.

Mirrlees, J., ``An Exploration in the Theory of Optimal Income Taxation,'' Review of Economic

Studies, April 1971.

Mirrlees, J., ``Optimal Commodity Taxation in a Two-Class Economy,'' Journal of Public

Economics, February 1975.

Mirrless, J., ``Optimal Tax Theory: A Synthesis,'' Journal of Public Economics, November 1976.

Sadka, E., ``On Income Distribution, Incentive EVects, and Optimal Income Taxation,'' Review

of Economic Studies, June 1976.

Samuelson, P. A., ``Social IndiVerence Curves,'' Quarterly Journal of Economics, February 1956.

Seade, J., ``On the Shape of Optimal Tax Schedules,'' Journal of Public Economics, April 1977.

Sheshinski, E., ``The Optimal Linear Income Tax,'' Review of Economic Studies, July 1972.

Stern, N., ``On the SpeciWcation of Models of Optimum Income Taxation,'' Journal of Public

Economics, July/August 1976.

Stiglitz, J., and Dasgupta, P., ``DiVerential Taxation, Public Goods and Economic EYciency,''

Review of Economic Studies, April 1971.

14. THE SECOND-BEST THEORY OF TAXATION WITH GENERAL PRODUCTION 483

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