Public Finance, 2nd Edition

13

THE SECOND-BEST THEORY OF

TAXATION IN ONE-CONSUMER

ECONOMIES WITH LINEAR

PRODUCTION TECHNOLOGY

GENERAL EQUILIBRIUM PRICE MODELS

THE MEASUREMENT OF LOSS FROM DISTORTING TAXES

The Geometry of Loss Measurement: Partial Equilibrium Analysis

The Geometry of Loss Measurement: General Equilibrium Analysis

The Analytics of General Equilibrium Loss Measurement

Policy Implications of the Loss Measures

THE OPTIMAL PATTERN OF COMMODITY TAXES

Policy Implications of the Optimal Tax Rule

SUBSTITUTIONS AMONG TAXES: IMPLICATIONS FOR

WELFARE LOSS

The Corlett and Hague Analysis

The second-best theory of taxation explores the eVects of distorting taxes

on social welfare. A distorting tax is one that prevents at least one of the Wrst-

best pareto-optimal conditions from holding; that is, it forces society inside

its Wrst-best utility-possibilities frontier. The Wrst-best pareto-optimal condi-

tions are equalities between marginal rates of substitutions and marginal

rates of transformation. As such, they require that agents face the same prices

in a market economy. Distorting taxes prevent the equalities from holding

because they force at least two economic agents in the same market to face

diVerent prices in an otherwise perfectly competitive economy. Virtually all

taxes actually employed by governments introduce some distortion into the

economy, whether they be sales, excise, income, or wealth taxes. (Transfer

payments are automatically included in the analysis because transfers are

analytically equivalent to negative taxes.)

Because tax distortion is deWned relative to pareto optimality, much of

the literature on second-best tax theory has treated it strictly as an allocational

399

issue, concerned only with questions of economic eYciency. Consequently,

the analysis often occurs within the context of one-consumer economies, a

simpliWcation that makes sense if one is willing to ignore distributional

concerns. As Chapter 12 noted, however, second-best analysis has shown

that allocational and distributional issues do not dichotomize in a second-

best environment without lump-sum taxes and transfers, thereby raising

questions about the policy relevance of considering the eYciency aspects of

distorting taxes independently from their distributional consequences. Prob-

ably no one today would recommend a set of taxes simply on the basis of

their eYciency properties. Nonetheless, it is analytically convenient to isolate

the eYciency eVects of taxes by using one-consumer economy models. We

can then consider the tax rules in many-person economies as combinations of

eYciency and distributional elements, with the latter represented by the social

welfare weights derived from an individualistic social welfare function. This is

the approach we will take in developing the second-best theory.

The theory of distorting taxation addresses three main questions, one

associated with welfare loss, another with optimality, and a third with tax

reform:

1. Welfare lossÐRelative to the Wrst-best optimum, what is the loss in

social welfare associated with any given set of distorting taxes (including a

single tax)? Harold Hotelling provided the Wrst rigorous analysis of this issue

in his 1938 article, ``The General Welfare in Relation to Problems of Tax-

ation and of Railway and Utility Rates.''

1

Arnold Harberger rekindled

interest in this question in two separate articles appearing in 1964, ``Taxation,

Resource Allocation and Welfare'' and ``The Measurement of Waste.''

2

By

now the literature is voluminous, with these three articles standing as the

seminal contributions.

2. OptimalityÐRelative to the Wrst-best optimum, what pattern of dis-

torting taxes minimizes the loss in social welfare for any given amount of tax

revenue the government might wish to raise? This question has been explored

under two separate assumptions: (a) that the government can tax all goods

and factors, and (b) that a subset of goods and factors must remain untaxed.

The study of optimal taxation under the Wrst assumption is commonly re-

ferred to as the optimal commodity tax problem, with seminal contributions

by Frank Ramsey in ``A Contribution to the Theory of Taxation'' (1927), and

Peter Diamond and James Mirrlees' ``Optimal Taxation and Public Produc-

1

H. Hotelling, ``The General Welfare in Relation to Problems of Taxation and of Railway

and Utility Rates,'' Econometrica, July 1938.

2

A. Harberger, ``Taxation, Resource Allocation and Welfare,'' in National Bureau of

Economic Research and the Brookings Institution, The Role of Direct and Indirect Taxes in the

Federal Revenue System, (Princeton University Press, Princeton N.J., 1964; A. Harberger, ``The

Measurement of Waste,'' American Economic Association Papers and Proceedings, May 1964. An

excellent recent reference for the early literature is J. Green and E. Sheshinski, ``Approximating

the EYciency Gains of Tax Reforms,'' Journal of Public Economics, April 1979.

400 THE SECOND-BEST THEORY OF TAXATION IN ONE-CONSUMER ECONOMIES