Public Finance, 2nd Edition

A BRIEF HISTORY OF SECOND-BEST THEORY

Second-best theorizing swept into public sector economics to stay in the

1970s and has been at the forefront of the discipline ever since. The impetus

was provided by two seminal articles that appeared about ten years apart:

``The General Theory of Second-Best,'' by Archibald Lipsey and Kelvin

Lancaster, and ``Optimal Taxation and Public Production,'' by Peter Dia-

mond and James Mirrlees.

2

The two articles approached second-best analysis

from diVerent perspectives and each became a template for distinct branches

of the second-best literature that followed.

The Lipsey±Lansacter paper took the natural Wrst step away from the

Samuelson's Wrst-best general equilibrium model. Their model assumes that

price exceeds marginal cost in at least one market, either because of private

monopoly power or distorting government taxes, and that the government is

unwilling or unable to remove the distortion. Otherwise, the government has

as much freedom to act as it has in the Wrst-best model, including the ability to

redistribute income lump sum.

Lipsey and Lancaster were speciWcally interested in the following

question: Given maintained distortions in some markets, are the Wrst-best

pareto-optimal rules for other markets still consistent with social welfare

maximization? The answer turned out to be ``no'' in general, a result that

became known as the ``theorem of the second best.'' Subsequent research has

expanded their analysis to consider the eVects of maintained distortions on

Wrst-best public expenditure decision rules and on the welfare implications of

changing the pattern of distorting taxes. One can ask, for example, whether

substituting one set of distorting taxes for another while holding tax revenue

constant increases social welfare, given the existence of still other distortions.

These are issues of policy reform in a second-best environment, by now a huge

body of literature in the Lipsey±Lancaster mold.

The Diamond±Mirrlees model was also only one step removed from

Samuelson's Wrst-best model, but they asked a diVerent question from Lip-

sey±Lancaster. The only maintained restriction in their model is that the

2

R. Lipsey and K. Lancaster, ``The General Theory of Second-Best,'' Review of Economic

Studies, Vol. 24 (1), No. 63, pp. 1956±57; P. Diamond and J. Mirrlees, ``Optimal Taxation and

Public Production,'' American Economic Review, March, June 1971 (2 parts; Part I: Production

EYciency, Part II: Tax Rules). The Diamond/Mirrlees paper was completed in 1968 and widely

circulated as an MIT Working Paper. It was well known and widely cited by the time it was

published in 1971. Two other early articles are worth mentioning, one on production and one on

taxation: M. Boiteux, ``On the Management of Public Monopolies Subject to Budgetary Con-

straints,'' Journal of Economic Theory, September 1971 (Boiteux's article Wrst appeared in the

January 1956 Econometrica in French); and J. Stiglitz and P. Dasgupta, ``DiVerential Taxation,

Public Goods, and Economic EYciency,'' Review of Economic Studies, April 1971. These articles

are frequently referenced in the second-best literature. For an excellent (but diYcult) summary of

second-best methodology, see H. Green, ``Two Models of Optimal Pricing and Taxation,''

Oxford Economic Papers, November 1975.

390 A BRIEF HISTORY OF SECOND-BEST THEORY