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In Praise of Frank Ramsey's Contribution to the Theory of Taxation
Article first published online: 29 MAR 2015
DOI: 10.1111/ecoj.12187
© 2015 The Authors. The Economic Journal published by John Wiley & Sons Ltd on behalf of Royal Economic Society.
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The Economic Journal
Special Issue: 125TH ANNIVERSARY ISSUE
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- I owe a great debt to my co-authors with whom I have written work that may be considered to follow in Ramsey's footsteps – Richard Arnott, Bob Brito, Shahe Emran, John Hamilton, Raaj Sah, Steve Slutsky and most especially Tony Atkinson and Partha Dasgupta; and like all those who toil in these fields, I owe a debt to Peter Diamond and James Mirrlees, who not only shaped the modern theory of optimal taxation but also shaped my own thinking. I am indebted to Frederic Vermeulen and an anonymous referee for their helpful comments on an earlier draft and to Sandesh Dhungana and Eamon Kircher-Allen for research and editorial assistance. Financial support from INET is gratefully acknowledged.
Frank
Ramsey's brilliant 1927 paper, modestly entitled, ‘A contribution to
the theory of taxation’, is a landmark in the economics of public
finance. Nearly a half century later, through the work of Diamond and
Mirrlees (1971) and Mirrlees (1971), his paper can be thought of as launching the field of optimal taxation and revolutionising public finance.1
Ramsey, in his short life, made pathbreaking contributions to two other fields, the theory of optimal growth (Ramsey, 1928) and the theory of subjective probability (Ramsey, 1926).2
Here, he addresses a question which he says was posed to him by A. C.
Pigou: given that commodity taxes are distortionary, what is the best
way of raising revenues, i.e. what is the set of taxes to raise a given
revenue which maximises utility. The answer is now commonly referred to
as Ramsey taxes. The basic insight was that taxes should be set so as to
reduce the consumption of each good (along its compensated demand
curve) equi-proportionately. He establishes this result in two contexts:
- if the government needs to raise only a small amount of tax revenue; and
- if utility functions are quadratic.
The
analysis is beautiful, mathematically sophisticated, making use of all
the artillery in the theory of consumer behaviour, including the
symmetry of the Slutsky relations. The conclusion overturned simplistic
analyses that somehow continue to prevail in some quarters for decades
after Ramsey's paper and, in some subfields of economics, continue to
this day. Some economists argued against differential taxation on the
grounds that it is best just to have a single tax (typically on wages). A
wage tax introduces a single distortion – between the marginal rate of
substitution between labour and consumption and the marginal rate of
transformation. Interest income taxes and commodity taxes introduce
additional distortions. (Interestingly, Ramsey's analysis has, wrongly,
continued to be used by some economists to argue against the taxation of
capital.)3
As
another example of such simplistic economics, some macroeconomists
continue to argue that monetary authorities should only interfere with
the market in setting short-term interest rates.
Ramsey
showed that efficient taxation required imposing a complete array of
taxes – not just a single tax. A large number of small distortions,
carefully constructed, is better than a single large distortion. And he
showed precisely what these market interventions would look like. (He
even explains that the optimal intervention might require subsidies –
what he calls bounties – for some commodities. ‘A tax on sugar might
reduce the consumption of damsons more than in proportion to the
reduction in the total consumption of sugar and so require to be offset
by a bounty on damsons’, Ramsey, 1927,
p. 54). Similar reasoning would suggest that if there are a variety of
tools for managing the macroeconomy, in general, they should all be
employed.
In this short celebratory article, I briefly describe Ramsey's basic insights (Section 'Major Insights'), and the early history of the development of the ideas based on Ramsey's paper (Section 'Earlier Dissemination').
While several of these crucial developments showed that Ramsey's
conclusions held under more general conditions than he had assumed,
later analyses showed crucial qualifications, so that the policy
relevance of Ramsey's analysis may be limited.