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  • Could a Basic Result in Optimum Commodity Taxation Theory Have Been Derived Much Earlier than It Was?
  • Alan Martina

An important new theoretical result in any academic discipline is one that probably reflects a different way of thinking about a relevant problem. Once this initial theoretical result has been published, it seems reasonable to surmise, however, that related additional results would follow reasonably quickly. This is especially so if the new way of thinking can be combined with other relevant results to be found in the relevant literature. This conjecture is not supported, however, by some of the history of economic thought concerning the theory of optimum taxation. Rather there was a considerable delay between the publication in 1927 of the important initial result by Frank Ramsey of his proposition in commodity taxation theory and the generalizations of this result provided by Diamond and Mirrlees in 1971.

The central thesis developed here is that this delay in deriving this generalization was longer than it needed to have been. In support of this thesis it will be argued that all the additional analytical tools required to derive the Diamond-Mirrlees generalization of Ramsey’s initial result were available in the relevant Italian economic literature by 1916. Thus the Diamond-Mirrlees generalization of the Ramsey result could have been provided in 1927—that is if Ramsey, or some capable person, had been familiar with the relevant literature.

Even if this argument is not accepted, it still can be demonstrated [End Page 139] that the Ramsey result could have been generalized in either 1927 or 1938. The one generalization, which is less general than that provided by Diamond and Mirrlees, could have been provided by drawing on various relevant results to be found in the Italian economic literature by 1915 and the utilitarian social welfare function alluded to in Sidgwick 1887. In contrast, the Diamond-Mirrlees generalization could have been provided by again drawing on the Italian economic literature of 1915 but now exploiting the insights to be found in Bergson’s (1938) discussion of the concept of the social welfare function.

The delay in deriving the Diamond-Mirrlees generalization is to be regretted. The reason, as indicated later, is that whereas Ramsey considered a problem that had an obvious optimum solution—in short, there was no problem to consider—Diamond and Mirrlees did consider an important problem. This implies that, compared to the Ramsey result, the Diamond-Mirrlees generalization provided far greater insights into the formulation of taxation policy.

In the next section a derivation is provided of Ramsey’s taxation result—a derivation that draws on the analysis provided by Ramsey. In addition, an apparently new and theoretically more satisfactory derivation of Ramsey’s taxation result is provided by drawing on a result to be found in the Italian economic literature of 1915. In section 2 attention turns to consider the differential form of the social welfare function (swf) discussed by Pareto (1913, 1916). It is argued that a reasonable interpretation of that discussion is that Pareto suggested a nonutilitar-ian form of the swf that Bergson (1938) discussed later. Within this context it also is noted that the more restrictive, utilitarian form of the swf was clearly alluded to in Sidgwick’s (1887) classic discussion of utilitarianism. Both these forms of the social welfare function are employed in section 3 to derive generalizations of the Ramsey commodity taxation result—derivations that also exploit relevant tools of analysis presented in the Italian economic literature before 1927. In the final section an attempt is made to explain the delay in the derivations of the generalizations of Ramsey’s initial result.

1. A Sketch of the Proof for the Ramsey Result

The main result presented in Ramsey’s paper is that “in raising an infinitesimal revenue by proportionate taxes on given commodities the taxes [End Page 140] should be such as to diminish in the same proportion the production of each commodity taxed” (1927, 47). Given that all markets are in equilibrium, the proportionate fall in the level of production must also result in the same proportionate fall in the level of demand for the goods with commodity taxes imposed on them. The...


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pp. 139-157
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Archived 2005
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