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Incidence of Taxation. — Under this head it may be expected that I should dwell upon the triumphs won in this field by mathematical reasoning. But as I have here nothing to add to those achievements, I pass over the subject, justifying the omission by the following rather fine distinction. It is true that the problems of incidence exemplify the applications of the Differential Calculus. But they are not maximum problems. Let me illustrate the distinction by reference to a recent brilliant application of mathematical reasoning by Professor Pigou, to determine the effects of a differential tax on wheat imported into the United Kingdom from foreign countries1. The first step is to obtain an equation between the demand of the United Kingdom for wheat and the supply from three sources, the United Kingdom itself, the Colonies, and foreign countries. Such an equation, it is to be considered in the light of the preceding analysis (though it is not always necessary to repeat explicitly), is presented by a problem of the sort with which this paper purports to deal; the equation expresses the conditions of a certain maximum. From this equation by attributing a small change to the demand in the home country for foreign wheat — for so the small impost may be described — we derive another equation which is in effect that which Professor Pigou uses. But this derivation may be treated as an affair the Differential Calculus only, not involving a (further) calculation of maxima.
Monopoly. — The distinction which has just been taken may be used to justify our omitting the incidence of taxation under the head of monopoly also. According to this distinction Cournot’s equations formulating monopoly price express a maximum condition. But his equations showing the variation in price consequent on a variation in cost of production exemplify indeed the Differential Calculus, but not its application to determine maximum advantage. As I shall have to recur to Monopoly and the adjacent category of Duopoly, to use the happy phrase of Professor Jannacone, I content myself here with a mere reference to M. Colson’s use of the principle which underlies what has been called above «incipient taxation», with reference to a state-regulated monopoly.
- Import duties.