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The Use of the Elasticity Concept in Economic Theory

Published online by Cambridge University Press:  07 November 2014

E. E. Reilly
E. E. Reilly*
Affiliation:
The University of Western Ontario
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Extract

It is well recognized that the imposition of a tax on a commodity will produce certain changes in its production and consumption, and in particular, that the primary incidence of a commodity tax is a function of the elasticities of the relevant supply and revenue curves at the point of intersection. This study attempts to add to the precision, and to extend the usefulness, of the elasticity concept in economic theory, with particular reference to the taxing of commodities. The effect of commodity taxes in restricting business activity (and consumption) is of increasing economic significance. To facilitate the analysis of these effects, the term “Elasticity of the Market” is introduced. It measures the change in the quantity produced and sold, for a given vertical change in the supply curve, or in the revenue curve, or in both. Within the limits of the assumptions given, it is possible to determine from the elasticity of the market, the effect of a change in tax rates on the tax revenues, and the point of maximum fiscal revenue. The conditions of monopoly and competition offer a number of interesting comparisons, not only in the economic effects of commodity taxes, but also for general economic theory.

Dalton proposes that a commodity tax is divided between buyers and sellers in the ratio of the elasticity of supply to the elasticity of demand.

Type
Articles
Information
Canadian Journal of Economics and Political Science/Revue canadienne de economiques et science politique , Volume 6 , Issue 1 , February 1940 , pp. 39 - 55
Copyright
Copyright © Canadian Political Science Association 1940

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References

1 Much of the material appearing here was used by the writer in a paper given at the Political Economy Seminar in the University of Toronto, March, 1939. The writer is deeply indebted to Colonel Arthur Woods, Doctors Gordon Magee and Alex Cook for mathematical suggestions in the development and simplification of certain of the proofs involved in this study.

2 Dalton, Hugh, Principles of Public Finance (9th ed., London, 1936), pp. 73–81.Google Scholar

3 It may be noted that there are three possible cases of a first degree supply or demand function with constant elasticity, viz. E = 0, ∞ or +1. The functions are X = a, Y = a, and Y = bX. In these special cases the elasticities of the respective average and marginal curves are equal.

4 Robinson, Joan, The Economics of Imperfect Competition (London, 1933), p. 36.Google Scholar Using inverse elasticities, the equation is given as, , where M equals marginal value, A equals average value, and E equals the elasticity of the average curve.

5 Jenkin, Fleeming, Laws of Supply and Demand (London School of Economics, reprint no. 9, 1931), pp. 113, 114.Google Scholar “If the tax be large, … the tax will be unproductive, and … the excess of injury to the buyers and sellers will be large, compared with the produce of the tax. There is a certain magnitude of tax which will produce the maximum of revenue or value ….” But Jenkin drops the subject here to discuss the relative suffering inflicted on buyers and sellers from a tax.

6 The use of the term profit in this sense may be questioned. During the short run it appears quite legitimate. In the short run, and during the long run, such gains would tend to disappear, or remain in the form of rent, or quasi-rent.

7 As Em is a combination of Es and Ed , functional relationships may be developed in these terms. Most of the functions are shortened by the use of Em and are more readily comprehended.

8 The reciprocals of the various elasticities are so frequently useful that the term cöelasticity might well be introduced into economic terminology. With fixed coordinates, note the relationship of Ed and Es to b and (by 4 and 5).

9 If a linear supply curve has an elasticity of less than unity, its ordinate will have a value of zero while the abscissa is still a positive quantity. It is assumed that a limit occurs when a supply curve cuts the X axis, as production is restricted, although in the case of bonused production it could theoretically go lower. The function covering the degree to which a monopolist will reduce production is presumed to be limited to this point, that is, where

Negative values for Es have not been included in the tables. Decreasing cost, however, is not compatible with short run equilibrium. Note later comment on long run supply.

10 The expression “as supply becomes elastic” has a limited meaning. The elasticity of supply may move through positive numbers from zero to infinity and through negative numbers approaching minus one. In an economic sense the latter condition is more elastic than a constant cost curve (Es , = ∞).

11

which is identical with (12) from which table III was prepared. With respect to profits this is the coefficient of monopoly ability to resist commodity taxes. Stated more directly, it indicates the amount of taxes paid under competition for each dollar profit, compared with tax payments under monopoly for each dollar profit.

12 (By 11) .

13 This is Dalton's equation, modified by a consideration of signs.

14 Viner, Jacob, “Cost Curves and Supply Curves” (Zeitschrift für Nalionalökonomie, Sept., 1931).Google Scholar