Henry Schultz

Interrelations of Demand, Price, and Income

T WHAT income, as well as price, affects the demand for a commodity is of course a truism, although the relations existing between these variables for the economy as a whole still remain to be determined. For an individual consumer, however, the interrelations of demand, income, and price are essentially at hand in the writings of Vilfredo Pareto, Eugen Slutsky, and J. R. Hicks and R. G. D. Allen; and some of these relations also hold for aggregate market phenomena. The main objectives of this paper are: (i) to develop these interrelations in a simple, logical manner; (2) to show their bearing on the theory of the demand for completing and competing goods and on the elasticity of substitution; (3) to call attention to some unsolved problems in this field; and (4) to compare the theoretical results with those yielded by the concrete, statistical demand curves of beef, pork, and mutton.

The Italian School of Mathematical Economics

ing a constant, which serves to fix the unit of measure, we may obtain an unequivocal correspondence between the quantities given by experience which serve to determine the lines, or the varieties (in hyperspace) of indifference, and the pleasures (ophelimities) which the individual enjoys who having reached the point x, y .... t consumes dx, dy,. . . . dt in the two following cases: I. When the order of consumption is indifferent, and when we know that the pleasure resulting from the consumption of dx depends only on x, that resulting from the consumption of dy depends only on y, etc.; II. When the pleasure is different depending on the order of consumption; if we assume that it is possible to make the necessary experiments for this determination. The case which remains excluded is, therefore, that in which the order of consumption is indifferent, and the pleasure resulting from the consumption of dx depends on x, y, . . . . t, that resulting from the consumption of dy depends on x, y, .... t, etc. In the case where the order of consumption is indifferent, there exists a function of x, y, . . . . t such that the partial derivatives of this unique function represent the indices of pleasure or the pleasures of the consumption of dx, dy .... dt brought about by leaving the point x, y, .... t. In the case when the order of consumption influences the pleasure, this unique function does not exist as long as the path to be taken is not deter-