IT IS THE PURPOSE of this paper to generalize the demand theory of Hicks and Allen2 for the dynamic case. It also could give a somewhat firmer theoretical foundation to the dynamic demand theory of the Econometrists, especially G. C. Evans3 and C. F. Roos.4 We propose to derive income, price, and interest elasticities of demand under the assumption that the individual has definite plans for the future and definite expectations of future incomes, prices, and interest rates. Hence uncertainty in the sense of F. H. Knight5 is ruled out, whereas risk may be taken into account. We make the same assumptions as in the previous paper on Maximization of Utility over Time.6 The individual plans for n discontinuous points in time in the discontinuous case, where utility is a mere function. Utility becomes a functional rather than a function in the continuous case.

SUPPOSE provisionally the existence of a utility function F. Let us assume further that the individual in question consumes only three goods x, y, and z. The argument can easily be extended later to any number of commodities. The individual is at the point in time 0 and plans for the period of time 1, 2, , n. Consumption takes place at these n discontinuous points in time. We denote by xi the quantity of the commodity x which the individual plans to consume at the point in time j; similarly, y2 and zj. He does not accumulate any commodity stocks. The utility function F will depend on those quantities which the individual expects to consume: