Design of the Demand Law and a New Form

Abraham Wald was the first scholar to tackle the demand law in a scientific way. Let p be price, and f(p) be the demand at price p:

This is the law of demand.

Fig. 2.4 A normal case for the Pareto-Slutsky equation: 4p4f 0

It then holds that:

Now suppose that:

Then:

The law describes the variation between a price p_i and its demand f(p_i). That is to say, a higher price corresponds to a lower demand in a strict form, and a non-decreasing price corresponds to a non-increasing demand in a weak form. This formulation is exempt from any specification of preference. Wald (1933) thus examined the mathematical property of f(p_i). This can be shown by geometry on two-dimensional coordinates (see Fig. 2.6).

2.2.3