A problem in economics

Qualitative economics is usually considered to have originated with the work of Samuelson [11, Chapter III] who discussed the possibility of determining unambiguously the qualitative behavior of solution values of A system of equations. In his pioneering paper [6] (see also [4] and [7, 8]) Lancaster put it this way: Economists believed for A very long time, and most economists would still hope it to be so, that A considerable body of sensible economic propositions could be expressed in A qualitative way, that is, in A form in which the algebraic sign of some effect is predicted from A knowledge of the signs, only, of the relevant structural parameters of the system.

Consider the following example, similar to one discussed in Samuelson [11], of A market for A product, say bananas, where the price and quantity are determined by the intersection of its supply and demand curves. We introduce A shift parameter α into the demand curve, and assume that an increase in A shifts the demand curve upward and to the right. For instance, α might represent people's taste for bananas, and as people's taste for bananas increases so does their demand for bananas. Let S(p) denote the number x of bananas that farmers will produce if the price per banana is p. Simple economic principles tell us that as the price p increases farmers will supply more bananas. This gives A supply curve as indicated in Figure 1.1.

Let D(p,a) denote the number x of bananas that consumers will demand if the price per banana is p and people's taste for bananas is α.