Economic Mathematics and Financial Mathematics

Author: M.Anthony et al.
Publisher:
Publish Date: 1998-08-01
Features:
Fragment: We shall refer to this as the demand set forth for the particular good. In economics you will learn reasons why it ought to look rather like it does in our diagram, a smooth, downwards sloping curve. Suppose the demand set D contains the point (30, 5). This means that when the price p = 5 is given, the corresponding demand will be for q = 30 units. In general, provided D has the 'right' shape, as in Figure 1.1, then for each value of p there will be a uniquely determined value of q. In this situation we say that D determines a demand function, qD. The value written qD(p) is the quantity which would be sold if the price were p, so that qD(5) = 30, for example. There is another way of looking at the relationship between q and p. If we suppose that the quantity q is given, then the value of p for which (q, p) is in the demand set D is the price that consumers would be prepared to pay if q is the quantity available. From this viewpoint we are expressing p in terms of q, instead of the other way round. We write pD(q) for the value of p corresponding to a given q, and we call pD the inverse demand function. Example (continued) Taking the same set D as before, we can now rearrange the equation of the line in the form p = (125 - 6q)/8. So the inverse demand function is Next we turn to the supply side. We assume that there is a supply set S consisting of those pairs (q, p) for which q would be the amount supplied to the market if the price were p. There are good economic reasons for supposing that S has the general form shown in Figure 1.2.