R Pq

the AR curve can also be regarded as a curve relating price P to output Q: P = f(Q). Viewed in this light, the AR curve is simply the inverse of the demand curve for the product of the firm, i.e., the demand curve plotted after the P and Q axes are reversed. Under pure competition, the AR curve is a horizontal straight line, so that /'(£>) = 0 and, from (7.7'), MR - AR = 0 for all possible values of Q. Thus the MR curve and the AR curve must coincide. Under imperfect competition, on the other hand, the AR curve is normally downward-sloping, as in Fig. 7.2, so that f'(Q) < 0 and, from (7.7'), MR - AR < 0 for all positive levels of output. In this case, the MR curve must lie below the AR curve.

The conclusion just stated is qualitative in nature; it concerns only the relative positions of the two curves. But (7.7') also furnishes the quantitative information that the MR curve will fall short of the AR curve at any output level Q by precisely the amount Qf'(Q). Let us look at Fig. 7.2 again and consider the particular output level N. For that output, the expression Qf'(Q) specifically becomes Nf'(N); if we can find the magnitude of Nf'(N) in the diagram, we shall know how far below the average-revenue point G the corresponding marginal-revenue point must lie.

The magnitude of N is already specified. And f'(N) is simply the slope of the AR curve at point G (where Q = N), that is, the slope of the tangent line JM measured by the ratio of two distances OJ/OM. However, we see that OJ/OM =

0 0

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