B

Figure 8.3

the marginal falls short of the average in numerical value; thus the function is inelastic at point A. The exact opposite is true in diagram b.

Sometimes, we are interested in locating a point of unitary elasticity on a given curve. This can now be done easily. If the curve is negatively sloped, as in Fig. 8.3a, we should find a point C such that the line OC and the tangent BC will make the same-sized angle with the x axis, though in the opposite direction. In the case of a positively sloped curve, as in Fig. 8.3b, one has only to find a point C such that the tangent line at C, when properly extended, passes through the point of origin.

We must warn you that the graphical method just described is based on the assumption that the function 7 = /(x) is plotted with the dependent variabley on the vertical axis. In particular, in applying the method to a demand curve, we should make sure that Q is on the vertical axis. (Suppose that Q is actually plotted on the horizontal axis. How should our method of reading the point elasticity be modified?)

2 Given the import function M = /(Y), where M is imports and Y is national income, express the income elasticity of imports emy in terms of the propensities to import.

3 Given the consumption function C = a + bY (with a > 0; 0 < b < 1):

(a) Find its marginal function and its average function.

(b) Find the income elasticity of consumption ecy, and determine its sign, assuming

(c) Show that this consumption function is inelastic at all positive income levels.

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