10.10 Input demand elasticities The own-price elasticities of contingent input demand for labor and capital are defined as al w ak v awa ke

a. Calculate

e, and 6,, for each of the cost functions shown in Example 10.2.

b. Show that, in general, e,+, 0.

c. Show that the cross-price derivatives of contingent demand functions are equal--that is, show that al/a =ak/aw. Use this fact to show that sense, where sj, s, are, respectively, the share of labor in total cost (w//C) and of capital in total cost (pk/C).

d. Use the results from parts

(b) and

(c) to show that 5, +5, = 0.

c. Interpret these various elasticity relationships in words and discuss their overall relevance to a general theory of input demand.