4. The own-price elasticities of contingent input demand for labor and capital are defined as al w ak' v erw = dwic ken av kc Consider the following cost function: C(w, v, q) = wx+ vy, which is the cost function, given a fixed proportions production function. (1x3 = 3 points) 4.1 Calculate eye,w and eke,v- (Hint: Shephard's Lemma will be useful.) 4.2. Show that the cross-price derivatives of contingent demand functions are equal, Le., show that = = 2- Use this fact to show that sel ,v = Skekew where s = wl/C and sk = vk/C are the shares of labor and capital in total cost. 4.3. Now, use all the results we have so far to show that the sum of all own- and cross-price elasticities with respect to labor income, w, sum to zero. In other words, show that sel,,w + Skekaw = 0.|