Question

5. Prove that when the production function is homogeneous of degree one, it may be as f(x) 2MP(x)x where MPi(x) is the marginal product of input i. Hint use Euler's Theorem. 6. Derive the cost function for the linear technology y f(xix2)-axi+bx 7. Given the production function fxi)aIxa In(x), derive the firm's supply function assuming an interior solution, assuming that a>0 and a 0. 8. Consider a duopoly facing an industry demand function, p-a-bQ, where Q tg respective cost functions are C(q) ciq and C(q)-cq Suppose the (a) Determine the best response functions for each of these firms. (b) Graph the best response functions with the output of firm 1 on the vertical axis and the output of firm 2 on the horizontal. (c) Solve the Cournot equilibrium quantities, qi,q the market price, p* and the respective profits.