econ 301

2. (26 marks) Consider a firm's production function y = 24/x; + 24/x;, where the price of x; is wy, 1 = and the marginal the price of x; is w,, the price of output is p, the marginal product of x, is product of x; is v,%_ To begin, assume that the amount of x; is fixed at &,. 2 a. (2 marks) Derive the firm's factor demand functions for x; and x,. b. (2 marks) Briefly explain how a change in input and output prices affects the answers in part (a). Assume that the firm can now change the amount of x, and is given a budget of Cj. c. (2 marks) Calculate the firm's marginal rate of technical substitution. d. (2 marks) Use part (c) to calculate the firm's optimal amount of x, to employ as a function of x, and the input prices. e. (2 marks) Use part (d) to determine the firm's optimal amount of each input as a function of w,, w; and C,. f. (2 marks) Use part (d) to determine the firm's optimal amount of each input as a function of wy, w, and y. g. 2 marks) Use part (f) to determine the firm's cost function as a function of w,, w, and y. h. (2 marks) Graph the cost function. (Be sure to label your axes properly.) i. (2 marks) Use part (g) to determine the firm's average cost function as a function of w;, w, and y. The marginal cost function is given by MC = m) V. Wy +w, j- (2 marks) Graph the firm's average and marginal cost functions. (Be sure to label your axes properly.) Assume that the market is perfectly competitive. k. (2 marks) Use part (g) to determine the firm's profit function as a function of p, W1, W2 and y. 1. (2 marks) Determine the firm's supply function. m. (2 marks) Use parts (k) and (1) to determine the firm's profit function as a function of p, w, and W2- n. (2 marks) Use part (m) to calculate producer surplus as a function of p, w, and w2