2. (25 points) Suppose a competitive firm has the production function of f (x1, (2) = 1 202. The output and input markets are competitive, and their prices are denoted by p, w1, and w2. Moreover, there are no fixed costs. (a) Write down the equation for the firm's profit maximization problem. 3 (b) Derive the firm's supply function y(p, w1, w2). If p increases, does this firm produce more? If w1 and w2 decrease, does this firm produce more? Are they intuitive? (c) Derive the firm's factor demand functions for both inputs (i.e., x1(p, w1, w2) and x2(p, W1, W2)). (d) Write down the equation for the first stage of the firm's cost minimization problem. (e) Derive the firm's conditional factor demand functions for both inputs (i.e., x1(y, w1, W2) and x2(y, w1, W2)). (f) Construct the firm's cost function (i.e., c(w1, w2, y)). (g) Write down the equation for the second stage of the firm's cost minimization problem. Then, derive the firm's supply function. Is it equivalent to the one from (b)? (h) Answer (a) and (d) again if the government imposes the firm an ad-valorem tax when it buys input 1 (just (a) and (d), nothing else)