1. Suppose that the firm has a Cobb-Douglas production function f(1,12) =1x2, with a > 0. Suppose all input and output markets are perfectly competitive (i.e., the firm is a price taker in all markets). Let the input price vector be (w1,W2) = (1,1), and the output price is p=3. (a) Write down the first-order conditions for profit maximization in the one-step approach, and find the (art,x3) that satisfies these conditions. (b) If a=1/3, does the production technology exhibit DRS, CRS or IRS? Is this input vector indeed profit-maximizing? (c) If a= 1, does the production technology exhibit DRS, CRS or IRS? Is this input vector still profit-maximizing