4.A firm uses two factors x1 and x2 for production y = x 1/3 1 x 1/3 2 . The price of the product is 2. The price of x1 is w1. The price of x2 is w2. The firm is endowed with one unit of x2. (a) In the short run, the firm can not adjust x2, and x2 = 1. Write down the short-run profit-maximizing problem. What is the profit-maximizing output? What is the factor demand curve of x1? (b) In the long run, the firm can adjust x2. Write down the long-run profitmaximizing problem. What is the profit-maximizing output when w1 = 1 and w2 = 1? (c) Is the production function constant returns to scale, increasing returns to scale, or decreasing returns to scale? Prove it.