6. Venture capitalist Sarah purchases two firms to produce widgets. Each firm produces identical products using the identical production function requiring capital (denoted by K) and labor (denoted by L) as inputs: q = VKZ . The firms differ, however, in the amount of capital equipment each has in the short run. In particular, firm 1 has K, = 25, whereas firm 2 has K, = 100. Rental rates for K and L are given by w, = w, =$1. a) Calculate the marginal product of labor for the two firms. Explain the intuition behind any difference that you find between them. b) If Sarah wishes to minimize the short-run total cost of production, how would output be allocated between the two firms? c) Given that output is optimally allocated between the two firms, derive the short-run total, marginal, and average cost as a function of the total quantity of output. d) How should Sarah allocate widget production across the two firms in the long run? Calculate the long-run total, marginal, and average cost for widget production. Why does these cost functions look the way they look? e) How would your answer to part c) change if both firms exhibited diminishing returns to scale? You don't need to do any calculations