1. This first question focuses on the idea of different types of production functions. (a) (3 points) To begin, assume that a firm is producing using q = h(K, L) K(1/3) [(1/3). Suppose the firm currently owns 128 machines, the price of the good = is P = $96, the rental rate of capital is r = $4, and the wage rate is w = $16. What level of Labour would be hired? How much would be produced? Would the firm make a profit or a loss? - Suppose there are two other methods of production using the same machines: q = g(K, L) = min{}K, {} or q = f(K, L) = K(1/4) L(3/4). (b) (2 points) Using production 9(K, L), if the capital remains fixed and the firm wants to keep output the same, what level of labour would be hired? What are the profits made here? (c) (3 points) Continuing to use production g(K, L) with the capital fixed, how much would the firm produce if the did not keep output the same? What are the profits here ? (d) (2 points) Would the firm ever be willing to switch from using h(K, L) to using g(K, L) with capital at 128 machines? Explain. (e) (2 points) Using production f(K, L), if the capital remains fixed and the firm wants to keep output the same, what level of labour would be hired? What are the profits made here? (f) (3 points) Continuing to use production f ( K, L) with the capital fixed, how much would the firm produce if the did not keep output the same? What are the profits CS here ? Scanned with CamScanner(g) (2 points) Would the firm ever be willing to switch from using h(K, L) to using f(K, L) with capital at 128 machines? Explain. - Continuing to use the three production functions: q = h(K, L) = K(1/3) L(1/3), q =g(K, L) = min{}K, {L}, and q = f(K, L) = K(1/4) [(3/4). (h) (6 points) What is the Long Run Cost curve for each of these when r = $4 and W = $16? (i) (6 points) What are the Long Run Average Cost here? How about the Marginal Cost? (j) (4 points) Provide a convincing argument that a firm using with h(K, L) or g(K, L) would select K* = 128 in the Long Run given P = $96, w = $16, and r = $4. (Hint: for h(K, L) try maximizing profits when K and L are adjustable.) CS Scalathemwith man on Gagethedre are 50 identical consumers and 200 iden- tical firms. Each individual consumer has the following demand function for widgets OP(P) = 100