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a firm produces output according to the following function q= f(L,K) = L^1/2K^3/2. The cost of...

a firm produces output according to the following function q= f(L,K) = L^1/2K^3/2. The cost of labor is $2 per hour and the rental cost of capital is $12 per hour. a) Determine the returns to scale for this function. b) Suppose the firm wishes to produce at cost $56. How Much capital and how much labor does the firm employ? c. Derive the short-run cost function with optimal amount of K from part b. d. Suppose that there are 10 firms in a market and the market is Qd = 1600 - 80p, each firms with the cost function from part c. Find the equilibrium market quantity and price. e) Assume that the short-run profit or loss from part d. is representative of the current long-run prospects in this market. You may further assume that there are no barriers to entry or exit in the market. What will be the expected long-run profit? Why?

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