Question

(2) Consider the production function f(L, K) = 2K √ L. The marginal products of labor...

(2) Consider the production function f(L, K) = 2K √ L. The marginal products of labor and capital for this function are given by MPL = K √ L , MPK = 2√ L. Prices of inputs are w = 1 per hour of labor and r = 4 per machine hour. For the following questions suppose that the firm currently uses K = 2 machine hours, and that this can’t be changed in the short–run.

(e) What is the (short–run) efficient scale of production? What is the (short–run) average cost at the efficient scale of production?

(f) Assume that in the short run the r ∗ K = 4 ∗ 2 = 8 dollars that the firm pays for its capital are sunk. What is the short–run profit maximizing quantity as a function of the market price p? Draw the short–run supply curve of the firm. What are the firm’s profits (as a function of p)?

(g) How would the short–run supply curve change if the fixed cost (of 8 dollars) is avoidable instead of sunk?

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