Suppose that a firm's fixed proportion production function is given by q = min(2k, 4L), and that the rental rates for capital and labor are given by v = 1, w = 3.
A) Calculate the firm's long-run total, average, and marginal cost curves.
B) Graph these curves.
C) Suppose that k is fixed at 10 in the short run. Calculate the firm's short-run total, average, and marginal cost curves and graph them.
D) Now suppose in the long run the firm faces a market demand for its products of: 10 d (q^d)=10-P Where P is the price charged by the firm. Find the profit maximizing output for this firm and the price it charges.
NOTE: I did not answer sub part D, as the question is unclear. PLEASE CLARIFY WHAT IS THE MARKET DEMAND FUNCTION.
The fixed proportion production function is given as :
To produce "q" units of output, the firm wants to use q/2 units of K and q/4 units of L, irrespective of the input prices.So, the conditional input demands are:
(A).The firm's long run total cost is
The firm's average cost is
The firm's marginal cost is
(B) The below plot shows the Total cost curve(TC) for various output levels. The marginal cost curve(MC) and the average cost are constant and both are same.
(C)
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