A firm has production function q = K1/3L1/3. The firm sells output for p = 48 and acts as a price taker. They purchase inputs competitively for w = 1 and r = 4 and produce an output level to maximize profits. a. Derive and graph the firm’s long-run MC and AC curves. Illustrate and quantify the profit-maximizing level of output as Bundle A. b. Beginning in August the price of labor will permanently increase to w = 4. The firm will not be able to vary your capital stock. Derive the firm’s short-run SMC and SATC curves. Update your diagram to illustrate and quantify the profit-maximizing level of output as Bundle B. c. In September, the firm can vary both capital and labour. Derive the firm’s long-run MC and AC curves. Update your diagram to illustrate and quantify the profit maximizing level of output as Bundle C.
A firm has production function q = K1/3L1/3. The firm sells output for p = 48 and acts as a
purchase inputs competitively for w = 1 and r = 4 and produce an output level to maximize profits.
a. Derive and graph the firm’s long-run MC and AC
level of output as Bundle A.
b. Beginning in August the price of labor will permanently increase to w = 4. The firm will not be able to
vary your capital stock. Derive the firm’s short-run SMC and SATC curves. Update your diagram to
illustrate and quantify the profit-maximizing level of output as Bundle B.
c. In September, the firm can vary both capital and labour. Derive the firm’s long-run MC and AC curves.
Update your diagram to illustrate and quantify the profit maximizing level of output as Bundle C.
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