Consider a firm with production function: q = 2LK + K, where L is the amount of labor used and K is the amount of capital used. Let w represents the price of labor and r represents the price of capital. a) Consider the long-run cost minimization problem of the firm for a given level of output q. Derive the conditional factor demand function for L and K as a function of q, w and r. b) Derive the marginal cost as a function of q, w and r. Now, suppose that in the short-run, capital input is fixed at 100, and w = 2, r = 2. c) Write down the short-run cost minimization problem. Then derive the short-run total cost function as a function of. Determine the firm's short-run variable cost and fixed cost.
Consider a firm with production function: q = 2LK + K, where L is the amount of labor used and K is the amount of capital used. Let w represents the price of labor and r represents the price of capital. a) Consider the long-run cost minimization problem of the firm for a given level of output q. Derive the conditional factor demand function for L and K as a function of q, w and r. b) Derive the marginal cost as a function of q, w and r. Now, suppose that in the short-run, capital input is fixed at 100, and w = 2, r = 2. c) Write down the short-run cost minimization problem. Then derive the short-run total cost function as a function of. Determine the firm's short-run variable cost and fixed cost.
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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Transcribed Image Text:Consider a firm with production function: q = 2LK + K, where L is the amount of labor used and K is the amount of capital
used. Let w represents the price of labor and r represents the price of capital.
a) Consider the long-run cost minimization problem of the firm for a given level of output q. Derive the conditional factor
demand function for L and K as a function of q, w and r.
b) Derive the marginal cost as a function of q, w and r.
Now, suppose that in the short-run, capital input is fixed at 100, and w = 2, r = 2.
c) Write down the short-run cost minimization problem. Then derive the short-run total cost function as a function of .
Determine the firm's short-run variable cost and fixed cost.
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