A firms production technology is given by the production function Q = LK where L

Question

A firms production technology is given by the production function

Q = LK

where L represents labor hours, K machine hours and Q the amount of output. The market wage and rental rates are, w= $64 and r = $400.

The firm is operating in the long run where it can adjust both inputs.

(a) Suppose that the firm currently is using equal amounts of labor and capital. Is it minimizing its long run total cost? If so, why so and if not why not? Explain. If it is not minimizing its long run cost, how should it adjust its input usage? Explain. Provide appropriate calculations.

(b) Suppose that the firm wants to produce 100 units of output. Determine the cost minimizing combination of L and K. Calculate the resulting long run total cost. Show and explain all calculations.

(c) Calculate the short run total cost if Q =100 and w= $64 and r = $400, but capital, K is fixed at 2.

(d) Without assuming a specific numerical production target, but using w= $64 and r = $400 calculate the equation for the long run total cost function (in terms of Q).

(Hint: Assume that the level of output is Q. Using the above w, r values first determine the least cost combinations of L and K)

Explanation / Answer

Let

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