A firm producing backpacks has a production function given by Q = 2K1 Lt. The wa

Question

A firm producing backpacks has a production function given by Q = 2K1 Lt. The wage rate (w) is $4, the rental rate (r) is $2, the market price (p) the backpacks is $30, and capital is fixed in the short run at 16. Answer the following (1) What is the short run production function? (2) Write down the firm's profit maximization condition. (3) Given the above, how many workers should the firm hire? 4) How many backpacks can the firm produce with the workers they hire? (5) What is the profit that the firm makes?

Explanation / Answer

K = 16

1) SR production function: Q = 2 x (16)1/4 x L1/2 = 4L1/2

2) MPL/MPK = w/r (profit maximization condition)

MPL = dQ/dL , MPK = dQ/dK

K1/4L-1/2 / (0.5 x K-3/4 x L1/2) = 2

K = L

3) L = 16

4) Q = 2 x (16)1/4 x 161/2 = 16

5) Profit = P x Q - (wL + rK) = 16 x 30 - (16 x 2 + 16 x 4) = 384

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