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Question 2 Consider a firm with a production function of q LK. Cost of labor and raw material are 2 and 1 respectively. If the firm wants to minimize its costs, what is the optimal level of L and K? What is the cost function? Show your steps. Answer:
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Answer #1

q=LK

MPL = K

MPK = L

w = $2

r= $1

At optimal input combination : MPL/MPK = w/r

K/L = 2/1

K= 2L

q= LK

q= L(2L)

q= 2L2

L = (q/2)1/2

K = 2(q/2)1/2

Cost = wL + rK

Cost = 2L + K

Cost = 2(q/2)1/2 + (2)(q/2)1/2

= 4(q/2)1/2

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