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Answer to Question #42784 in Microeconomics for Reny

Question #42784
Firm's technology: 3K^0.2 L^0.7. Assume labour supply:w=5+4L and find labour hired by firm
Expert's answer
Firm's technology: Q = 3K^0.2*L^0.7. Assume labour supply:w=5+4L
The profit maximizing rule is MRPL = MCL. The marginal revenue product MRPL = ∆TR/∆L. Product of marginal revenue and the marginal product of labor or MRPL = MR x MPL. So, MCL = MRx MPL
MCL = w' = (5 + 4L)' = 4
MPL = Q'(L) =
MR = w = 5 + 4L

In our case we need to know amount of K to find the derivative of Q and then labour hired by firm.

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