Question: A firm has a production function Q = 10L + 30K. Suppose the price of labor services w is $5 per unit, and the price

A firm has a production function Q = 10L + 30K. Suppose the price of labor services w is $5 per unit, and the price of capital services r is also $5 per unit. Using the method of Lagrange, find the optimal input combination given that the firm wishes to produce 900 units of output. Verify that the solution satisfies the conditions for an optimum at a corner point, equations (7.10), (7.11), and (7.12) in the text. Then verify that the solution satisfies the conditions for an optimum at a corner point, equations (7.16), (7.17), and (7.18) in the text.

Equations

w - MP = 0; r-MPK = 0; f(L,K)-Q=0; L>0 K>0 2

> 0 (7.10) (7.11) (7.12)

w - MP = 0; r-MPK = 0; f(L,K)-Q=0; L>0 K>0 2 > 0 (7.10) (7.11) (7.12)

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The Lag rang ian function is L 10 L 30 K 900 10 L 30 K The first order conditions are L L 10 0 and L ... View full answer

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