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handout 7 answers - Microeconomics Handout 7 Microeconomics...

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Microeconomics Handout 7 Microeconomics, Fall 2007, Dr. Laury A Mathematical Treatment of Production and Cost Theory Let L =labor and K =capital. Your production function is a Cobb-Douglas one of the form q = K 0.5 L 0.5 . You are told that the wage rate is $5 and the rental rate of capital is $20. You would like to produce an output of 100 sweets. Notice that here we are fixing output and letting cost vary. (Note in theory of consumer choice, we did not fix utility. Rather, we had a given income and allowed utility to vary.) Because of duality, however, we can really do either. How much capital and labor should you choose? (Hint: find the MRTS and set this equal to w/r; next, solve for the optimal ratio of labor to capital, then for q = 100, determine how much L and K you need) L K MP MRTS MP = Recall that you find the MP by taking the derivative of the production function with respect to the variable you’re interested in. For example, the marginal product of labor is the derivative of the production function with respect to L.
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