Solutions to Two open Problems from Midterm 2 2009

Solutions to Two open Problems from Midterm 2 2009 - This...

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This document contains the solutions to two open problems of Midterm 2, 2009. The problems are listed below, and the solutions are on the following page. Problem 1 (20 Points) Denote by w and r the price of labour (L) and capital (K) respectively. Consider the production function Q =6LK (2/3) . The marginal product of labour and capital are MP L =6K (2/3) and MP K =4L(K) (-1/3) respectively. a. (5 Points) Find the long run input demand function for labour and capital. b. (5 Points) Assume w=3 and r=2. Find the long run total cost function for this firm as a function of the level of output. c. (5 Points) Assume that in the short run the level of capital is fixed to K=27. Find the short run input demand functions for labour and capital. d. (5 Points) Assume that in the short run the level of capital is fixed to K=27. Find the short run total cost function as a function of the wage rate (w) the cost of capital (K) and the level of output. The price of labour is w and the price of capital is r.
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