midterm2solutions

midterm2solutions - Solutions to 14.01 Midterm 2 Short...

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Solutions to 14.01 Midterm 2 Short Questions: 1. ( TOTAL: 25 points ) Explain whether each of the following statements is True or False. (Note: You will not get points for a correct answer without an explanation.) a) ( 5 points ) In the short run, a competitive firm will never produce at levels where the marginal product of labor is increasing (assume labor markets are perfectly competitive). Answer: TRUE. Under these conditions the firm can increase its profits by increasing production. b) (5 points) If a production function has constant returns to scale, the marginal products of labor and capital should be constant. Answer: FALSE. Counter-example: A CRS Cobb-Douglas production function. Key thing: marginal products keep one of the factors constant. c) (5 points) A firm's short-run average cost curve is tangent to its long-run average cost curve only at a level of output where short-run marginal cost equals long-run marginal cost. (Use a diagram to explain your answer) Answer: TRUE. (See graph 1, similar to figure 7.9 in book). d) (5 points) If resources are put to their best use, their opportunity cost is always zero. Answer: FALSE. The opportunity cost is greater than zero if there is an alternative use for the resources. e) (5 points) If the production of the only 2 goods in an economy is characterized by Constant Returns to Scale, then the marginal rate of transformation (MRT) between the two is a constant. Answer: TRUE. The MRT is the ratio of the marginal costs. If the production function of a good has CRS the marginal cost is a constant, therefore the MRT between the two goods has to be a constant.
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Long Questions: 2. ( TOTAL: 25 points ) A firm producing widgets faces the following production function: L K Q = where K is capital and L is labor. The rental rate for capital is $4 and wage rate for labor is $16. a) (5 points) In the short-run, capital is fixed at 4 units. Calculate the demand for labor as a function of output, and derive the short-run cost function of the firm 16 ) ( 4 . 16 . ) ( 16 4 4 2 2 2 2 * + = + = = = = Q Q C r Q w Q C Q Q L L Q
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b) (5 points) Calculate the short-run average cost, average variable cost, average fixed cost, and marginal cost. Show these functions on a diagram. Q SRMC Q SRAFC Q SRAVC Q Q SRAC 2 16 16 = = = + = c) (8 points) In the long-run, all factors are variable. Calculate the demands for labor and for capital, each as a function of output, and derive the long-run cost function of the firm.
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This note was uploaded on 04/20/2010 for the course ECON 14.01 taught by Professor Pindyck during the Spring '08 term at MIT.

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midterm2solutions - Solutions to 14.01 Midterm 2 Short...

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