Homework 51 Econ 4001.03, Fall 2013 Prof. Lixin Ye Homework 5 Due October 31 (Thursday) 1. True and False, and explain briefly. 1) If marginal product is greater than average product, total product must be increasing. 2) You decide to purchase a new car for $12,000. Upon driving the car off of the lot, the resale value of the car falls to $9,000. The opportunity cost of using the car is $12,000. 2. Identify the returns to scale (increasing, constant, or decreasing) for the following production functions. 1) 22100Q KL= 2) 113322QK L=+ 3. Suppose a firm has the production function 50Q KL= 1) If the wage rate is $10 per unit of labor and the rental rate of capital is $5 per unit of capital, how much capital and labor should the firm employ in the long run to minimize the cost of producing 40,000 units? 2) Using the solution in part 1), what will the firm’s long-run total cost be? 4. Consider a production process where capital and labor are perfect complements – two units of capital are required for each unit of labor to produce four units of output. 1) Derive the production function for this production process. 2) If the wage rate is $5 per unit of labor and the rental rate of capital is $8 per unit of capital, how much capital and labor should the firm employ to minimize the cost of producing 100 units? 3) What will the total cost be to produce the 100 units using the quantities of capital and labor determined in part 2)? 5. Suppose a firm has the production function 1/2 1/4 1/4Q K LM The wage rate 16w , rental rate 2r , and the price of the materials 1m . 1) Suppose in the short run, K is fixed at *K. What’s the solution to the firm’s short run cost-minimization problem?2 2) What is the solution to the firm’s long run cost minimization problem given that the firm wants to produce Q units of output? 3) Suppose that *10, 20QK. Compare the long run and short run
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