ECON 310 – Fall 2006. Chapter 7 – “Costs and Cost Minimization.” “Review Questions” (page 253): 4, 5, 6, and 9. “Problems” (pages 254-256): 7.4, 7.5, 7.6, 7.7, 7.9, 7.12, 7.14, 7.15, 7.18, 7.19, and 7.24. Additional Questions: 1) Clearly explain the difference between the “short run” and the “long run.” Consider a firm wishing to produce Q units of output. Why must the short run costs of producing this level of output always be greater than the long run costs of doing so? 2) Consider a firm with the production function LKKLF 20),( = , which leads to LKLMP 10= and KLKMP 10= . a. Graphically illustrate the solution to the long run cost minimization problem. b. Graphically illustrate how the cost minimizing level of labor, the cost minimizing level of capital, and total costs of production would change if the rental rate on capital were to increase. c. Determine functional forms of ),,(*qrwLLR, ),,(*qrwKLR, and ),,(*qrwCLR. Based upon these functions, determine how each value would change if the rental rate on capital were to increase. Are your answers to parts (b) and (c) consistent with each other? Explain. For the remainder of the problem suppose the firm is operating in the short run with capital fixed at 100=K . d. Graphically illustrate the solution to the short run cost minimization problem. e. Graphically illustrate how the cost minimizing level of labor, the cost minimizing level of capital, and total costs of production would change if the wage rate for labor were to increase. f. Determine functional forms of ),,(*qrwLSR, ),,(*qrwKSR, and ),,(*qrwCSR. Based upon these functions, determine how each value would change if the wage rate for labor were to increase. Are your answers to parts (e) and (f) consistent with each other? Explain.3) Consider a firm that produces output according to the production function ),( KLFq = . The “ 500=q isoquant” is illustrated below. Also illustrated is a single isocost line. Assume throughout that the per unit price of Capital is 50=r . a. What is the per unit price of Labor? Explain. b. Suppose the firm is operating in the Long Run and wants to produce 500=q units of output. Explain why each of the following combinations of ),( KL could or could not be the solution to the firm’s Cost Minimization problem: )50,150(; )0,400(; )30,250(; )30,200( ; and )30,150(. c. Suppose the firm is operating in the Short Run with 50=K units of capital and wants to produce 500=q units of output. Explain why each of the following combinations of ),( KL could or could not be the solution to the firm’s Cost Minimization problem: )50,150( ; )50,100( ; )50,200( ; )30,200( ; and )30,250( . d. If the firm is operating in the Long Run and wants to produce 500=q units of output, are the minimum costs of production greater than, less than, or equal to $4,000? Explain. What if instead the firm wanted to produce 450=q units of output? Explain. e. If the firm is operating in the Short Run with 50=K units of capital and wants to produce 500=q units of output, are the minimum costs of production greater than, less than, or equal to $4,000? Explain. What if instead the firm wanted to produce 400=q units of output? What if instead the firm wanted to produce 600=q units of output? Explain. K L 0 0 150 400 50 80 Q=500 30 200 2504) The solution to the Long Run Cost Minimization problem for “Firm A” is illustrated by the figure on the left below; the solution to the Long Run Cost Minimization problem for “Firm B” is illustrated by the figure on the right below. For which firm would you expect the Price Elasticity of Demand for Labor to be smaller (that is, “more negative”)? For which firm would you expect the Price Elasticity of Demand for Capital to be smaller (that is, “more negative”)? Explain. K L Firm A Q=200 K L Firm B
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