Review Questions – Chapter 9. ECON 500 – Spring 2004. Chapter #9 (“Costs”): Review Questions: 3, 4, 6, and 7. Problems and Applications: 1, 2, 4, 5, and 8. Additional Questions: 1) Consider the production function KLLKF 4),( = . For this function LKMPL2= and KLMPK2= . a. Suppose the firm is operating in the long run. Graphically illustrate the solution to the long run cost minimization problem for a firm with this production function. Determine the long run cost minimizing levels of labor and capital. Determine the long run cost function of this firm, as well as the long run average cost function of this firm. b. Suppose the firm is operating in the short run with KK= units of capital. Graphically illustrate the solution to the short run cost minimization problem for a firm with this production function. Determine the short run cost minimizing level of labor. Determine the short run cost function of this firm. Decompose short run costs in to variable costs and fixed costs. From here, determine the functional forms of average variable costs, average fixed costs, and average costs of production. 2) Consider a firm with the production function 45.25.5),( LKLKF = . a. Suppose this firm is operating in the short run with 81=K units of capital. Graphically illustrate the solution to the run costs minimization problem for this firm. b. Based upon the graph drawn in part (a), argue that for any specific target level of output, long run total costs are never greater than short run total costs.3) Consider a firm that produces output from only one input, according to the production function αLLF )25(.)( = (each unit of L costs 0>w ). a. Determine the minimum costs of producing 0>q units of output. b. Determine average costs of production as a function of the level of output. c. Graphically illustrate total costs for 1=α, 21=α, and 2=α. Based upon the shape of total costs, determine the returns to scale of this technology for each of these values of α. d. Graphically illustrate average costs for 1=α, 21=α, and 2=α. Based upon the shape of average costs, determine the returns to scale of this technology for each of these values of α. e. For each of the three values of α considered in parts (c) and (d), are marginal costs of production be increasing, decreasing, or constant? Clearly
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