Review Questions – WN Chapters 5, 6, and 7. ECON 500 – Summer 2004. WN Chapter #5 (“Production”): Review Questions: 2, 3, and 9. Problems: 5.1, 5.2, 5.3, 5.7, 5.8, 5.9, and 5.10. Additional Questions: 1) Consider the production function LKLKF22),( = . For this function 22KMPL= and KLMPK4= . a. How much output can the firm produce with )5,2(),(=LK ? b. Determine KLMRTS,. Is the Marginal Rate of Technical Substitution “Diminishing”? Explain. c. Sketch the isoquant associated with 40=Q . d. Identify an input combination that leads to more than 40 units of output being produced. Illustrate this input combination graphically (in relation to the 40=Q isoquant). e. Identify an input combination that leads to less than 40 units of output being produced. Illustrate this input combination graphically (in relation to the 40=Q isoquant). f. Does this production function exhibit increasing, decreasing, or constant returns to scale? Explain. 2) Determine if each of the following production functions exhibits Increasing, Decreasing, or Constant Returns to Scale: a. KLLKF 5),( = b. LKLKF 23),( += c. LKLKF +=),( d. 38.25.10),( LKLKF = e. },min{),( KLLKF = f. α}7,3min{),( KLLKF = , with 1<α g. α}4,5min{),( KLLKF = , with 1>α h. XYZZYXF 8),,( =WN Chapter #6 (“Costs”): Review Questions: 2, 3, 4, and 10. Problems: 6.1, 6.2, 6.4, 6.5, 6.9, and 6.10. 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 this firm. Determine the long run cost minimizing levels of labor and capital. Determine the long run cost function and 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 this firm. 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 that produces output from only one input, according to the production function αLLF 2)( = (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 explain. 3) Consider a firm with the production function 25.20.10),( LKLKF = . a. Suppose this firm is operating in the short run with 024,1=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.WN Chapter #7 (“Profit Maximization and Supply”): Review Questions: 5, 7, and 8. Problems: 7.1, 7.3, 7.4, 7.6 and 7.9. Additional Questions: 1) Consider a competitive firm with Short Run costs as illustrated below. a. Graphically illustrate the firm’s Short Run Supply curve. b. For what range of prices (if any) will the firm choose to “shutdown” in the Short Run? Clearly explain. c. For what range of prices (if any) will the firm be able to earn a positive profit in the Short Run? Clearly explain. 2) Consider a competitive firm with Short Run costs of production given by CqqqCSR++=250200)( . For this firm qqMCSR100200)(+=. a. Determine Variable Costs and Fixed Costs of production. b. Determine Average Variable Costs of production. c. For what levels of output are Marginal Costs greater than Average Variable Costs? d. Determine the Short Run Supply of this firm as a function of price (clearly specifying the range of prices, if any, for which the firm will choose to “shutdown”). e. Suppose 400=p . Determine the Short Run profit of this firm, as a function of C . For what values of C is the firm able to earn a positive profit? Explain. MCAVC
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