Review Questions – WN Chapters 5, 6, 7, and 10. ECON 500 – Fall 2004. WN Chapter #5 (“Production”): Review Questions: 2, 3, and 9. Problems: 5.1, 5.2, 5.3, 5.4, 5.7, 5.8, and 5.10. Additional Questions: 1) Consider the production function LKKLF 2),( = . For this function LKMPL= and KLMPK= . a. How much output can the firm produce with )9,4(),(=LK? b. Determine KLMRTS,. Is the Marginal Rate of Technical Substitution “Diminishing”? Explain. c. Sketch the isoquant associated with 12=Q . d. Identify an input combination that leads to more than 12 units of output being produced. Illustrate this input combination graphically (in relation to the 12=Q isoquant). e. Identify an input combination that leads to less than 12 units of output being produced. Illustrate this input combination graphically (in relation to the 12=Q isoquant). 2) Determine if each of the following production functions exhibits Increasing, Decreasing, or Constant Returns to Scale: a. 24),( KLLKF = b. LKLKF 53),( += c. LKLKF 2),( += d. 42.63.8),( LKLKF = e. },min{),(KLLKF = f. α},min{),( KLLKF = , with 1<α g. α},min{),( KLLKF = , with 1>α h. XYZZYXF =),,(WN Chapter #6 (“Costs”): Review Questions: 3, 4, and 10. Problems: 6.1, 6.2, 6.4, 6.5, 6.8, 6.9, and 6.10. Additional Questions: 1) Consider the production function KLLKF 8),( = . For this function LKMPL4= and KLMPK4= . 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. 3) Consider a firm with the production function 2.5.20),( LKLKF = . a. Suppose this firm is operating in the short run with 400=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.4) Consider a firm producing output q using three inputs, =L labor, =Kcapital, and =J land, according to the production function LKJJKLF 4),,( = . For this production function: LKJMPL2= , KLJMPK2= , and JLKMPJ2= . Each unit of labor costs 0>w ; each unit of capital costs 0>r ; each unit of land costs 0>v . Consider the decision of how to produce output in the current period, when the firm is restricted to using 25=J units of land, but is free to choose any level of L and any level of K. a. Is the firm currently operating in the “Long Run” or the “Short Run”? Clearly explain. b. Suppose the firm wishes to produce q units of output as inexpensively as possible. Determine the optimal amount of each input for the firm to hire. c. Determine the minimum costs of producing a target level of output q . d. Clearly explain how your answers to parts (b) and (c) would differ as: d.i. the target level of output is increased. d.ii. 0>w is increased. d.iii. 0>r is increased. d.iv. 0>v is increased. WN Chapter #7 (“Profit Maximization and Supply”): Review Questions: 5 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 of production given by Α++=252)( qqqCSR. For this firm qqMCSR102)(+=. 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 16=p . Determine the Short Run profit of this firm, as a function of Α. For what values of Α is the firm able to earn a positive profit? Explain.2) 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. WN Chapter #10 (“Monopoly”): Review Questions: 1, 3, and 6. Problems: 10.1, 10.2, 10.3, and 10.7. Additional Questions: 1) Consider a monopolist with CqqC=)( operating in a market with inverse demand given by qqP−= 500)(. Suppose 5000<≤C . a. State the profit of this monopolist as a function of output. b. For this monopolist, CqMC=)( and qqMR 2500)(−=. Determine: b.i. *p , the profit maximizing price. b.ii. *q , the profit maximizing quantity. b.iii. *π, the resulting level of profit. b.iv. *DWL, the resulting deadweight loss. b.v. *CS , the resulting level of consumers’ surplus. c. Determine how each quantity in part (b) changes as 500<C increases. d. Redo the above question if instead qAqP−=)( , in which case qAqMR 2)( −= (now assume AC<≤0 ). MC AVC AC2) Consider a monopolist with costs given by FqqC+=43)( (so that 43)( =qMC ) operating in a market in which demand is given by the function 4500)(ppD = . a. Determine the price and