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1、Chapter NineteenProfit-MaximizationEconomic ProfituA firm uses inputs j=1,m to make products i=1,n.uOutput levels are y1,yn.uInput levels are x1,xm.uProduct prices are p1,pn.uInput prices are w1,wm.The Competitive FirmuThe competitive firm takes all output prices p1,pn and all input prices w1,wm as
2、given constants.Economic ProfituThe economic profit generated by the production plan(x1,xm,y1,yn)isEconomic ProfituOutput and input levels are typically flows.(流量）流量）uE.g.x1 might be the number of labor units used per hour.（每小时劳动投入（每小时劳动投入量）量）uAnd y3 might be the number of cars produced per hour.（每小
3、时产出量）（每小时产出量）uConsequently,profit is typically a flow also;e.g.the number of dollars of profit earned per hour.Economic ProfituHow do we value a firm?如何为一个公如何为一个公司订价？司订价？uSuppose the firms stream of periodic economic profits is P P0 0,P,P1 1,P P2 2,and r is the rate of interest.uThen the present-val
4、ue of the firms economic profit stream isEconomic ProfituA competitive firm seeks to maximize its present-value.一个竞争一个竞争性企业为最大化利润流现值。性企业为最大化利润流现值。uHow?Economic ProfituSuppose the firm is in a short-run circumstance in which（假定公司处于（假定公司处于短期的生产环境）短期的生产环境）uIts short-run production function isEconomic P
5、rofituSuppose the firm is in a short-run circumstance in which uIts short-run production function isuThe firms fixed cost isand its profit function isShort-Run Iso-Profit Lines短期等利润线uA$P P iso-profit line（等利润线）（等利润线）contains all the production plans that provide a profit level$P P.uA$P P iso-profit
6、lines equation isShort-Run Iso-Profit LinesuA$P P iso-profit line contains all the production plans that yield a profit level of$P P.uThe equation of a$P P iso-profit line isuI.e.Short-Run Iso-Profit Lines短期等利润线has a slope ofand a vertical intercept ofShort-Run Iso-Profit LinesIncreasing profityx1Sh
7、ort-Run Profit-Maximization短期公司利润最大化uThe firms problem is to locate the production plan that attains the highest possible iso-profit line,given the firms constraint on choices of production plans.（给定公司的生产计（给定公司的生产计划约束，使生产计划尽可能地达到最高划约束，使生产计划尽可能地达到最高的等利润线上。）的等利润线上。）uQ:What is this constraint?（生产计划（生产计
8、划约束？）约束？）Short-Run Profit-MaximizationuThe firms problem is to locate the production plan that attains the highest possible iso-profit line,given the firms constraint on choices of production plans.（生产计划的选择约束）（生产计划的选择约束）uQ:What is this constraint?（技术约束）（技术约束）uA:The production function.（生产函数）（生产函数）Sh
9、ort-Run Profit-Maximizationx1TechnicallyinefficientplansyThe short-run production function andtechnology set for Short-Run Profit-Maximizationx1Increasing profityShort-Run Profit-Maximizationx1yShort-Run Profit-Maximizationx1yGiven p,w1 and the short-runprofit-maximizing plan is Short-Run Profit-Max
10、imizationx1yGiven p,w1 and the short-runprofit-maximizing plan is And the maximumpossible profitis Short-Run Profit-Maximizationx1yAt the short-run profit-maximizing plan,the slopes of the short-run production function and the maximaliso-profit line areequal.Short-Run Profit-Maximizationx1yAt the sh
11、ort-run profit-maximizing plan,the slopes of the short-run production function and the maximaliso-profit line areequal.Short-Run Profit-Maximization is the marginal revenue product ofinput 1,the rate at which revenue increaseswith the amount used of input 1（要素（要素1的边的边际产品收益）际产品收益）.If then profit incr
12、eases with x1.If then profit decreases with x1.Short-Run Profit-Maximization;A Cobb-Douglas ExampleSuppose the short-run productionfunction isThe marginal product of the variableinput 1 isThe profit-maximizing condition isShort-Run Profit-Maximization;A Cobb-Douglas ExampleSolvingfor x1 givesShort-R
13、un Profit-Maximization;A Cobb-Douglas ExampleSolvingfor x1 givesThat is,Short-Run Profit-Maximization;A Cobb-Douglas ExampleSolvingfor x1 givesThat is,soShort-Run Profit-Maximization;A Cobb-Douglas Exampleis the firmsshort-run demandfor input 1 when the level of input 2 is fixed at units.Short-Run P
14、rofit-Maximization;A Cobb-Douglas Exampleis the firmsshort-run demandfor input 1 when the level of input 2 is fixed at units.The firms short-run output level is thusComparative Statics of Short-Run Profit-Maximizationu比较静态分析比较静态分析uWhat happens to the short-run profit-maximizing production plan as th
15、e output price p changes?Comparative Statics of Short-Run Profit-MaximizationThe equation of a short-run iso-profit lineisso an increase in p causes -a reduction in the slope,and -a reduction in the vertical intercept.Comparative Statics of Short-Run Profit-Maximizationx1yComparative Statics of Shor
16、t-Run Profit-Maximizationx1yComparative Statics of Short-Run Profit-Maximizationx1yComparative Statics of Short-Run Profit-MaximizationuAn increase in p,the price of the firms output,causesan increase in the firms output level(the firms supply curve slopes upward),andan increase in the level of the
17、firms variable input(the firms demand curve for its variable input shifts outward).Comparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isand its short-runsupply isComparative Statics of Short-Run Profit-Maximizatio
18、nThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isincreases as p increases.and its short-runsupply isComparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isincreases as p incre
19、ases.and its short-runsupply isincreases as p increases.Comparative Statics of Short-Run Profit-MaximizationuWhat happens to the short-run profit-maximizing production plan as the variable input price w1 changes?Comparative Statics of Short-Run Profit-MaximizationThe equation of a short-run iso-prof
20、it lineisso an increase in w1 causes -an increase in the slope,and -no change to the vertical intercept.Comparative Statics of Short-Run Profit-Maximizationx1yComparative Statics of Short-Run Profit-Maximizationx1yComparative Statics of Short-Run Profit-Maximizationx1yComparative Statics of Short-Ru
21、n Profit-MaximizationuAn increase in w1,the price of the firms variable input,causesa decrease in the firms output level(the firms supply curve shifts inward),anda decrease in the level of the firms variable input(the firms demand curve for its variable input slopes downward).Comparative Statics of
22、Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isand its short-runsupply isComparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isdecreases as w1 i
23、ncreases.and its short-runsupply isComparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isdecreases as w1 increases.decreases as w1 increases.and its short-runsupply isLong-Run Profit-Maximization长期利润最大化uNow allow t
24、he firm to vary both input levels.uSince no input level is fixed,there are no fixed costs.Long-Run Profit-MaximizationuBoth x1 and x2 are variable.uThink of the firm as choosing the production plan that maximizes profits for a given value of x2,and then varying x2 to find the largest possible profit
25、 level.Long-Run Profit-MaximizationThe equation of a long-run iso-profit lineisso an increase in x2 causes -no change to the slope,and -an increase in the vertical intercept.Long-Run Profit-Maximizationx1yLong-Run Profit-Maximizationx1yLarger levels of input 2 increase theproductivity of input 1.Lon
26、g-Run Profit-Maximizationx1yLarger levels of input 2 increase theproductivity of input 1.The marginal productof input 2 isdiminishing.Long-Run Profit-Maximizationx1yLarger levels of input 2 increase theproductivity of input 1.The marginal productof input 2 isdiminishing.Long-Run Profit-Maximizationx
27、1y for each short-runproduction plan.Long-Run Profit-Maximizationx1yThe marginal productof input 2 isdiminishing so.for each short-runproduction plan.Long-Run Profit-Maximizationx1ythe marginal profitof input 2 isdiminishing.for each short-runproduction plan.Long-Run Profit-MaximizationuProfit will
28、increase as x2 increases so long as the marginal profit of input 2uThe profit-maximizing level of input 2 therefore satisfiesLong-Run Profit-MaximizationuProfit will increase as x2 increases so long as the marginal profit of input 2uThe profit-maximizing level of input 2 therefore satisfiesuAnd is s
29、atisfied in any short-run,so.Long-Run Profit-MaximizationuThe input levels of the long-run profit-maximizing plan satisfyuThat is,marginal revenue equals marginal cost for all inputs.andLong-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1
30、isand its short-runsupply isShort-run profit is therefore Long-Run Profit-MaximizationLong-Run Profit-MaximizationLong-Run Profit-MaximizationLong-Run Profit-MaximizationLong-Run Profit-MaximizationWhat is the long-run profit-maximizinglevel of input 2?Solveto getLong-Run Profit-MaximizationWhat is
31、the long-run profit-maximizinginput 1 level?Substituteintoto getLong-Run Profit-MaximizationWhat is the long-run profit-maximizinginput 1 level?Substituteintoto getLong-Run Profit-MaximizationWhat is the long-run profit-maximizingoutput level?Substituteintoto getLong-Run Profit-MaximizationWhat is t
32、he long-run profit-maximizingoutput level?Substituteintoto getLong-Run Profit-MaximizationSo given the prices p,w1 and w2,andthe production functionthe long-run profit-maximizing productionplan isReturns-to-Scale and Profit-MaximizationuIf a competitive firms technology exhibits decreasing returns-t
33、o-scale then the firm has a single long-run profit-maximizing production plan.（该竞争性企业若存在规模报酬递减的技术，（该竞争性企业若存在规模报酬递减的技术，则会存在唯一一个长期利润最大化的产出计划）则会存在唯一一个长期利润最大化的产出计划）Returns-to Scale and Profit-Maximizationxyy*x*Decreasingreturns-to-scaleReturns-to-Scale and Profit-MaximizationuIf a competitive firms tech
34、nology exhibits exhibits increasing returns-to-scale then the firm does not have a profit-maximizing plan.Returns-to Scale and Profit-Maximizationxyy”xIncreasingreturns-to-scaleyx”Increasing profitReturns-to-Scale and Profit-MaximizationuSo an increasing returns-to-scale technology is inconsistent w
35、ith firms being perfectly competitive.（因此，（因此，规模报酬递增的技术假设与竞争性企业规模报酬递增的技术假设与竞争性企业假定是矛盾的）假定是矛盾的）Returns-to-Scale and Profit-MaximizationuWhat if the competitive firms technology exhibits constant returns-to-scale?Returns-to Scale and Profit-Maximizationxyy”xConstantreturns-to-scaleyx”Increasing profit
36、Returns-to Scale and Profit-MaximizationuSo if any production plan earns a positive profit,the firm can double up all inputs to produce twice the original output and earn twice the original profit.Returns-to Scale and Profit-MaximizationuTherefore,when a firms technology exhibits constant returns-to
37、-scale,earning a positive economic profit is inconsistent with firms being perfectly competitive.uHence constant returns-to-scale requires that competitive firms earn economic profits of zero.Returns-to Scale and Profit-Maximizationxyy”xConstantreturns-to-scaleyx”P P=0Revealed Profitability显示利润uCons
38、ider a competitive firm with a technology that exhibits decreasing returns-to-scale.uFor a variety of output and input prices we observe the firms choices of production plans.uWhat can we learn from our observations?Revealed ProfitabilityuIf a production plan(x,y)is chosen at prices(w,p)we deduce th
39、at the plan(x,y)is revealed to be profit-maximizing for the prices(w,p).Revealed Profitabilityxy is chosen at prices Revealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.Revealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.would give hi
40、gherprofits,so why is it notchosen?Revealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.would give higherprofits,so why is it notchosen?Because it isnot a feasible plan.Revealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.would give hig
41、herprofits,so why is it notchosen?Because it isnot a feasible plan.So the firms technology set must lie under theiso-profit line.Revealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.So the firms technology set must lie under theiso-profit line.The technologyset is som
42、ewherein hereRevealed Profitabilityxy is chosen at prices so maximizes profit at these prices.would provide higherprofit but it is not chosenRevealed Profitabilityxy is chosen at prices so maximizes profit at these prices.would provide higherprofit but it is not chosenbecause it is not feasibleRevea
43、led Profitabilityxy is chosen at prices so maximizes profit at these prices.would provide higherprofit but it is not chosenbecause it is not feasible sothe technology set lies underthe iso-profit line.Revealed Profitabilityxy is chosen at prices so maximizes profit at these prices.The technology set
44、 isalso somewhere inhere.Revealed ProfitabilityxyThe firms technology set must lie underboth iso-profit linesRevealed ProfitabilityxyThe firms technology set must lie underboth iso-profit linesThe technology setis somewherein this intersectionRevealed ProfitabilityuObserving more choices of producti
45、on plans by the firm in response to different prices for its input and its output gives more information on the location of its technology set.Revealed ProfitabilityxyThe firms technology set must lie underall the iso-profit linesRevealed ProfitabilityxyThe firms technology set must lie underall the
46、 iso-profit linesRevealed ProfitabilityxyThe firms technology set must lie underall the iso-profit linesRevealed ProfitabilityuWhat else can be learned from the firms choices of profit-maximizing production plans?Revealed ProfitabilityxyThe firms technology set must lie underall the iso-profit lines
47、 is chosen at prices so is chosen at prices soRevealed ProfitabilityandsoandAdding givesRevealed ProfitabilitysoThat is,is a necessary implication of profit-maximization.（这是利润最大化的必要条（这是利润最大化的必要条件）件）Revealed Profitabilityis a necessary implication of profit-maximization.Suppose the input price does n
48、ot change.Then D Dw=0 and profit-maximizationimplies ;i.e.,a competitivefirms output supply curve cannot slopedownward.（竞争性厂商的供给线不能为向下（竞争性厂商的供给线不能为向下的斜率）的斜率）Revealed Profitabilityis a necessary implication of profit-maximization.Suppose the output price does not change.Then D Dp=0 and profit-maximizationimplies ;i.e.,a competitivefirms input demand curve cannot slopeupward.（要素需求曲线的斜率不能是向上的）（要素需求曲线的斜率不能是向上的）