讲义 利润最大化.pptx

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1、Economic ProfitA firm uses inputs j=1,m to make products i=1,n.Output levels are y1,yn.Input levels are x1,xm.Product prices are p1,pn.Input prices are w1,wm.第1页/共72页The Competitive FirmThe competitive firm takes all output prices p1,pn and all input prices w1,wm as given constants.第2页/共72页Economic

2、ProfitThe economic profit generated by the production plan(x1,xm,y1,yn)is第3页/共72页Economic ProfitOutput and input levels are typically flows.E.g.x1 might be the number of labor units used per hour.And y3 might be the number of cars produced per hour.Consequently,profit is typically a flow also;e.g.th

3、e number of dollars of profit earned per hour.第4页/共72页Opportunity Costs(机会成本机会成本)All inputs must be valued at their market value.LaborCapital第5页/共72页Economic ProfitHow do we value a firm?Suppose the firms stream of periodic economic profits is P0,P1,P2,and r is the rate of interest.Then the present-

4、value of the firms economic profit stream is第6页/共72页Profit MaximizationA competitive firm seeks to maximize its present-value.How?第7页/共72页Suppose the firm is in a short-run circumstance in which Its short-run production function isThe firms fixed cost isand its profit function isShort-Run Profit Max

5、imization第8页/共72页Short-Run Iso-Profit LinesA$P iso-profit line(等利润线)contains all the production plans that yield a profit level of$P.The equation of a$P iso-profit line isI.e.第9页/共72页Short-Run Iso-Profit Lineshas a slope ofand a vertical intercept of第10页/共72页Short-Run Iso-Profit LinesIncreasing prof

6、ityx1第11页/共72页Short-Run Profit-MaximizationThe 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.Q:What is this constraint?A:The production function.第12页/共72页Short-Run Profit-Maximizationx1Techni

7、callyinefficientplansyThe short-run production function andtechnology set for 第13页/共72页Short-Run Profit-Maximizationx1Increasing profity第14页/共72页Short-Run Profit-Maximizationx1y第15页/共72页Short-Run Profit-Maximizationx1yGiven p,w1 and the short-runprofit-maximizing plan is 第16页/共72页Short-Run Profit-Ma

8、ximizationx1yGiven p,w1 and the short-runprofit-maximizing plan is And the maximumpossible profitis 第17页/共72页Short-Run Profit-Maximizationx1yAt the short-run profit-maximizing plan,the slopes of the short-run production function and the maximaliso-profit line areequal.第18页/共72页Short-Run Profit-Maxim

9、izationx1yAt the short-run profit-maximizing plan,the slopes of the short-run production function and the maximaliso-profit line areequal.第19页/共72页Short-Run Profit-Maximization is the marginal revenue product(边际收益产量)of input 1,the rate at which revenue Increases with the amount used of input 1.If th

10、en profit increases with x1.If then profit decreases with x1.第20页/共72页Short-Run Profit-Maximization;A Cobb-Douglas ExampleSuppose the short-run productionfunction isThe marginal product of the variableinput 1 isThe profit-maximizing condition is第21页/共72页Short-Run Profit-Maximization;A Cobb-Douglas E

11、xampleSolvingfor x1 gives第22页/共72页Short-Run Profit-Maximization;A Cobb-Douglas ExampleSolvingfor x1 givesThat is,第23页/共72页Short-Run Profit-Maximization;A Cobb-Douglas ExampleSolvingfor x1 givesThat is,so第24页/共72页Short-Run Profit-Maximization;A Cobb-Douglas Exampleis the firmsshort-run demandfor inpu

12、t 1 when the level of input 2 is fixed at units.第25页/共72页Short-Run Profit-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 thus第26页/共72页Comparative Statics of Short-Run Profit-MaximizationWhat h

13、appens to the short-run profit-maximizing production plan as the output price p changes?第27页/共72页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.第28页/共72页C

14、omparative Statics of Short-Run Profit-Maximizationx1y第29页/共72页Comparative Statics of Short-Run Profit-Maximizationx1y第30页/共72页Comparative Statics of Short-Run Profit-Maximizationx1y第31页/共72页Comparative Statics of Short-Run Profit-MaximizationAn increase in p,the price of the firms output,causesan i

15、ncrease in the firms output level(the firms supply curve slopes upward),andan increase in the level of the firms variable input(the firms demand curve for its variable input shifts outward).第32页/共72页Comparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms shor

16、t-rundemand for its variable input 1 isand its short-runsupply is第33页/共72页Comparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isincreases as p increases.and its short-runsupply is第34页/共72页Comparative Statics of Sho

17、rt-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isincreases as p increases.and its short-runsupply isincreases as p increases.第35页/共72页Comparative Statics of Short-Run Profit-MaximizationWhat happens to the short-run profit-maximizing p

18、roduction plan as the variable input price w1 changes?第36页/共72页Comparative Statics of Short-Run Profit-MaximizationThe equation of a short-run iso-profit lineisso an increase in w1 causes -an increase in the slope,and -no change to the vertical intercept.第37页/共72页Comparative Statics of Short-Run Pro

19、fit-Maximizationx1y第38页/共72页Comparative Statics of Short-Run Profit-Maximizationx1y第39页/共72页Comparative Statics of Short-Run Profit-Maximizationx1y第40页/共72页Comparative Statics of Short-Run Profit-MaximizationAn increase in w1,the price of the firms variable input,causesa decrease in the firms output

20、 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).第41页/共72页Comparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variabl

21、e input 1 isand its short-runsupply is第42页/共72页Comparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isdecreases as w1 increases.and its short-runsupply is第43页/共72页Comparative Statics of Short-Run Profit-Maximization

22、The 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 is第44页/共72页Long-Run Profit-MaximizationNow allow the firm to vary both input levels,i.e.,both x1 and x2 are variable.Since no input leve

23、l is fixed,there are no fixed costs.第45页/共72页The profit-maximization problem isFOCs are:Long-Run Profit-Maximization第46页/共72页Factor Demand FunctionsDemand for inputs 1 and 2 can be solved as,第47页/共72页Inverse Factor Demand FunctionsFor a given optimal demand for x2,inverse demand function for x1 isFo

24、r a given optimal demand for x1 inverse demand function for x2 is第48页/共72页Inverse Factor Demand Curvesx1w1第49页/共72页Example:C-D Production FunctionThe production function isFirst-order conditions are:第50页/共72页Solving for x1 and x2:Plug-in production function to get:Example:C-D Production Function第51页

25、/共72页Returns-to-Scale and Profit-MaximizationIf a competitive firms technology exhibits decreasing returns-to-scale then the firm has a single long-run profit-maximizing production plan.第52页/共72页Returns-to Scale and Profit-Maximizationxyy*x*Decreasingreturns-to-scale第53页/共72页Returns-to-Scale and Pro

26、fit-MaximizationIf a competitive firms technology exhibits exhibits increasing returns-to-scale then the firm does not have a profit-maximizing plan.第54页/共72页Returns-to Scale and Profit-Maximizationxyy”xIncreasingreturns-to-scaleyx”Increasing profit第55页/共72页Returns-to-Scale and Profit-MaximizationSo

27、 an increasing returns-to-scale technology is inconsistent with firms being perfectly competitive.第56页/共72页Returns-to-Scale and Profit-MaximizationWhat if the competitive firms technology exhibits constant returns-to-scale?第57页/共72页Returns-to Scale and Profit-Maximizationxyy”xConstantreturns-to-scal

28、eyx”Increasing profit第58页/共72页Returns-to Scale and Profit-MaximizationSo 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.第59页/共72页Returns-to Scale and Profit-MaximizationTherefore,when a firms te

29、chnology exhibits constant returns-to-scale,earning a positive economic profit is inconsistent with firms being perfectly competitive.Hence constant returns-to-scale requires that competitive firms earn economic profits of zero.第60页/共72页Returns-to Scale and Profit-Maximizationxyy”xConstantreturns-to

30、-scaleyx”P=0第61页/共72页Revealed ProfitabilityConsider a competitive firm with a technology that exhibits decreasing returns-to-scale.For a variety of output and input prices we observe the firms choices of production plans.What can we learn from our observations?第62页/共72页Revealed ProfitabilityIf a pro

31、duction plan(x,y)is chosen at prices(w,p)we deduce that the plan(x,y)is revealed to be profit-maximizing for the prices(w,p).第63页/共72页Revealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.第64页/共72页Revealed Profitabilityxy is chosen at prices so is profit-maximizing at

32、these prices.would give lowerprofits,so第65页/共72页Revealed Profitabilityxy is chosen at prices so(x”,y”)is chosen at prices(w”,p”)so(x”,y”)is profit-maximizing at these prices.第66页/共72页Weak Axiom of Profit Maximizationxy is chosen at prices so is chosen at prices so第67页/共72页Revealed Profitabilityandso

33、andAdding gives第68页/共72页Revealed ProfitabilitysoThat is,is a necessary implication of profit-maximization.第69页/共72页Revealed Profitabilityis a necessary implication of profit-maximization.Suppose the input price does not change.Then Dw=0 and profit-maximizationimplies ;i.e.,a competitivefirms output supply curve cannot slopedownward.第70页/共72页Revealed Profitabilityis a necessary implication of profit-maximization.Suppose the output price does not change.Then Dp=0 and profit-maximizationimplies ;i.e.,a competitivefirms input demand curve cannot slopeupward.第71页/共72页感谢您的观看！第72页/共72页