利潤最大化范里安英文ppt課件

1、Chapter NineteenProfit-Maximization.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. .The Competitive FirmThe competitive firm takes all output prices p1,pn and all input prices w1,wm as

2、 given constants.Economic ProfitThe economic profit generated by the production plan (x1,xm,y1,yn) is.Economic ProfitOutput and input levels are typically flows.(流量E.g. x1 might be the number of labor units used per hour.每小時勞動投入量And y3 might be the number of cars produced per hour.每小時產(chǎn)出量Consequently

3、, profit is typically a flow also; e.g. the number of dollars of profit earned per hour.Economic ProfitHow do we value a firm?如何為一個公司訂價？ Suppose the firms stream of periodic economic profits is P0, P1, P2, and r is the rate of interest.Then the present-value of the firms economic profit stream is.Ec

4、onomic ProfitA competitive firm seeks to maximize its present-value.一個競爭性企業(yè)為最大化利潤流現(xiàn)值。How?.Economic ProfitSuppose the firm is in a short-run circumstance in which假定公司處于短期的消費環(huán)境 Its short-run production function is.Economic ProfitSuppose the firm is in a short-run circumstance in which Its short-run pr

5、oduction function isThe firms fixed cost isand its profit function is.Short-Run Iso-Profit Lines短期等利潤線A $P iso-profit line 等利潤線contains all the production plans that provide a profit level $P .A $P iso-profit lines equation is.Short-Run Iso-Profit LinesA $P iso-profit line contains all the productio

6、n plans that yield a profit level of $P .The equation of a $P iso-profit line isI.e.Short-Run Iso-Profit Lines短期等利潤線has a slope ofand a vertical intercept of.Short-Run Iso-Profit LinesIncreasing profityx1.Short-Run Profit-Maximization短期公司利潤最大化The firms problem is to locate the production plan that a

7、ttains the highest possible iso-profit line, given the firms constraint on choices of production plans.給定公司的消費方案約束，使消費方案盡能夠地到達最高的等利潤線上。Q: What is this constraint?消費方案約束？.Short-Run Profit-MaximizationThe firms problem is to locate the production plan that attains the highest possible iso-profit line,

8、 given the firms constraint on choices of production plans.消費方案的選擇約束Q: What is this constraint?技術約束A: The production function.消費函數(shù).Short-Run Profit-Maximizationx1TechnicallyinefficientplansyThe short-run production function andtechnology set for .Short-Run Profit-Maximizationx1Increasing profity.Sho

9、rt-Run Profit-Maximizationx1y.Short-Run Profit-Maximizationx1yGiven p, w1 and the short-runprofit-maximizing plan is .Short-Run Profit-Maximizationx1yGiven p, w1 and the short-runprofit-maximizing plan is And the maximumpossible profitis .Short-Run Profit-Maximizationx1yAt the short-run profit-maxim

10、izing plan, the slopes of the short-run production function and the maximaliso-profit line areequal.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-Maximization is the ma

11、rginal revenue product ofinput 1, the rate at which revenue increaseswith the amount used of input 1要素1的邊沿產(chǎn)品收益.If then profit increases with x1.If then profit decreases with x1. .Short-Run Profit-Maximization; A Cobb-Douglas ExampleSuppose the short-run productionfunction isThe marginal product of t

12、he variableinput 1 isThe profit-maximizing condition is.Short-Run Profit-Maximization; A Cobb-Douglas ExampleSolvingfor x1 gives.Short-Run Profit-Maximization; A Cobb-Douglas ExampleSolvingfor x1 givesThat is,.Short-Run Profit-Maximization; A Cobb-Douglas ExampleSolvingfor x1 givesThat is,so.Short-R

13、un Profit-Maximization; A Cobb-Douglas Exampleis the firmsshort-run demandfor input 1 when the level of input 2 is fixed at units. .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 lev

14、el is thus.Comparative Statics of Short-Run Profit-Maximization比較靜態(tài)分析What happens to the short-run profit-maximizing production plan as the 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 reductio

15、n in the slope, and - a reduction in the vertical intercept.Comparative Statics of Short-Run Profit-Maximizationx1y.Comparative Statics of Short-Run Profit-Maximizationx1y.Comparative Statics of Short-Run Profit-Maximizationx1y.Comparative Statics of Short-Run Profit-MaximizationAn increase in p, th

16、e 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 firms variable input (the firms demand curve for its variable input shifts outward).Comparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas

17、 example: When then the firms short-rundemand for its variable input 1 isand its short-runsupply is.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.Compara

18、tive 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 isincreases as p increases.Comparative Statics of Short-Run Profit-MaximizationWhat happens to the short-run profit-m

19、aximizing production plan as the variable input price w1 changes?.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.Comparative Statics of Short-Run Profit

20、-Maximizationx1y.Comparative Statics of Short-Run Profit-Maximizationx1y.Comparative Statics of Short-Run Profit-Maximizationx1y.Comparative Statics of Short-Run Profit-MaximizationAn increase in w1, the price of the firms variable input, causesa decrease in the firms output level (the firms supply

21、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 Short-Run Profit-MaximizationThe Cobb-Douglas example: When then the firms short-rundemand for its variable input 1 isand its short-runs

22、upply is.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.Comparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example: When then the firms

23、 short-rundemand for its variable input 1 isdecreases as w1 increases.decreases as w1 increases.and its short-runsupply is.Long-Run Profit-Maximization長期利潤最大化Now allow the firm to vary both input levels.Since no input level is fixed, there are no fixed costs.Long-Run Profit-MaximizationBoth x1 and x

24、2 are variable.Think 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 level.Long-Run Profit-MaximizationThe equation of a long-run iso-profit lineisso an increase in x2 causes - no change to the slope,

25、 and - an increase in the vertical intercept.Long-Run Profit-Maximizationx1y.Long-Run Profit-Maximizationx1yLarger levels of input 2 increase theproductivity of input 1.Long-Run Profit-Maximizationx1yLarger levels of input 2 increase theproductivity of input 1.The marginal productof input 2 isdimini

26、shing.Long-Run Profit-Maximizationx1yLarger levels of input 2 increase theproductivity of input 1.The marginal productof input 2 isdiminishing.Long-Run Profit-Maximizationx1y for each short-runproduction plan.Long-Run Profit-Maximizationx1yThe marginal productof input 2 isdiminishing so . for each s

27、hort-runproduction plan.Long-Run Profit-Maximizationx1ythe marginal profitof input 2 isdiminishing. for each short-runproduction plan.Long-Run Profit-MaximizationProfit will increase as x2 increases so long as the marginal profit of input 2The profit-maximizing level of input 2 therefore satisfies.L

28、ong-Run Profit-MaximizationProfit will increase as x2 increases so long as the marginal profit of input 2The profit-maximizing level of input 2 therefore satisfiesAnd is satisfied in any short-run, so .Long-Run Profit-MaximizationThe input levels of the long-run profit-maximizing plan satisfyThat is

29、, marginal revenue equals marginal cost for all inputs.and.Long-Run Profit-MaximizationThe Cobb-Douglas example: When then the firms short-rundemand for its variable input 1 isand its short-runsupply isShort-run profit is therefore .Long-Run Profit-Maximization.Long-Run Profit-Maximization.Long-Run

30、Profit-Maximization.Long-Run Profit-Maximization.Long-Run Profit-MaximizationWhat is the long-run profit-maximizinglevel of input 2? Solveto get.Long-Run Profit-MaximizationWhat is the long-run profit-maximizinginput 1 level? Substituteintoto get.Long-Run Profit-MaximizationWhat is the long-run prof

31、it-maximizinginput 1 level? Substituteintoto get.Long-Run Profit-MaximizationWhat is the long-run profit-maximizingoutput level? Substituteintoto get.Long-Run Profit-MaximizationWhat is the long-run profit-maximizingoutput level? Substituteintoto get.Long-Run Profit-MaximizationSo given the prices p

32、, w1 and w2, andthe production functionthe long-run profit-maximizing productionplan is.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.該競爭性企業(yè)假設存在規(guī)模報酬遞減的技術，那么會存在獨一一個長期

33、利潤最大化的產(chǎn)出方案.Returns-to Scale and Profit-Maximizationxyy*x*Decreasingreturns-to-scale.Returns-to-Scale and Profit-MaximizationIf a competitive firms technology exhibits exhibits increasing returns-to-scale then the firm does not have a profit-maximizing plan.Returns-to Scale and Profit-Maximizationxyy

34、xIncreasingreturns-to-scaleyxIncreasing profit.Returns-to-Scale and Profit-MaximizationSo an increasing returns-to-scale technology is inconsistent with firms being perfectly competitive.因此，規(guī)模報酬遞增的技術假設與競爭性企業(yè)假定是矛盾的.Returns-to-Scale and Profit-MaximizationWhat if the competitive firms technology exhib

35、its constant returns-to-scale?.Returns-to Scale and Profit-MaximizationxyyxConstantreturns-to-scaleyxIncreasing profit.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

36、original profit.Returns-to Scale and Profit-MaximizationTherefore, when a firms technology 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 profi

37、ts of zero.Returns-to Scale and Profit-MaximizationxyyxConstantreturns-to-scaleyxP = 0.Revealed Profitability顯示利潤Consider 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

38、we learn from our observations?.Revealed ProfitabilityIf a production 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).Revealed Profitabilityxy is chosen at prices .Revealed Profitabilityxy is chosen at prices so is profit-ma

39、ximizing at these prices.Revealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices. would give higherprofits, 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? Bec

40、ause it isnot a feasible plan.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.So the firms technology set must lie under theiso-profit line.Revealed Profitabilityxy is chosen at p

41、rices so is profit-maximizing at these prices.So the firms technology set must lie under theiso-profit line.The technologyset is somewherein here.Revealed Profitabilityxy is chosen at prices so maximizes profit at these prices. would provide higherprofit but it is not chosen.Revealed Profitabilityxy

42、 is chosen at prices so maximizes profit at these prices. would provide higherprofit but it is not chosenbecause it is not feasible.Revealed 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 isalso somewhere inhere.Revealed ProfitabilityxyThe firms technology set must lie underboth iso-profit lines.Revealed ProfitabilityxyThe