利润管理及经营管理知识分析.pptx

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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,w

2、m as given constants.Economic ProfituThe economic profit generated by the production plan (x1,xm,y1,yn) is p yp yw xwxn nm m1 11 1.Economic 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 num

3、ber of cars produced per hour.（每小时产出量）（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 0 0, , 1 1, , 2 2, , and r is the r

4、ate of interest.uThen the present-value of the firms economic profit stream isPVrr 012211()Economic ProfituA competitive firm seeks to maximize its present-value.一个竞争性企业为最一个竞争性企业为最大化利润流现值。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

5、环境） uIts short-run production function isyf xx (,).12xx22 .Economic ProfituSuppose the firm is in a short-run circumstance in which uIts short-run production function isuThe firms fixed cost isand its profit function isyf xx (,).12 pyw xw x1 12 2.xx22 .FCw x 2 2Short-Run Iso-Profit Lines短期等利润线uA $ i

6、so-profit line （等利润线）（等利润线）contains all the production plans that provide a profit level $ .uA $ iso-profit lines equation is pyw xw x1 12 2.Short-Run Iso-Profit LinesuA $ iso-profit line contains all the production plans that yield a profit level of $ .uThe equation of a $ iso-profit line isuI.e. p

7、yw xw x1 12 2.ywpxw xp 112 2 .Short-Run Iso-Profit Lines短期等利润线ywpxw xp 112 2 has a slope of wp1and a vertical intercept of w xp2 2.Short-Run Iso-Profit Lines Increasing profityx1Slopeswp 1Short-Run Profit-Maximization短期公司利润最大化uThe firms problem is to locate the production plan that attains the highe

8、st 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（生产计划约束？）约束？）Short-Run Profit-MaximizationuThe firms problem is to locate the production plan that attains the h

9、ighest 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）Short-Run Profit-Maximizationx1TechnicallyinefficientplansyThe short-run production function andtechnology

10、set for xx22 .yf xx (,)12Short-Run Profit-Maximizationx1Increasing profitSlopeswp 1yyf xx (,)12 Short-Run Profit-Maximizationx1y Slopeswp 1x1*y*Short-Run Profit-Maximizationx1ySlopeswp 1Given p, w1 and the short-runprofit-maximizing plan is x1*y*xx22 ,(,).*xxy12Short-Run Profit-Maximizationx1ySlopes

11、wp 1Given p, w1 and the short-runprofit-maximizing plan is And the maximumpossible profitis xx22 ,(,).*xxy12 . x1*y*Short-Run Profit-Maximizationx1ySlopeswp 1At the short-run profit-maximizing plan, the slopes of the short-run production function and the maximaliso-profit line areequal. x1*y*Short-R

12、un Profit-Maximizationx1ySlopeswp 1At the short-run profit-maximizing plan, the slopes of the short-run production function and the maximaliso-profit line areequal.MPwpat xxy1112 (,)* x1*y*Short-Run Profit-MaximizationMPwppMPw1111 pMP 1 is the marginal revenue product ofinput 1, the rate at which re

13、venue 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 increases with x1.If then profit decreases with x1. pMPw 11pMPw 11Short-Run Profit-Maximization; A Cobb-Douglas ExampleSuppose the short-run productionfunction isyxx 11/321/3.The marginal product of the variableinpu

14、t 1 isMPyxxx1112 321/313 /.The profit-maximizing condition isMRPpMPpxxw1112 321/313 ().*/Short-Run Profit-Maximization; A Cobb-Douglas Examplepxxw312 321/31()*/ Solvingfor x1 gives().*/xwpx12 3121/33 Short-Run Profit-Maximization; A Cobb-Douglas Examplepxxw312 321/31()*/ Solvingfor x1 gives().*/xwpx

15、12 3121/33 That is,()*/xpxw12 321/313 Short-Run Profit-Maximization; A Cobb-Douglas Examplepxxw312 321/31()*/ Solvingfor x1 gives().*/xwpx12 3121/33 That is,()*/xpxw12 321/313 soxpxwpwx121/313 213 221/233*/. Short-Run Profit-Maximization; A Cobb-Douglas Examplexpwx113 221/23*/ is the firmsshort-run

16、demandfor input 1 when the level of input 2 is fixed at units. x2Short-Run Profit-Maximization; A Cobb-Douglas Examplexpwx113 221/23*/ is the firmsshort-run demandfor input 1 when the level of input 2 is fixed at units. x2The firms short-run output level is thusyxxpwx*(). 11/321/311/221/23Comparativ

17、e 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 the output price p changes?Comparative Statics of Short-Run Profit-Maximizationywpxw xp 112 2 The equation of a short-run iso-profit lineisso an increase in p causes - a reducti

18、on in the slope, and - a reduction in the vertical intercept.Comparative Statics of Short-Run Profit-Maximizationx1 Slopeswp 1yyf xx (,)12x1*y*Comparative Statics of Short-Run Profit-Maximizationx1Slopeswp 1yyf xx (,)12x1*y*Comparative Statics of Short-Run Profit-Maximizationx1Slopeswp 1yyf xx (,)12

19、x1*y*Comparative 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 firms variable input (the firms demand curve for its variable input shifts

20、 outward).Comparative Statics of Short-Run Profit-Maximizationxpwx113 221/23*/ The Cobb-Douglas example: When then the firms short-rundemand for its variable input 1 isyxx 11/321/3ypwx*. 311/221/2and its short-runsupply isComparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:

21、When then the firms short-rundemand for its variable input 1 isyxx 11/321/3x1*increases as p increases.and its short-runsupply isxpwx113 221/23*/ ypwx*. 311/221/2Comparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example: When then the firms short-rundemand for its variable input 1

22、 isyxx 11/321/3y*increases as p increases.and its short-runsupply isx1*increases as p increases.xpwx113 221/23*/ ypwx*. 311/221/2Comparative Statics of Short-Run Profit-MaximizationuWhat happens to the short-run profit-maximizing production plan as the variable input price w1 changes?Comparative Sta

23、tics of Short-Run Profit-Maximizationywpxw xp 112 2 The 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-Maximizationx1 Slopeswp 1yyf xx (,)12x1*y*Comparative Statics of

24、Short-Run Profit-Maximizationx1Slopeswp 1yyf xx (,)12x1*y* Comparative Statics of Short-Run Profit-Maximizationx1Slopeswp 1yyf xx (,)12x1*y* Comparative Statics of Short-Run Profit-MaximizationuAn increase in w1, the price of the firms variable input, causesa decrease in the firms output level (the

25、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 Short-Run Profit-Maximizationxpwx113 221/23*/ The Cobb-Douglas example: When then the firms short-rundemand for its variabl

26、e input 1 isyxx 11/321/3ypwx*. 311/221/2and its short-runsupply isComparative Statics of Short-Run Profit-Maximizationxpwx113 221/23*/ The Cobb-Douglas example: When then the firms short-rundemand for its variable input 1 isyxx 11/321/3x1*decreases as w1 increases.ypwx*. 311/221/2and its short-runsu

27、pply isComparative Statics of Short-Run Profit-Maximizationxpwx113 221/23*/ The Cobb-Douglas example: When then the firms short-rundemand for its variable input 1 isyxx 11/321/3x1*decreases as w1 increases.y*decreases as w1 increases.ypwx*. 311/221/2and its short-runsupply isLong-Run Profit-Maximiza

28、tion长期利润最大化uNow allow the 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 th

29、e largest possible profit level.Long-Run Profit-Maximizationywpxw xp 112 2 The 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-Maximizationx1yyf xx (,)12Long-Run Profit-Maximizationx1yyf xx (,)1

30、22yf xx (,)12yf xx (,)123Larger levels of input 2 increase theproductivity of input 1.Long-Run Profit-Maximizationx1yyf xx (,)122yf xx (,)12yf xx (,)123Larger levels of input 2 increase theproductivity of input 1.The marginal productof input 2 isdiminishing.Long-Run Profit-Maximizationx1yyf xx (,)12

31、2yf xx (,)12yf xx (,)123Larger levels of input 2 increase theproductivity of input 1.The marginal productof input 2 isdiminishing.Long-Run Profit-Maximizationx1yyf xx (,)122yf xx (,)12yf xx (,)123yx*() 2xx12*() xx122*() xx123*() yx*()22 yx*()32 pMPw 110 for each short-runproduction plan.Long-Run Pro

32、fit-Maximizationx1yyf xx (,)122yf xx (,)12yf xx (,)123The marginal productof input 2 isdiminishing so .yx*() 2xx12*() xx122*() xx123*() yx*()22 yx*()32 for each short-runproduction plan.pMPw 110Long-Run Profit-Maximizationx1yyf xx (,)122yf xx (,)12yf xx (,)123the marginal profitof input 2 isdiminish

33、ing.yx*() 2xx12*() xx122*() xx123*() yx*()22 yx*()32 for each short-runproduction plan.pMPw 110Long-Run Profit-MaximizationuProfit will increase as x2 increases so long as the marginal profit of input 2uThe profit-maximizing level of input 2 therefore satisfiespMPw 220.pMPw 220.Long-Run Profit-Maxim

34、izationuProfit will increase as x2 increases so long as the marginal profit of input 2uThe profit-maximizing level of input 2 therefore satisfiesuAnd is satisfied in any short-run, so .pMPw 110pMPw 220.pMPw 220.Long-Run Profit-MaximizationuThe input levels of the long-run profit-maximizing plan sati

35、sfyuThat is, marginal revenue equals marginal cost for all inputs.pMPw 220.pMPw 110andLong-Run Profit-Maximizationxpwx113 221/23*/ The Cobb-Douglas example: When then the firms short-rundemand for its variable input 1 isyxx 11/321/3ypwx*. 311/221/2and its short-runsupply isShort-run profit is theref

36、ore Long-Run Profit-Maximization pyw xw xppwxwpwxw x*/1 12211/221/2113 221/22233Long-Run Profit-Maximization pyw xw xppwxwpwxw xppwxwpwpww x*/1 12211/221/2113 221/22211/221/21111/22233333Long-Run Profit-Maximization pyw xw xppwxwpwxw xppwxwpwpww xppwxw x*/1 12211/221/2113 221/22211/221/21111/22211/2

37、21/22233333233Long-Run Profit-Maximization pyw xw xppwxwpwxw xppwxwpwpww xppwxw xpwx*/1 12211/221/2113 221/22211/221/21111/22211/221/222311/22333332334271/222 w x.Long-Run Profit-Maximization 427311/221/222pwxw x.What is the long-run profit-maximizinglevel of input 2? Solve0124272311/221/22 xpwxwto

38、get.*xxpw w22312227 Long-Run Profit-MaximizationWhat is the long-run profit-maximizinginput 1 level? Substitutexpwx113 221/23*/ xpw w2312227* intoto getLong-Run Profit-MaximizationWhat is the long-run profit-maximizinginput 1 level? Substitutexpwx113 221/23*/ xpw w2312227* intoto getxpwpw wpw w113 2

39、31221/2312232727*/. Long-Run Profit-MaximizationWhat is the long-run profit-maximizingoutput level? Substitutexpw w2312227* intoto getypwx* 311/221/2Long-Run Profit-MaximizationWhat is the long-run profit-maximizingoutput level? Substitutexpw w2312227* intoto getypwpw wpw w*. 327911/231221/2212ypwx*

40、 311/221/2Long-Run Profit-MaximizationSo given the prices p, w1 and w2, andthe production functionyxx 11/321/3the long-run profit-maximizing productionplan is(,),.*xxypw wpw wpw w123122312221227279 Returns-to-Scale and Profit-MaximizationuIf a competitive firms technology exhibits decreasing returns

41、-to-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，则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）会存在唯一一个长期利润最大化的产出计划）Returns-to Scale and Profit-Maximizationxyyf x ( )y*x*Decreasingreturns-to-scaleReturns-to-Scale and Profit-MaximizationuIf a competitive f

42、irms technology exhibits exhibits increasing returns-to-scale then the firm does not have a profit-maximizing plan.Returns-to Scale and Profit-Maximizationxyyf x ( )y”xIncreasingreturns-to-scaleyx”Increasing profitReturns-to-Scale and Profit-MaximizationuSo an increasing returns-to-scale technology

43、is inconsistent with 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-Maximizationxyyf x ( )y”xConstantreturns-to-

44、scaleyx”Increasing profitReturns-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 e

45、xhibits constant returns-to-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-Maximizationxyyf x ( )y”xConstantreturns-to-scaleyx”

46、 = 0Revealed Profitability显示利润uConsider 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)

47、 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 ProfitabilityxySlopewp x y(,) x y is chosen at prices (,) w pRevealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.Slopewp x y(,) x y(,) w p(,) x

48、yRevealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.Slopewp x y(,) x y(,) w p(,) x y x y(,) xy would give higherprofits, so why is it notchosen?Revealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.Slopewp x y(,) x y(,) w p(,) x y x y(

49、,) xy 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.Slopewp x y(,) x y(,) w p(,) x y x y(,) xy would give higherprofits, so why is it notchosen? Because it isnot a feasible plan.

50、So the firms technology set must lie under theiso-profit line.Revealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.Slopewp x y(,) x y(,) w p(,) x y x ySo the firms technology set must lie under theiso-profit line.The technologyset is somewherein hereRevealed Profitabi