生产技术与利润最大化0910301学习教案.pptx

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1、会计学1生产技术生产技术(jsh)与利润最大化与利润最大化0910301第一页，共53页。27.1 技术技术(jsh)（Technologies）7.1.1 7.1.1 什么叫技术？什么叫技术？技术是投入技术是投入(tur)(tur)转换为产出的过程转换为产出的过程E.g.labor,a computer,a projector,electricity,and software are E.g.labor,a computer,a projector,electricity,and software are being combined being combined toto produce

2、this lecture.produce this lecture.Usually several technologies will produce the same product.Usually several technologies will produce the same product.a blackboard and chalk can be used instead of a computer and a blackboard and chalk can be used instead of a computer and a projector.a projector.Wh

3、ich technology is“best”?Which technology is“best”?How do we compare technologies?How do we compare technologies?第1页/共53页第二页，共53页。37.1.2 Production Functionsn ny denotes the output level.n nThe technologys production function states the maximum amount of output possible from an input bundle.第2页/共53页第

4、三页，共53页。4Production Functions-One input,one outputy=f(x)x1Input LevelxOutput Levely1y1=f(x1)is the maximal output level obtainable from x1 input units.第3页/共53页第四页，共53页。5Technologies with Multiple Inputsn nSuppose the production function is(x1,x2)=(1,8)(x1,x2)=(8,8)第4页/共53页第五页，共53页。6Technologies with

5、 Multiple InputsOutput,yx1x2(8,1)(8,8)第5页/共53页第六页，共53页。7Isoquants with Two Variable Inputsy 8 8y 4 4x1x2第6页/共53页第七页，共53页。8用产量用产量(chnling)面面表示生产函数表示生产函数LOKTPK1L1L2K2AABBCCDDQ1Q2E1F1G1E2F2G2E1E2G1G2第7页/共53页第八页，共53页。9Isoquants with Two Variable InputsOutput,yx1x2y 8 8y 4 4第8页/共53页第九页，共53页。10Cobb-Dougla

6、s Technologiesn nA Cobb-Douglas production function is of the form第9页/共53页第十页，共53页。11Fixed-Proportions Technologiesn nA fixed-proportions production function is of the form第10页/共53页第十一页，共53页。12Fixed-Proportions Technologiesx2x1minx1,2x2=144814247minx1,2x2=8minx1,2x2=4x1=2x2第11页/共53页第十二页，共53页。13Perfe

7、ct-Substitutes Technologiesn nA perfect-substitutes production function is of the form第12页/共53页第十三页，共53页。14Perfect-Substitution Technologies93186248x1x2x1+3x2=9x1+3x2=18x1+3x2=24第13页/共53页第十四页，共53页。15有限种投入有限种投入(tur)比的技术比的技术1234567812345678R1X2:X1=8:1R2X2:X1=3:1R3X2:X1=1:1R4X2:X1=1:4现有(xin yu)6单位x1和3单

8、位x22单位x1和2单位x2用于R3，生产(shngchn)产品50单位；4单位x1和1单位x2用于R4，生产产品50单位产量100单位的等产量线第14页/共53页第十五页，共53页。167.1.3 Marginal(Physical)Productsn nThe marginal product of input i is the rate-of-change of the output level as the level of input i changes,holding all other input levels fixed.n nThat is,第15页/共53页第十六页，共53

9、页。17Marginal(Physical)Products第16页/共53页第十七页，共53页。187.1.4 Returns-to-Scalen nMarginal products describe the change in output level as a single single input level changes.n nReturns-to-scaleReturns-to-scale describes how the output level changes as describes how the output level changes as allall inpu

10、t levels change in input levels change in direct proportiondirect proportion(e.g.e.g.all input all input levels doubled,or halved).levels doubled,or halved).第17页/共53页第十八页，共53页。19Constant returns-to-scaleConstant returns-to-scaleIf,for any input bundle(xIf,for any input bundle(x1 1,x,xn n),),then the

11、 technology described by thethen the technology described by theproduction function f exhibits production function f exhibits constantconstantreturns-to-scalereturns-to-scale.E.gE.g.(k=2)doubling all input levels.(k=2)doubling all input levelsdoubles the output level.doubles the output level.第18页/共5

12、3页第十九页，共53页。20Constant returns-to-scaley=f(x)xxInput LevelOutput Levely2x2yConstantreturns-to-scale第19页/共53页第二十页，共53页。21Diminishing returns-to-scaleDiminishing returns-to-scaleIf,for any input bundle(xIf,for any input bundle(x1 1,x,xn n),),then the technology exhibits then the technology exhibits di

13、minishing returns-to-diminishing returns-to-scalescale.E.gE.g.(k=2)doubling all input levels less than doubles.(k=2)doubling all input levels less than doubles the output level.the output level.第20页/共53页第二十一页，共53页。22Diminishing returns-to-scaley=f(x)xxInput LevelOutput Levelf(x)2xf(2x)2f(x)Decreasin

14、greturns-to-scale第21页/共53页第二十二页，共53页。23Increasing returns-to-scaleIf,for any input bundle(x1,xn),then the technology exhibits increasingreturns-to-scale.E.g.(k=2)doubling all input levelsmore than doubles the output level.第22页/共53页第二十三页，共53页。24Increasing returns-to-scaley=f(x)xxInput LevelOutput Lev

15、elf(x)2xf(2x)2f(x)Increasingreturns-to-scale第23页/共53页第二十四页，共53页。25Returns-to-Scaley=f(x)xInput LevelOutput LevelDecreasingreturns-to-scaleIncreasingreturns-to-scale第24页/共53页第二十五页，共53页。26Examples of Returns-to-ScaleThe perfect-substitutes productionfunction isThe perfect-substitutes productionfunctio

16、n exhibits constant returns-to-scale.第25页/共53页第二十六页，共53页。27Examples of Returns-to-ScaleThe perfect-complements productionfunction isThe perfect-complements productionfunction exhibits constant returns-to-scale.第26页/共53页第二十七页，共53页。28Examples of Returns-to-ScaleThe Cobb-Douglas production function is第

17、27页/共53页第二十八页，共53页。29Examples of Returns-to-Scalen nThe Cobb-Douglas technologys returns-to-scale isn nconstantconstant if if a a1 1+a+an n =1 =1n nincreasing if aincreasing if a1 1+a+an n 1 1n ndecreasingdecreasing if if a a1 1+a+an n 1 1第28页/共53页第二十九页，共53页。30Question and answern nQ:在边际产出递减(djin)的情

18、况下，是否能存在规模报酬递增现象？n nA:Yes.n nE.g.第29页/共53页第三十页，共53页。31Returns-to-Scalediminishes as x1 increasesdiminishes as x1 increases所以，即使边际产出是递减的，规模(gum)报酬也可能是递增的。第30页/共53页第三十一页，共53页。327.1.5 Technical Rate-of-Substitutionn nAt what rate can a firm substitute one input for another without changing its output l

19、evel?第31页/共53页第三十二页，共53页。33Technical Rate-of-Substitutionx2x1y100100The slope of an isoquant is its technical rate-of-substitution.第32页/共53页第三十三页，共53页。34技术技术(jsh)替代率的计算替代率的计算0第33页/共53页第三十四页，共53页。357.1.6 长期长期(chngq)和短期和短期n nThe long-runThe long-run is the circumstance in which a firm is circumstance

20、in which a firm is unrestrictedunrestricted in its choice of in its choice of all input levelsall input levels.n nThere are many possible short-runs.n nA short-runA short-run is is a a circumstance in which a firm is circumstance in which a firm is restricted restricted in in some way in its choice

21、of some way in its choice of at least one input levelat least one input level.第34页/共53页第三十五页，共53页。36长期长期(chngq)和短期和短期 is the long-run productionfunction(both x1 and x2 are variable).The short-run production function whenx2 1 isThe short-run production function when x2 10 is第35页/共53页第三十六页，共53页。37x1y长

22、期长期(chngq)和短期和短期Four short-run production functions.第36页/共53页第三十七页，共53页。387.2 Profit-Maximization7.2.1 Economic Profit厂商用投入 j=1,m 生产产品 i=1,n.产出水平 y1,yn，投入水平 x1,xm.产品价格 p1,pn，投入价格 w1,wm.厂商是价格接受者，即p1,pn 和 w1,wm 给定。经济(jngj)利润：第37页/共53页第三十八页，共53页。39经济经济(jngj)利润利润n n投入量、产出量及利润(lrn)均为流量；n n经济成本第38页/共53页第三

23、十九页，共53页。407.2.2 企业企业(qy)现值现值n n某厂商若干时期(shq)的经济利润为 0,1,2,利率为 r，厂商经济利润的现值为第39页/共53页第四十页，共53页。417.2.3 不变要素不变要素(yo s)和可变要和可变要素素(yo s)n n数量固定的生产要素称为(chn wi)不变要素（固定要素）。n n可以按不同的数量使用的生产要素称为(chn wi)可变要素（变动要素）。n n长期、短期与不变要素、可变要素第40页/共53页第四十一页，共53页。427.2.4 短期短期(dun q)利润最大化利润最大化n n假定要素2的投入水平 保持(boch)不变，厂商的利润最

24、大化问题就可以表示为销售收入变动(bindng)成本固定成本第41页/共53页第四十二页，共53页。43利润利润(lrn)最大化最大化n n生产要素的边际(binj)产品价值(the marginal revenue product of input 1)应该等于它的价格x1￥pMP1w1x*1第42页/共53页第四十三页，共53页。44几何几何(j h)法法n n等利润(lrn)线(Iso-Profit Lines)slopevertical intercept第43页/共53页第四十四页，共53页。45Iso-Profit LinesIncreasing profityx1第44页/共53

25、页第四十五页，共53页。46Short-Run Profit-Maximizationx1y第45页/共53页第四十六页，共53页。47Short-Run Profit-Maximization;A Cobb-Douglas Example第46页/共53页第四十七页，共53页。487.2.5 比较比较(bjio)静态学静态学n n产品价格p变动(bindng)x1y低价格(jig)高价格第47页/共53页第四十八页，共53页。49比较比较(bjio)静态学静态学n n投入价格(jig)w1变动x1y高价格(jig)低价格第48页/共53页第四十九页，共53页。50Comparative St

26、atics of Short-Run Profit-Maximizationn nAn increase in p,the price of the firms output,causesn nan increase in the firms output level(the firms supply curve slopes upward),andn nan increase in the level of the firms variable input(the firms demand curve for its variable input shifts outward).第49页/共

27、53页第五十页，共53页。51Comparative Statics of Short-Run Profit-Maximizationn nAn increase in w1,the price of the firms variable input,causesn na decrease in the firms output level(the firms supply curve shifts inward),andn na decrease in the level of the firms variable input(the firms demand curve for its variable input slopes downward).第50页/共53页第五十一页，共53页。527.2.6长期长期(chngq)利润最大化利润最大化n n所有要素(yo s)的使用量都可以自由的变动要素需求(xqi)曲线第51页/共53页第五十二页，共53页。537.2.7 反要素反要素(yo s)需求曲线需求曲线x1￥w1x1pMP1w”1x”1w1第52页/共53页第五十三页，共53页。