生产技术与利润最大化.ppt

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1、17.生产技术与利润最大化227.1 技术（Technologies）7.1.1 什么叫技术？技术是投入转换为产出的过程E.g.labor,a computer,a projector,electricity,and software are being combined to produce this lecture.Usually several technologies will produce the same product.a blackboard and chalk can be used instead of a computer and a projector.Which t

2、echnology is“best”?How do we compare technologies?337.1.2 Production Functionsy denotes the output level.The technologys production function states the maximum amount of output possible from an input bundle.44Production Functions-One input,one outputy=f(x)x1Input LevelxOutput Levely1y1=f(x1)is the m

3、aximal output level obtainable from x1 input units.55Technologies with Multiple InputsSuppose the production function is(x1,x2)=(1,8)(x1,x2)=(8,8)66Technologies with Multiple InputsOutput,yx1x2(8,1)(8,8)77Isoquants with Two Variable Inputsy 8 8y 4 4x1x288用产量面表示生产函数LOKTPK1L1L2K2AABBCCDDQ1Q2E1F1G1E2F2

4、G2E1E2G1G299Isoquants with Two Variable InputsOutput,yx1x2y 8 8y 4 41010Cobb-Douglas TechnologiesA Cobb-Douglas production function is of the form1111Fixed-Proportions TechnologiesA fixed-proportions production function is of the form1212Fixed-Proportions Technologiesx2x1minx1,2x2=144814247minx1,2x2

5、=8minx1,2x2=4x1=2x21313Perfect-Substitutes TechnologiesA perfect-substitutes production function is of the form1414Perfect-Substitution Technologies93186248x1x2x1+3x2=9x1+3x2=18x1+3x2=241515有限种投入比的技术123456781 2 3 4 5 6 7 8R1X2:X1=8:1R2X2:X1=3:1R3X2:X1=1:1R4X2:X1=1:4现有6单位x1和3单位x22单位x1和2单位x2用于R3，生产产品5

6、0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16167.1.3 Marginal(Physical)ProductsThe 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.That is,1717Marginal(Physical)Products18187.1.4 Returns-to-ScaleMarginal products

7、 describe the change in output level as a single input level changes.Returns-to-scale describes how the output level changes as all input levels change in direct proportion(e.g.all input levels doubled,or halved).1919Constant returns-to-scaleIf,for any input bundle(xIf,for any input bundle(x1 1,x,xn

8、 n),),then the 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

9、 level.2020Constant returns-to-scaley=f(x)xxInput LevelOutput Levely2x2yConstantreturns-to-scale2121Diminishing 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 diminishing returns-diminishing returns-to-scaleto

10、-scale.E.gE.g.(k=2)doubling all input levels less than.(k=2)doubling all input levels less than doubles the output level.doubles the output level.2222Diminishing returns-to-scaley=f(x)xxInput LevelOutput Levelf(x)2xf(2x)2f(x)Decreasingreturns-to-scale2323Increasing returns-to-scaleIf,for any input b

11、undle(x1,xn),then the technology exhibits increasingreturns-to-scale.E.g.(k=2)doubling all input levelsmore than doubles the output level.2424Increasing returns-to-scaley=f(x)xxInput LevelOutput Levelf(x)2xf(2x)2f(x)Increasingreturns-to-scale2525Returns-to-Scaley=f(x)xInput LevelOutput LevelDecreasi

12、ngreturns-to-scaleIncreasingreturns-to-scale2626Examples of Returns-to-ScaleThe perfect-substitutes productionfunction isThe perfect-substitutes productionfunction exhibits constant returns-to-scale.2727Examples of Returns-to-ScaleThe perfect-complements productionfunction isThe perfect-complements

13、productionfunction exhibits constant returns-to-scale.2828Examples of Returns-to-ScaleThe Cobb-Douglas production function is2929Examples of Returns-to-ScaleThe Cobb-Douglas technologys returns-to-scale isconstant if a1+an =1increasing if a1+an 1decreasing if a1+an 13030Question and answerQ:在边际产出递减的

14、情况下，是否能存在规模报酬递增现象？A:Yes.E.g.3131Returns-to-Scalediminishes as x1 increasesdiminishes as x1 increases所以，即使边际产出是递减的，规模报酬也可能是递增的。32327.1.5 Technical Rate-of-SubstitutionAt what rate can a firm substitute one input for another without changing its output level?3333Technical Rate-of-Substitutionx2x1y1001

15、00The slope of an isoquant is its technical rate-of-substitution.3434技术替代率的计算035357.1.6 长期和短期The long-run is the circumstance in which a firm is unrestricted in its choice of all input levels.There are many possible short-runs.A short-run is a circumstance in which a firm is restricted in some way i

16、n its choice of at least one input level.3636长期和短期 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 is3737x1y长期和短期Four short-run production functions.38387.2 Profit-Maximization7.2.1 Economic Pro

17、fit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。经济利润：3939经济利润投入量、产出量及利润均为流量；经济成本40407.2.2 企业现值某厂商若干时期的经济利润为 0,1,2,利率为 r，厂商经济利润的现值为41417.2.3 不变要素和可变要素数量固定的生产要素称为不变要素（固定要素）。可以按不同的数量使用的生产要素称为可变要素（变动要素）。长期、短期与不变要素、可变要素42427.2.4 短期利润最大化假定要素2的投入水平 保持不变，厂商的利

18、润最大化问题就可以表示为销售收入变动成本固定成本4343利润最大化生产要素的边际产品价值(the marginal revenue product of input 1)应该等于它的价格x1￥pMP1w1x*14444几何法等利润线(Iso-Profit Lines)slopevertical intercept4545Iso-Profit LinesIncreasing profityx14646Short-Run Profit-Maximizationx1y4747Short-Run Profit-Maximization;A Cobb-Douglas Example48487.2.5 比

19、较静态学产品价格p变动x1y低价格高价格4949比较静态学投入价格w1变动x1y高价格低价格5050Comparative Statics of Short-Run Profit-MaximizationAn 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 dem

20、and curve for its variable input shifts outward).5151Comparative 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 curve shifts inward),anda decrease in the level of the firms variable input(the firms demand curve for its variable input slopes downward).52527.2.6长期利润最大化所有要素的使用量都可以自由的变动要素需求曲线53537.2.7 反要素需求曲线x1￥w1x1pMP1w”1x”1w1