生产技术与利润最大化0910301.pptx

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1、17.1 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 technology is“b

2、est”?How do we compare technologies?第1页/共53页27.1.2 Production Functionsy denotes the output level.The technologys production function states the maximum amount of output possible from an input bundle.第2页/共53页3Production Functions-One input,one outputy=f(x)x1Input LevelxOutput Levely1y1=f(x1)is the m

3、aximal output level obtainable from x1 input units.第3页/共53页4Technologies with Multiple InputsSuppose the production function is(x1,x2)=(1,8)(x1,x2)=(8,8)第4页/共53页5Technologies with Multiple InputsOutput,yx1x2(8,1)(8,8)第5页/共53页6Isoquants with Two Variable Inputsy 8 8y 4 4x1x2第6页/共53页7用产量面表示生产函数LOKTPK1

4、L1L2K2AABBCCDDQ1Q2E1F1G1E2F2G2E1E2G1G2第7页/共53页8Isoquants with Two Variable InputsOutput,yx1x2y 8 8y 4 4第8页/共53页9Cobb-Douglas TechnologiesA Cobb-Douglas production function is of the form第9页/共53页10Fixed-Proportions TechnologiesA fixed-proportions production function is of the form第10页/共53页11Fixed-Pro

5、portions Technologiesx2x1minx1,2x2=144814247minx1,2x2=8minx1,2x2=4x1=2x2第11页/共53页12Perfect-Substitutes TechnologiesA perfect-substitutes production function is of the form第12页/共53页13Perfect-Substitution Technologies93186248x1x2x1+3x2=9x1+3x2=18x1+3x2=24第13页/共53页14有限种投入比的技术123456781 2 3 4 5 6 7 8R1X2

6、: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157.1.3 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.

7、That is,第15页/共53页16Marginal(Physical)Products第16页/共53页177.1.4 Returns-to-ScaleMarginal products 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

8、halved).第17页/共53页18Constant returns-to-scaleConstant returns-to-scaleIf,for any input bundle(xIf,for any input bundle(x1 1,x,xn n),),then the technology described by thethen the technology described by theproduction function f exhibits production function f exhibits constantconstantreturns-to-scaler

9、eturns-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53页19Constant returns-to-scaley=f(x)xxInput LevelOutput Levely2x2yConstantreturns-to-scale第19页/共53页20Diminishing returns-to-scaleDiminishing returns-to-scaleIf,

10、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-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 th

11、e output level.第20页/共53页21Diminishing returns-to-scaley=f(x)xxInput LevelOutput Levelf(x)2xf(2x)2f(x)Decreasingreturns-to-scale第21页/共53页22Increasing 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 doub

12、les the output level.第22页/共53页23Increasing returns-to-scaley=f(x)xxInput LevelOutput Levelf(x)2xf(2x)2f(x)Increasingreturns-to-scale第23页/共53页24Returns-to-Scaley=f(x)xInput LevelOutput LevelDecreasingreturns-to-scaleIncreasingreturns-to-scale第24页/共53页25Examples of Returns-to-ScaleThe perfect-substitu

13、tes productionfunction isThe perfect-substitutes productionfunction exhibits constant returns-to-scale.第25页/共53页26Examples of Returns-to-ScaleThe perfect-complements productionfunction isThe perfect-complements productionfunction exhibits constant returns-to-scale.第26页/共53页27Examples of Returns-to-S

14、caleThe Cobb-Douglas production function is第27页/共53页28Examples of Returns-to-ScaleThe Cobb-Douglas technologys returns-to-scale isconstant if a1+an =1increasing if a1+an 1decreasing if a1+an 1第28页/共53页29Question and answerQ:在边际产出递减的情况下，是否能存在规模报酬递增现象？A:Yes.E.g.第29页/共53页30Returns-to-Scalediminishes as

15、 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。第30页/共53页317.1.5 Technical Rate-of-SubstitutionAt what rate can a firm substitute one input for another without changing its output level?第31页/共53页32Technical Rate-of-Substitutionx2x1y100100The slope of an isoquant is its technical rat

16、e-of-substitution.第32页/共53页33技术替代率的计算0第33页/共53页347.1.6 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 in its choice of at least one inpu

17、t level.第34页/共53页35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 is第35页/共53页36x1y长期和短期Four short-run production functions.第36页/共53页377.2 Profit-Maximization7.2.1 Economic Profit厂商用投入 j=1

18、,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：第37页/共53页38经济利润投入量、产出量及利润均为流量；经济成本第38页/共53页397.2.2 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第39页/共53页407.2.3 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、可变要素第40页/共53页417.2.4 短期利润最大化假定要素

19、2的投入水平 保持不变，厂商的利润最大化问题就可以表示为销售收入变动成本固定成本第41页/共53页42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*1第42页/共53页43几何法等利润线(Iso-Profit Lines)slopevertical intercept第43页/共53页44Iso-Profit LinesIncreasing profityx1第44页/共53页45Short-Run Profit-Maximizationx1y第45页/共53页46Short-Run Pr

20、ofit-Maximization;A Cobb-Douglas Example第46页/共53页477.2.5 比较静态学产品价格p变动x1y低价格高价格第47页/共53页48比较静态学投入价格w1变动x1y高价格低价格第48页/共53页49Comparative 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 upwar

21、d),andan increase in the level of the firms variable input(the firms demand curve for its variable input shifts outward).第49页/共53页50Comparative 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).第50页/共53页517.2.6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第51页/共53页527.2.7 反要素需求曲线x1￥w1x1pMP1w”1x”1w1第52页/共53页53感谢您的观看！第53页/共53页