生产技术与利润最大化.ppt

7.生产技术与利润最大化,2,7.1 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“best”?How do we compare technologies?,3,7.1.2 Production Functions,y denotes the output level.The technologys production function states the maximum amount of output possible from an input bundle.,4,Production Functions-One input,one output,y=f(x),x1,Input Level,y1,y1=f(x1)is the maximal output level obtainable from x1 input units.,5,Technologies with Multiple Inputs,Suppose the production function is,(x1,x2)=(1,8),(x1,x2)=(8,8),6,Technologies with Multiple Inputs,Output,y,x1,x2,(8,1),(8,8),7,Isoquants with Two Variable Inputs,8,用产量面表示生产函数,9,Isoquants with Two Variable Inputs,10,Cobb-Douglas Technologies,A Cobb-Douglas production function is of the form,11,Fixed-Proportions Technologies,A fixed-proportions production function is of the form,12,Fixed-Proportions Technologies,x2,x1,minx1,2x2=14,4,8,14,2,4,7,minx1,2x2=8,minx1,2x2=4,x1=2x2,13,Perfect-Substitutes Technologies,A perfect-substitutes production function is of the form,14,Perfect-Substitution Technologies,9,3,18,6,24,8,x1,x2,x1+3x2=9,x1+3x2=18,x1+3x2=24,15,有限种投入比的技术,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,R1,X2:X1=8:1,R2,X2:X1=3:1,R3,X2:X1=1:1,R4,X2:X1=1:4,现有6单位x1和3单位x2,2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,16,7.1.3 Marginal(Physical)Products,The 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,17,Marginal(Physical)Products,18,7.1.4 Returns-to-Scale,Marginal 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 halved).,19,Constant returns-to-scale,If,for any input bundle(x1,xn),then the technology described by theproduction function f exhibits constantreturns-to-scale.E.g.(k=2)doubling all input levelsdoubles the output level.,20,Constant returns-to-scale,21,Diminishing returns-to-scale,If,for any input bundle(x1,xn),then the technology exhibits diminishing returns-to-scale.E.g.(k=2)doubling all input levels less than doubles the output level.,22,Diminishing returns-to-scale,23,Increasing returns-to-scale,If,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.,24,Increasing returns-to-scale,25,Returns-to-Scale,y=f(x),x,Input Level,Output Level,Decreasingreturns-to-scale,Increasingreturns-to-scale,26,Examples of Returns-to-Scale,The perfect-substitutes productionfunction is,The perfect-substitutes productionfunction exhibits constant returns-to-scale.,27,Examples of Returns-to-Scale,The perfect-complements productionfunction is,The perfect-complements productionfunction exhibits constant returns-to-scale.,28,Examples of Returns-to-Scale,The Cobb-Douglas production function is,29,Examples of Returns-to-Scale,The Cobb-Douglas technologys returns-to-scale isconstant if a1+an=1increasing if a1+an 1decreasing if a1+an 1,30,Question and answer,Q: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.,31,Returns-to-Scale,diminishes as x1 increases,diminishes 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。,32,7.1.5 Technical Rate-of-Substitution,At what rate can a firm substitute one input for another without changing its output level?,33,Technical Rate-of-Substitution,The slope of an isoquant is its technical rate-of-substitution.,34,技术替代率的计算,0,35,7.1.6 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 input level.,36,长期和短期,is the long-run productionfunction(both x1 and x2 are variable).,The short-run production function whenx2 1 is,The short-run production function when x2 10 is,37,长期和短期,Four short-run production functions.,38,7.2 Profit-Maximization,7.2.1 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。经济利润：,39,经济利润,投入量、产出量及利润均为流量；经济成本,40,7.2.2 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,41,7.2.3 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,42,7.2.4 短期利润最大化,假定要素2的投入水平 保持不变，厂商的利润最大化问题就可以表示为,销售收入,变动成本,固定成本,43,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,pMP1,w1,x*1,44,几何法,等利润线(Iso-Profit Lines),slope,vertical intercept,45,Iso-Profit Lines,Increasing profit,46,Short-Run Profit-Maximization,47,Short-Run Profit-Maximization;A Cobb-Douglas Example,48,7.2.5 比较静态学,产品价格p变动,低价格,高价格,49,比较静态学,投入价格w1变动,高价格,低价格,50,Comparative Statics of Short-Run Profit-Maximization,An 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 outward).,51,Comparative Statics of Short-Run Profit-Maximization,An 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).,52,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,53,7.2.7 反要素需求曲线,w1,x1,pMP1,w”1,x”1,w1,