生产技术与利润最大化.ppt
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1、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
2、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 maxim
3、al 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,
4、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
5、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
6、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
7、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 fun
8、ction 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 dou
9、bles 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)
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