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关于柯布--道格拉斯生产函数的假设前提

响泉:

我的毕业论文里用到了柯布——道格拉斯生产函数(Y=AL**(a)K**(β))。
在论文答辩时一老师问我柯布——道格拉斯生产函数的假设前提是什么?
我答:(1)生产中只有资本和劳动两种投入。(2)资本和劳动可以相互替代。(3)资本和劳动均存在边际收益递减。
老师说应该还有一个假设前提,即规模报酬不变。
我辩:只有当a+β=1时经济才处于规模报酬不变。西方发达市场经济国家的经济是规模报酬不变的,这也是西方学者已经证明了的。所以一般的西方经济学教科书上在使用柯布——道格拉斯生产函数时都假设规模报酬不变。但我的论文讨论的中国的经济问题,我国还处于转型经济中,并不能简单地假设规模报酬不变......
现特请教经济学高手,规模报酬不变究竟是不是柯布——道格拉斯生产函数的假设前提。


Cecil:

响泉,The three assumptions you mentioned are generic, i.e. they are shared by many other types of production functions. If the question asked in the oral defence was "what are the assumptions of the Cobb-Duglas production functions?", the examiner may expect you to mention assumptions which are peculiar to the Cobb-Duglas production function. The constant return to scale assumption (alpha+beta=1) was used by Cobb and Duglas in their paper in 1928. The importance of assuming alpha+beta=1 is that K*MPK+L*MPL=Y. If you assume interest rate=MPK and wage rate=MPL, then the sum of factor shares equals output. If you assume alpha+beta>1, i.e. increasing return to scale, you need to make further assumptions about how the output is shared by K, L and the entrepreneur.

More importantly, the most important assumption behind the Cobb-Duglas production function is that the elasticity of substitution always equals to one no matter which value of alpha or beta you choose. That assumption led to the invention of the CES production function.


aydragon:

请教Cecil:什么是CES生产函数?什么是elasticity of substitution ?


Cecil:

Elasticity of substitution is defined as the % change in capital-labour (K/L) ratio with respect to 1% change in the relative price between wage rate and interest rate (w/r) at a given level of output (Y). Mathematically, it is

d(K/L) (w/r)
----- * ----- evaluated at a fixed level of Y.
d(w/r) (K/L)

To get the result that the elasticity of substitution for the Cobb-Duglas production function equals to one, you need to assume that wage rate =marginal product of labour (w=MPL) and interest rate=marginal product of capital (r=MPK).

CES stands for 'constant elasticity of substitution'. The CES production function was invented by Arrow, Chenery, Minhas, and Solow in 1961.

 

参阅:http://bbs.efnchina.com/dispbbs.asp?boardID=30&ID=43946

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