[求助]The CES utility function

别激动咯，呵呵。

我们没有在一个层面上讨论问题，我在说明基础知识，您在分析高层运用。

所以，您还是看论文吧，不必在意我的回复了。

以下是引用唐伯小猫在2009-2-13 11:39:00的发言：

猫版，海闻老师说的不是ces这种特殊形式，是一般形式啊。

不过还是有点疑问，CES函数到底有什么“特征”？

以至于可以做到“因为CES的特征，整个模型的总的需求量没有变”？

实际上，它只是一个替代弹性不变的效用函数而已，如何能够保证模型的总需求不改变呢？

当然，这就是个高深的问题了，我就不掺和了，呵呵。

猫版，把整个模型的数学公式自己算一遍，就会发现产出没有改变的，在贸易前和贸易后。

我可能说的有问题，应该是总的消费量没有变。不过这种模型消费量是等于需求量的。

多谢讨论，嘻嘻：）

以下是引用唐伯小猫在2009-2-13 15:39:00的发言：

猫版，把整个模型的数学公式自己算一遍，就会发现产出没有改变的，在贸易前和贸易后。

我可能说的有问题，应该是总的消费量没有变。不过这种模型消费量是等于需求量的。

您说了这么多遍模型，到底是哪个模型啊？

反正不会是一般的CES需求函数的模型吧？（它根本和贸易无关）

只要不是CES的特征导致了前后消费量不变，那就说明您的那个判断不成立咯。

[此贴子已经被作者于2009-2-13 16:20:18编辑过]

哈哈，深深学习猫版一丝不苟的精神 ！

我已经说了哪些模型啦？我说的数学公式的模型是Krugman(1980).

Constant elasticity of substitution                                                                                                                                        From Wikipedia, the free encyclopedia
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                                                                                                                                In economics, Constant elasticity of substitution (CES) is a property of some production functions and utility functions.
More precisely, it refers to a particular type of aggregator function which combines two or more types of consumption, or two or more types of productive inputs into an aggregate quantity. This aggregator function exhibits constant elasticity of substitution.

Contents [hide] 1 CES production function 2 CES utility function 3 References 4 External links

[edit] CES production functionThe CES production function is a type of production function that displays constant elasticity of substitution. In other words, the production technology has a constant percentage change in factor (e.g. labour and capital) proportions due to a percentage change in marginal rate of technical substitution. The two factor (Capital, Labor) CES production function introduced by Solow [1] and later made popular by Arrow, Chenery, Minhas, and Solow is:[2][3]
where

• Q = Output
• F = Factor productivity
• a = Share parameter
• K, L = Primary production factors (Capital and Labor)
• r =
• s = = Elasticity of substitution.

As its name suggests, the CES production function exhibits constant elasticity of substitution between capital and labor. Leontief, linear and Cobb-Douglas production functions are special cases of the CES production function. That is, in the limit as s approaches 1, we get the Cobb-Douglas function; as s approaches positive infinity we get the linear (perfect substitutes) function; and for s approaching 0, we get the Leontief (perfect complements) function. The general form of the CES production function is:
where

• Q = Output
• F = Factor productivity
• a = Share parameter
• X = Production factors (i = 1,2...n)
• s = Elasticity of substitution.

Extending the CES (Solow) form to accommodate multiple factors of production creates some problems, however. There is no completely general way to do this. Uzawa [4] showed the only possible n-factor production functions (n>2) with constant partial elasticities of substitution require either that all elasticities between pairs of factors be identical, or if any differ, these all must equal each other and all remaining elasticities must be unity. This is true for any production function. This means the use of the CES form for more than 2 factors will generally mean that there is not constant elasticity of substitution among all factors.
Nested CES functions are commonly found in partial/general equilibrium models. Different nests (levels) allow for the introduction of the appropriate elasticity of substitution.
The CES is a neoclassical production function.
[edit] CES utility functionSee also: Isoelastic utility
The same functional form arises as a utility function in consumer theory. For example, if there exist n types of consumption goods ci, then aggregate consumption C could be defined using the CES aggregator:
Here again, the coefficients ai are share parameters, and s is the elasticity of substitution. Therefore the consumption goods ci are perfect substitutes when s approaches infinity and perfect complements when s = 0. The CES aggregator is also sometimes called the Armington aggregator, which was discussed by Armington (1969).[5]
A CES utility function is one of the cases considered by Avinash Dixit and Joseph Stiglitz in their study of optimal product diversity in a context of monopolistic competition.[6]

好问题 ,  新贸易理论最基础的一个问题，一个核心命题，不懂这个，高贸等于没学，是有点难度，建议看看houthakker 1960,  syverson 2007  , campbell  hopenhayn,2005  mayer 2004   holmes stevens 2010 ,evgeny ahelobodko 2011, benassy j p 1996,  behrens,k2007的文章。
1  K. Behrens, Y. Murata, Gains from trade and efficiency under monopolistic competition: a variable elasticity case,CORE Discussion Paper #2006/49, Univ. catholique de Louvain.
2O.J. Blanchard, N. Kiyotaki, Monopolistic competition and the effects of aggregate demand, Amer. Econ. Rev. 77(1987) 647–666.
3 A.K. Dixit, J.E. Stiglitz, Monopolistic competition and optimum product diversity (May 1974), in: S. Brakman, B.J.Heijdra (Eds.), The Monopolistic Competition Revolution in Retrospect, Cambridge University Press, Cambridge,MA, 2004, pp. 70–88.
4X. Yang, B.J. Heijdra, Monopolistic competition and optimum product diversity: comment, Amer. Econ. Rev. 83
(1993) 295–301

bwhbwh 发表于 2009-2-11 22:10
A Homothetic Utility Function for Monopolistic Competition ModelsAn Assessment of CES and Cobb-Dougl ...

mark!! thanks

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