人民币论坛币一起赚：微观第二期悬赏600论坛币：斯卢茨基方程一篮子研究

没学得那么深入，只能来围观

哦，这些都是不同的经济学家研究出来的，之间的关系不是刻意联系的，别人解释的永远不如自己去琢磨，用生活中的实际例子，自己证明一下，都能用的上，慢慢就发现了

转:
Roy's identity (named for French economist Rene Roy) is a major result in microeconomics having applications in consumer choice and the theory of the firm. The lemma relates the ordinary (Marshallian) demand function to the derivatives of the indirect utility function. Specifically, where V(P,Y) is the indirect utility function, then the Marshallian demand function for good i can be calculated as:


Contents [hide]
1 Derivation of Roy's identity
2 Alternative Proof for the Differentiable Case
3 Application
4 References

[edit] Derivation of Roy's identity
Roy's identity reformulates Shephard's lemma in order to get a Marshallian demand function for an individual and a good (i) from some indirect utility function.

The first step is to consider the trivial identity obtained by substituting the expenditure function for wealth or income Y in the indirect utility function V(Y,P), at a utility of u:

V(e(P,u),P) = u
This says that the indirect utility function evaluated in such a way that minimizes the cost for achieving a certain utility given a set of prices (a vector p) is equal to that utility when evaluated at those prices.

Taking the derivative of both sides of this equation with respect to the price of a single good pi (with the utility level held constant) gives:

.
Rearranging gives the desired result:





[edit] Alternative Proof for the Differentiable Case
There is a simpler proof of Roy's Identity, stated for the two-good case for simplicity.

The indirect utility function V(p1,p2,Y) is the maximand of the constrained optimization problem characterized by the following Lagrangian:


By the envelope Theorem, the derivatives of the maximand V(p1,p2,Y) with respect to the parameters can be computed as such:



where  is the maximizer (i.e. the Marshallian demand function for good 1). Simple arithmetic then gives Roy's Identity:


[edit] Application
This gives a method of deriving the Marshallian demand function of a good for some consumer from the indirect utility function of that consumer. It is also fundamental in deriving the Slutsky equation.

[edit] References
Roy, René (1947). "La Distribution du Revenu Entre Les Divers Biens," Econometrica, 15, 205-225.
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Categories: Microeconomics | Underlying principles of microeconomic behavior | Microeconomics stubs

http://en.wikipedia.org/wiki/Roy's_identity

楼上好多牛叉的啊

唉，一下子感到我的知识不行了

凡是能提升初学者兴趣，能让初学者积极参与的都行，那样论坛将更加活跃
34# harbery

谢波特定理是对支出函数对价格求导，等于希克斯需求？