我有一些经管类的数学问题，请问本版是专署的答疑区吗？

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[此贴子已经被作者于2008-10-7 12:22:35编辑过]

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关键词：数学问题 经管类 数学 经管 专署

这是微观经济学的问题。

请问如何计算，这是一道出现在我数学书上的习题。谢谢！

help me,please!

[此贴子已经被作者于2008-10-9 18:42:08编辑过]

Here's the solution.

You need to treat the money as an unknown. Suppose you have $m amount of money. First you solve the following maximization problem

   max x^{1/2} y

s.t. x + 4 y = m

It gives U_max(m) = 8/sqrt{3} * m^{3/2}. That is the maximal utility you can achieve when you have $m money. 

Now the marginal utility with respect to money is the direvative of U_max with respect to the variable m, which gives 4 * sqrt{3} * sqrt{m}. It is 1 when m equals to 48.

以下是引用burrowu在2008-10-10 19:49:00的发言：

Here's the solution.

You need to treat the money as an unknown. Suppose you have $m amount of money. First you solve the following maximization problem

   max x^{1/2} y

s.t. x + 4 y = m

It gives U_max(m) = 8/sqrt{3} * m^{3/2}. That is the maximal utility you can achieve when you have $m money. 

Now the marginal utility with respect to money is the direvative of U_max with respect to the variable m, which gives 4 * sqrt{3} * sqrt{m}. It is 1 when m equals to 48.

"treat the money as an unknown".

That's the point,thanks.