国际经济学前沿I：CES效用函数.doc

离散CES效用函数下的需求函数_1 ，，替代弹性 ， F.O.C. （1） （2） 设数量指数为，则，代回一阶条件得 （3） 设P是一个价格指数，它恰好能使PQ=I成立，则（3）式变为 （4） P应该是多少呢？由（4）得 结果总结 结果总结 ，， 一个特殊情况： ， 离散CES效用函数下的需求函数_2 ，，替代弹性 F.O.C. （1） （2） 将代回一阶条件得到 两边同时次方：， 求和： 将代入上式得到 设数量指数为，价格指数为，则 结果总结 结果总结 ，， 连续CES效用函数下的需求函数 见The basics of Dixit-Stiglitz lite By Jonathan I.Dingle 1. Preferences ， 2. Demands , ※Let Now multiply both sides byand take the integral with respect to Let P is thus the true cost of living index, such that the expenditure function is e(P; u) = Pu, as can be seen ( while recalling that ): 3. Taste for Variety Suppose that all varieties have the same price p and are therefore consumed in equal amounts q, so that . Then I = npq and q = I/ np . Therefore: 4. Firms We write the labor demand function: It is assumed that there no economies of scope, so there is no reason for a firm to produce multiple varieties. Since consumers have an unbounded taste for variety, every firm will produce a distinct variety rather than producing another firms type and losing profits to competition. The result is one variety per firm and one firm per variety. Thus, the distinction between the number of firms and the number of varieties collapses in our discussion of those topics. 5. Free Entry Equilibrium