[求助]Suppose that people live for two periods

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Suppose that people live for two periods, working L hours in the first period for which they receive a wage of w dollars per hour, and living in retirement in the the second period. As they do not work during the second period, they provide for their retirement by saving S dollars during the first period and lending it to producers. During their retirement, they receive and spend their entire savings as well as the interest earned at a rate of r% per period.

People consume only rice, and their tastes are represented by the utility function:

U=C1.C2

C1=consumption of rice in the first period

C2=consumption of rice in the second period

Derive the demand functions for rice in each period.

My answer: WL-S=P1C1

S+r%.S=P2C2

P1C1+P2C2=WL+S+r%.S

Using Langange function: P1C1=P2C2=(WL+r%.S)/2

I feel this must be wrong, since I've already have had WL-S=P1C1,S+r%.S=P2C2

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关键词：Suppose Periods period People live 求助 帮忙

（1） C1＝W×L－S

（2） C2＝（1＋r）×S

通过（1）和（2）把 S 消掉，得到 Intertemporal Budge Constraint（IBC）。

然后选择 C1 和 C2 求 U＝C1×C2 的极大值，subjected to IBC。

把s消去答案就对了

Using Langange function: P1C1=P2C2=(WL+r%.S)/2

我是这样理解这个式子的，也就是说在这两个时期，他们的效用是相等的，但如上面三楼的兄弟说的那样，应该把＂s＂消掉，但是这样做就不考虑通货膨胀的因素了．