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