Yasmine’s income this period is $500 and she is certain that her income next per

Question

Yasmine’s income this period is $500 and she is certain that her income next period is $300. The current market interest rate is 10 percent. She plans to spend exactly her current income this period and her future income next period, with no borrowing or saving. Yasmine has a diminishing marginal rate of time preference.

(a) With the aid of a diagram, explain if you can determine Yasmine’s optimal consumption C1 and C2 in the two periods.

(b) Before Yasmine actually carries out her consumption plan, the market interest rate drops to 5 percent. Explain if she will change her consumption plan.

Explanation / Answer

a) She will distribute her income in such a way that she spends equally in two periods.

She will spend $405 in this perod and save $ 95 which will yield her an interest of $9.5 and her total income will be 300+95+9.5 for next period = $404.5 which is almost equal to $405

b) If rate of interest drops to 5% then she will spend $ 405 now and save $100 so that her income in next period = 300+95+5% of 95 = 300+95 +4.75 = 399.75 She will spend more now because she has preference for present expenditure than future.

It is assumed that he can save only in denominator fo 5.

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