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.