Lydia Lopokova is 40 years old. She has assets (wealth) of $80,000 and has no debts or liabilities. She knows that she will work for 30 more years and will live 10 years after that, when she will earn nothing. Her salary each year for the rest of her working career is $35,000. (There are no taxes.) She wants to distribute her consumption over the rest of her life in such a way that she consumes the same amount each year. She cannot consume in total more than her current wealth plus the sum of her income for the next 30 years. Assume that the rate of interest is zero and that Lopokova decides not to leave any inheritance to her children.

a. How much will Lydia consume this year and next year? How did you arrive at your answer?

b. Plot on a graph Lydia’s income, consumption, and wealth from the time she is 40 until she is 80 years old. What is the relationship between the annual increase in her wealth and her annual saving (income minus consumption)? In what year does Lydia’s wealth start to decline? Why? How much wealth does she have when she dies?

c. Suppose Lydia receives a tax rebate of $1,000 per year, so her income is $36,000 per year for the rest of her working career. By how much does her consumption increase this year and next year?

d. Now suppose Lydia receives a 1-year-only tax refund of $1,000—her income this year is $36,000; but in all succeeding years, her income is $35,000. What happens to her consumption this year? in succeeding years?