Adam Smith is 45 years old. He has assets (wealth) of $20,000 and has no debts or liabilities. He knows that he will work for 20 more years and will live 5 years after that, when he will earn nothing. His salary each year for the rest of his working career is $14,000. (There are no taxes.) He wants to distribute his consumption over the rest of his life in such a way that he consumes the same amount each year. He cannot consume in total more than his current wealth plus the sum of his income for the next 20 years. Assume that the rate of interest is zero and that Smith decides not to leave any inheritance to his children.
a. How much will Adam consume this year and next year? How did you arrive at your answer?
b. Plot on a graph Adam's income, consumption, and wealth from the time he is 45 until he is 70 years old. What is the relationship between the annual increase in his wealth and his annual saving (income minus consumption)? In what year does Adam's wealth start to decline? Why? How much wealth does he have when he dies?
c. Suppose Adam receives a tax rebate of $100 per year, so his income is $14,100 per year for the rest of his working career. By how much does his consumption increase this year and next year?
d. Now suppose Adam receives a 1-year-only tax refund of $100-his income this year is $14,100; but in all succeeding years, his income is $14,000. What happens to his consumption this year? in succeeding years?