Page 480 - The Principle of Economics

490 PART SEVEN ADVANCED TOPIC
plausible? Discuss. (Hint: Think about income and substitution effects.)
8. Suppose you take a job that pays $30,000 and set some of this income aside in a savings account that pays an annual interest rate of 5 percent. Use a diagram with a budget constraint and indifference curves to show how your consumption changes in each of the following situations. To keep things simple, assume that you pay no taxes on your income.
a. Your salary increases to $40,000.
b. The interest rate on your bank account rises to
8 percent.
9. As discussed in the text, we can divide an individual’s life into two hypothetical periods: “young” and “old.” Suppose that the individual earns income only when young and saves some of that income to consume when old. If the interest rate on savings falls, can you tell what happens to consumption when young? Can you tell what happens to consumption when old? Explain.
10. Suppose that your state gives each town $5 million in aid per year. The way in which the money is spent is currently unrestricted, but the governor has proposed that towns be required to spend the entire $5 million on education. You can illustrate the effect of this proposal on your town’s spending on education using a budget constraint and indifference-curve diagram. The two goods are education and noneducation spending.
a. Draw your town’s budget constraint under the existing policy, assuming that your town’s only source of revenue besides the state aid is a property tax that yields $10 million. On the same diagram, draw the budget constraint under the governor’s proposal.
b. Would your town spend more on education under the governor’s proposal than under the existing policy? Explain.
c. Now compare two towns—Youngsville and Oldsville—with the same revenue and the same state aid. Youngsville has a large school-age population, and Oldsville has a large elderly population. In which town is the governor’s proposal most likely to increase education spending? Explain.
11. (This problem is challenging.) The welfare system provides income to some needy families. Typically, the maximum payment goes to families that earn no income; then, as families begin to earn income, the welfare payment declines gradually and eventually
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disappears. Let’s consider the possible effects of this program on a family’s labor supply.
a. Draw a budget constraint for a family assuming
that the welfare system did not exist. On the same diagram, draw a budget constraint that reflects the existence of the welfare system.
b. Adding indifference curves to your diagram, show how the welfare system could reduce the number of hours worked by the family. Explain, with reference to both the income and substitution effects.
c. Using your diagram from part (b), show the effect of the welfare system on the well-being of the family.
(This problem is challenging.) Suppose that an individual owed no taxes on the first $10,000 she earned and 15 percent of any income she earned over $10,000. (This is a simplified version of the actual U.S. income tax.) Now suppose that Congress is considering two ways to reduce the tax burden: a reduction in the tax rate and an increase in the amount on which no tax is owed.
a. What effect would a reduction in the tax rate have
on the individual’s labor supply if she earned $30,000 to start? Explain in words using the income and substitution effects. You do not need to use a diagram.
b. What effect would an increase in the amount on which no tax is owed have on the individual’s labor supply? Again, explain in words using the income and substitution effects.
(This problem is challenging.) Consider a person deciding how much to consume and how much to save for retirement. This person has particular preferences: Her lifetime utility depends on the lowest level of consumption during the two periods of her life. That is,
Utility 􏰀 Minimum {consumption when young, consumption when old}.
a. Draw this person’s indifference curves. (Hint: Recall that indifference curves show the combinations of consumption in the two periods that yield the same level of utility.)
b. Draw the budget constraint and the optimum.
c. When the interest rate increases, does this person
save more or less? Explain your answer using income and substitution effects.
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