PROBLEMS AND APPLICATIONS

1. Brad spends his income on two goods: hair gel and toothpaste. Both goods are normal goods Suppose that the price of hair gel falls.

a. Show the effect of this price decrease on Brad’s budget constraint.

b. Show the effect of the price decrease on Brad’s optimal consumption bundle assuming that the income effect outweighs the substitution effect.

c. Show the effect of the price decrease on Brad’s optimal consumption bundle assuming that the substitution effect outweighs the income effect.

2. Compare the following two pairs of goods:

• Coke and Pepsi

• Skis and ski bindings

a. In which case are the two goods complements? In which case are they substitutes?

b. In which case do you expect the indifference curves to be fairly straight? In which case do vou expect the indifference curves to be very bowed?

c. In which case will the consumer respond more to a change in the relative price of the two goods?

3. Mario consumes only cheese and crackers.

a. Could cheese and crackers both be inferior goods for Mario? Explain.

b. Suppose that cheese is a normal good for Mario while crackers are an good, If the price of cheese falls, what happens to Mario’s consumption of crackers? What happens to his consumption of cheese? Explain.

4. Jim buys only milk and cookies.

a. In year 1, Jim earns $100, milk costs $2 per quart, and cookies cost $4 per dozen. Draw Jim’s budget constraint.

b. Now suppose that all prices increase by 10 percent in year 2 and that Jim’s salary increases by percent as well. Draw Jim’s new budget constraint. How would Jim’s optimal combination of milk and cookies in year 2 compare to his optimal combination in year .

5. Consider your decision about how many hours to work Draw your budget constraint assuming that you pay no taxes on ,your income On the same diagram, draw another budget constraint assuming that you pay 15 per’cent tax  Show how the tax might lead to more hours of work, fewer hours, or the same number of hours Explain.

6. Sarah is awake for 100 hours per week. Using one diagram, show Sarah’s budget constraints if she earns $6 per hour, $8 per hour, and $10 per hour. Now draw indifference curves such that Sarah’s labor-supply curve is upward sloping when-the wage is between $6 and $8 per hour, and backward sloping when the wage is between $8 and $10 per hour.

7. Draw the’indifference curve for’ someone deciding how much to work. Suppose the wage increases. Is it possible that the person’s consumption would fall? Is this 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 batik 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. Consider a couple’s decision about how many children to have. Assume that over a lifetime a couple has 200,000 hours of time to either work or raise children. The wag~ is $10 per Raising a child takes 20,000 hours of time.

a. Draw the budget constraint showing the trade-off between lifetime consumption and number of children. (Ignore the fact that children come only in whole numbers!) Show indifference curves and an optimum choice. .

b. Suppose the wage increases to $12 per hour. Show how the budget constraint shifts. Using income and substitution effects, discuss the impact of the change on number of children and lifetime consumption.

c. We observe that, as societies get richer and wages rise, people typically have fewer children. Is this fact consistent with this model? Explain.

11. Economist George  once wrote that, according to consumer theory, “if consumers do not buy . less of a commodity when their incomes rise, they will surely buy less when the price of the commodity rises.” Explain· this statement using the concepts of income and substitution effects.

12. 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 disappears. Let’s consider the possible effects (If 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 the existence of the welfare system.

b. Adding indifference curves to your diagram, show how the welfare system could reduce the number other VUL” worked by the family. Explain, with 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.

13. Suppose that an individual owed no taxes on the first $10,000 she earned and 15 percent on 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 draw 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.

14. 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 lever 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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