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4.5 End-of-Chapter Material

In Conclusion

Many decisions involve a trade-off between now and the future. Whenever we invest our time or money, we are giving up something today to obtain something in the future. So by saving some of our income, we give up consumption now for consumption in the future. When we go to a university, we give up income and leisure time today to get more consumption (through higher income) in the future.

Once you start thinking about trade-offs over time, it is difficult to avoid the reality that many of these decisions are made in the face of great uncertainty. When we save, we are not certain of the return on our saving. When we go to school, we are not guaranteed a job in the future nor are we guaranteed a specific salary. We have provided some insights into the nature of these uncertainties and how to deal with them. Discounted present value and expected value are techniques that are worthwhile to master, as they will help you make better decisions throughout your life.


  1. Explain why an increase in the interest rate reduces the discounted present value of income.
  2. What incentives exist for people to repay loans on education? On cars?
  3. Suppose the nominal interest rate is 20 percent, the price level in the first year is 50, and the price level in the second year is 60. What is the real interest rate? How could you alter this example so that the real interest rate is 0?
  4. Can the nominal interest rate ever be less than the real interest rate? If the real interest rate is negative, what happens to the slope of the budget line with two periods discussed in Chapter 4 "Life Decisions", Section 4.1 "Consumption and Saving"?
  5. Do households sometimes borrow and lend simultaneously? Why might that happen? Is the interest rate they borrow at usually higher or lower than the interest rate they receive, say in the form of bank deposits?
  6. In describing how changes in income influence the supply of loans, we assumed that the increase in income occurs this year. Suppose instead that the increase in income will occur next year even though everyone in the economy knew it would happen today. How would the news of a future increase in income influence the current loan supply curve?
  7. When the government changes taxes, do you know if it is permanent or temporary?
  8. (Advanced) One way that real wages received by workers can change is through a change in income taxes. Considering the information in this chapter, would you except temporary tax changes to have a bigger or a smaller impact on labor supply than a permanent tax change? What if the tax change is not through a change in the tax rate but rather through a fixed payment to households? What would that policy do to labor supply?
  9. Look back at Table 4.2 "Which Career Should You Choose?" in the section “Choosing a Career.” How would you edit the income entries in the table so that the insurance salesperson had a higher discounted present value than the lawyer even when the interest rate is 5 percent?
  10. Look back at Table 4.2 "Which Career Should You Choose?" in the section “Choosing a Career.” Explain why an increase in the interest rate makes it less attractive to be a lawyer.
  11. Besides discounted present values of income, what other factors are important in choosing a career? How do you balance these with differences in the discounted present value of income?
  12. What are the risks associated with choosing a particular career? How do those risks depend on whether the skills you learn at your job can be used in other jobs?
  13. Show the calculation of the discounted present value from work in Table 4.5 "Income from Going to College versus Taking a Job". Redo the comparison of college and work assuming an interest rate of 20 percent.
  14. (Advanced) Look back at Table 4.2 "Which Career Should You Choose?" in the section “Choosing a Career.” Suppose the income of a lawyer increases by 20 percent each year after year 2 and the income of the insurance salesperson increases by $10,000 each year. Extend Table 4.2 "Which Career Should You Choose?" to 5 years. Which is a better profession?
  15. Create your own version of Table 4.8 "Coin-Flipping Experiment" by flipping a coin 10 times. Imagine that each time the result is a head, you earn $1,000, and each time it is a tail, you lose $1,000. After you flip the coin 10 times, calculate how much you won (or lost). Now do this same experiment 20 times. Each time you flipped the coin 10 times, record how much you won (or lost), which will result in 20 numbers. What is the average of these 20 numbers? What is the expected value of how much money you will earn in each coin-flipping experiment??
  16. Many products, such as computers, come with the option of an extended warranty. Suppose you are buying a computer with a one-year warranty. Thereafter, you can purchase an extended warranty for one more year, at a cost of $50. The warranty will repair or replace your computer in the event of breakdown. Suppose the average cost to the manufacturer of repairing or replacing the computer is $1,000. If the manufacturer is making no money from this warranty, what is the implied probability that the computer will need repair?
  17. We wrote “As long as the insurance company has lots of policies in many locations, then, on average, the number of insurance claims will be nearly constant each year.” Why did we include the statement about many locations?
  18. Why is it difficult to diversify job risk? Is it possible to do some diversification within a family?
  19. In the United States, the provision of unemployment insurance is partly at the state level and partly at the federal level. For your state, find out what the benefits are and what federally funded unemployment insurance might be available to you.

Economics Detective

  1. Study the insurance policy you can buy when you purchase a new cell phone. Exactly what does this insurance protect you against? Given the price of the insurance and the coverage, what is the implied probability that you will make a claim for a new phone under the insurance? Is there a deductible? Why is it part of the policy?
  2. Look at the insurance policy (if you have one) for the place where you are living. What is the deductible? List the ways in which you take actions to reduce the risk of fire where you live.
  3. Our example of homeowners’ insurance did not use real numbers. Find a homeowners’ policy and determine the coverage, the premium, and the deductible.
  4. One form of insurance occurs when you rent a car. Using the Internet or phoning local insurance agents, find out the kinds of insurance that are available when you rent a car. What is the cost per day? Exactly what risks do these policies protect you against? Given the price of the insurance and the coverage, what is the implied probability that you will have an accident and make a claim under the insurance? Does this probability seem reasonable to you?
  5. What is the average price of a house in the United States? In your hometown?
  6. What does it cost to insure a $100,000 house in your city? What does it cost to insure a $1,000,000 house in your city? Explain the differences in the insurance costs.
  7. Pick a state in the Unites States. Suppose you work there and earn $2,000 each week as a manager. One day, the firm tells you that you are no longer needed. What unemployment insurance could you collect? Would you qualify for unemployment insurance? How much would the benefits be? How long would the benefits last?
  8. Go to your local bank and see if there are any signs that indicate deposit insurance is provided. Ask about details of the program.
  9. Use the Internet to find out about deposit insurance programs in the United States and in another country. How do these programs compare?
  10. For the state in which you live, does the government sponsor a lottery? If so, how are the funds used?
  11. In the financial crisis of 2008–9, was deposit insurance provided in the United States? In other countries?
  12. In the state you live in, find out about the unemployment insurance program. How long do you receive benefits and how generous are the benefits?

Spreadsheet Exercises

  1. Write a spreadsheet program to create a version of Table 4.8 "Coin-Flipping Experiment" for any combination of income flows and interest rates.
  2. (Advanced) Create a spreadsheet program to simulate the flipping of a coin. Do T experiments with 5 flips per experiment. For each experiment, calculate the mean of the outcome. When you are finished, you will have T means. What does the distribution of the T means look like? What is the mean of that distribution? What happens as T gets very large?