Problems

1.Suppose that a major city’s main thoroughfare, which is also an interstate highway, will be completely closed to traffic for two years, from January 2012 to December 2013, for reconstruction at a cost of $535 million. If the construction company were to keep the highway open for traffic during construction, the highway reconstruction project would take much longer and be more expensive. Suppose that construction would take four years if the highway were kept open, at a total cost of $800 million. The state Department of Transportation had to make its decision in 2011, one year before the start of construction (so that the first payment was one year away). So the Department of Transportation had the following choices:

  • (i) Close the highway during construction, at an annual cost of $267.5 million per year for two years.
  • (ii) Keep the highway open during construction, at an annual cost of $200 million per year for four years.
    • a. Suppose the interest rate is 10%. Calculate the present value of the costs incurred under each plan. Which reconstruction plan is less expensive?
    • b. Now suppose the interest rate is 80%. Calculate the present value of the costs incurred under each plan. Which reconstruction plan is now less expensive?

2.You have won the state lottery. There are two ways in which you can receive your prize. You can either have $1 million in cash now, or you can have $1.2 million that is paid out as follows: $300,000 now, $300,000 in one year’s time, $300,000 in two years’ time, and $300,000 in three years’ time. The interest rate is 20%. How would you prefer to receive your prize?

3.The drug company Pfizer is considering whether to invest in the development of a new cancer drug. Development will require an initial investment of $10 million now; beginning one year from now, the drug will generate annual profits of $4 million for three years.

  • a. If the interest rate is 12%, should Pfizer invest in the development of the new drug? Why or why not?
  • b. If the interest rate is 8%, should Pfizer invest in the development of the new drug? Why or why not?

4.You are considering buying a second-hand Volkswagen. From reading car magazines, you know that half of all Volkswagens have problems of some kind (they are “lemons”) and the other half run just fine (they are “plums”). If you knew that you were getting a plum, you would be willing to pay $10,000 for it: this is how much a plum is worth to you. You would also be willing to buy a lemon, but only if its price were no more than $4,000: this is how much a lemon is worth to you. And someone who owns a plum would be willing to sell it at any price above $8,000. Someone who owns a lemon would be willing to sell it for any price above $2,000.

  • a. For now, suppose that you can immediately tell whether the car that you are being offered is a lemon or a plum. Suppose someone offers you a plum. Will there be trade?
    Now suppose that the seller has private information about the car she is selling: the seller knows whether she has a lemon or a plum. But when the seller offers you a Volkswagen, you do not know whether it is a lemon or a plum. So this is a situation of adverse selection.
  • b. Since you do not know whether you are being offered a plum or a lemon, what is the most you are willing to pay for your vehicle? Why?

5.For each of the following situations describe whether it is a situation of moral hazard or of adverse selection. Then explain what inefficiency can arise from this situation and explain how the proposed solution reduces the inefficiency.

  • a. When you buy a second-hand car, you do not know whether it is a lemon (low quality) or a plum (high quality), but the seller knows. A solution is for sellers to offer a warranty with the car that pays for repair costs.
  • b. Some people are prone to see doctors unnecessarily for minor complaints like headaches, and health maintenance organizations do not know how urgently you need a doctor. A solution is for insurees to have to make a co-payment of a certain dollar amount (for example, $10) each time they visit a health care provider.
  • c. When airlines sell tickets, they do not know whether a buyer is a business traveler (who is willing to pay a lot for a seat) or a leisure traveler (who has a low willingness to pay). A solution for a profit-maximizing airline is to offer an expensive ticket that is very flexible (it allows date and route changes) and a cheap ticket that is very inflexible (it has to be booked in advance and cannot be changed).
  • d. When making a decision about hiring you, prospective employers do not know whether you are a productive or unproductive worker. A solution is for productive workers to provide potential employers with references from previous employers.

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