Econ 1 - Problem Set 5 With Solutions

Problem Set 5 Hard copies of your answers are due at the beginning of your section, either on Thursday, October 27, or Friday, October 28. For example, if your section starts at 10:00am on Friday, you should submit your answers to your TA in your section classroom at 10:00am on Friday, October 28. Late problems earn zero points. Note: you can work on these problems or your own, or in a small group with other current Econ 1 students. If you choose to work in a group, each student needs to hand in a separate, individual copy to his/her TA. 1. Suppose a local community builds an expressway that provides better access to its downtown area. The project is financed by raising the community’s property tax. If you live in a nearby town but often visit that community’s downtown area, are you a free-rider? Why? What can the community do to eliminate the free-rider problem? Explain. 2. Consider a three-person city that is considering a fireworks display. Bertha is willing to pay $100 for the proposed fireworks display, while Marian is willing to pay $30, and Sam is willing to pay $20. The cost of the fireworks display is $120. a. Will any single citizen provide the display on his or her own? Explain. b. If the cost of the fireworks display is divided equally among the citizens, will a majority vote in favor of the display? Explain. c. Describe a transaction that would benefit all three citizens.

Problem Set 5 Solutions Problem #1: Yes, you are a free rider. Why? Because you did not pay property taxes and are therefore consuming something which you did not pay for. Here, the expressway is a public good which is non-excludable and (barring traffic-jams) non-rival. How do we eliminate the free-rider problem? We can design mechanisms that will increase the excludability of the good. For example, we can finance the expressway with tollbooths instead of a property tax. Some things to think about: It might seem like a sales tax on downtown shops will eliminate the problem. However, this will do the job only under very restrictive circumstances: namely when the people who shop are exactly the same set of people who uses the expressway, and that the sales tax only applies to the downtown area served by the expressway (how feasible is that?). The main idea is you want to remedy the situation by targeting people who are directly affected; and the sales tax might distort the situation for other people who might not be expressway users. Problem #2: (a) No. The cost of the fireworks display is $120, which exceeds the individual willingness to pay of every citizen. Therefore, none of the citizens will provide the display on their own. (b) No. If the cost is divided equally, then each citizen pays $40 ($120/3). A cost of $40 exceeds the willingness to pay of Marian ($30) and of Sam ($20). Both Marian and Sam will vote against the display if the cost is to be shared equally. (c) The cost of the display can be shared in several ways that will benefit all three citizens. Since their total combined willingness to pay equals $150, the cost of $120 can clearly be afforded as a group. As long as each of them pays some amount less than their individual willingness to pay, each will benefit from the display. An example of such a division of the cost that treats all three citizens “fairly” is to split the total consumer surplus that is available ($150 of total willingness to pay minus $120 in total costs) evenly among the three citizens. This means each citizen pays $10 under his/her willingness to pay: Bertha pays $90, Marian pays $20, and Sam pays $10. In this case, they cover the cost of $120 and are each left with a consumer surplus of $10. Note, however, that since fireworks are a public good (one citizen watching them does not take away from another citizen’s enjoyment of them, and citizens cannot be kept from watching the display) there may be incentives for citizens, especially Marian and Sam, to free ride and not pay at all. Furthermore, it could be difficult to determine the benefit each citizen gained from watching fireworks, particularly since citizens would have incentive to understate their willingness to pay.