Problem Set #2 Suggested Solutions

Transcription

1 Economics 155 Stanford University Spring Quarter 2007 Problem Set #2 Suggested Solutions 1. An externality occurs when an agent s action directly affects the consumption or production of another agent, without the mediation of a market. One of the main reasons (although not the only one) for the lack of a functioning market is the absence of welldefined property rights that satisfy exclusivity, transferability and enforceability. (See p. 63 of the textbook for a fuller discussion of the relationship between property rights and externalities.) 2. a) The Internet is organized in such a fashion that each user within an Internet Service Provider typically pay a fixed cost to access the Internet, independently of how much data they download. However, the amount of data that can be sent through the network is limited, leading to congestion in times of peak demand. Since the transmission capacity of the network is shared, and users do not pay according to how much capacity they use, the transmission capacity of the Internet can be seen as a common-pool resource. (Software designers and content providers also benefit from the common-pool of transmission capacity without paying for the congestion they can create see for a fuller discussion of this issue.) b)

2 Speed (Dollar value of data received per minute) C MPC + optimal tax B A MPC Marginal Benefit Average Benefit Traffic (In minutes) The average benefit is just the data received per minute of use. The distance between the average benefit and the marginal benefit is equal to the marginal external cost it is the reduction in total data received due to an additional minute of traffic. The marginal private cost is just the opportunity cost of a minute of a user s time, plus the cost of electricity used, wear and tear on computer, etc. Point A is the open-access equilibrium, while point B is the social optimum. c) If a tax is imposed per minute of access during a period of congestion, the marginal private cost of a user increases. The tax should be equal to the marginal external cost at the social optimum, in order for the user to internalize this cost. Therefore, the optimal tax will move the equilibrium from point A to point C. If the tax were set equal to the marginal external cost at the open-access equilibrium (point A), it would be too large and lead to too little traffic in the new equilibrium (not shown above). d) Denying access would be inefficient because it does not take into account the possibility that different users place different values on access. If a minute of access is more valuable to a new user than an old user, it is socially more efficient, in the sense of maximizing total surplus, to transfer that minute of access to the new user. With an optimal tax, each user faces the marginal social cost of his actions in deciding how much time to use the Internet, so access will be allocated efficiently. 3. a) The aggregate total damage is just p 2 + 3p 2 = 4p 2. The aggregate marginal damage is just the derivative of this with respect to p, which is 8p. b) The marginal savings of pollution is just 20 2p.

3 $ Aggregate marginal damages Marginal savings Pollution c) Without regulation or bargaining, the factory will pollute p = 10. Society s optimal level of pollution is given by maximizing 20p p 2 4p 2, which gives us an optimal level of pollution p = 2. d) The marginal willingness to pay for abatement A is equal to 2(10 A) for workers and 6(10 A) for retirees, and 8(10 A) on aggregate. e) The marginal cost of abatement reducing pollution to the firm is just the lost savings from pollution, 20 2(10 A). The optimal level of A is given by setting marginal cost equal to marginal willingness to pay and is A = 8. f) Yes. No matter what the starting point, the optimal level of pollution is given by that point where the marginal savings of pollution to the firm are equal to the marginal costs of pollution to workers and retirees. 4. To solve this question, we need to assume that we can treat all global polluters as a single agent in parts (a) and (b) and treat each region s polluters as a single agent in part (c). a)

4 $ MC A Total MB 5 13 Pollution Reduction Note the kink at Q = 6. At this point, only region O is still willing to pay for additional pollution reduction. The socially efficient level of pollution reduction is Q = 5, where the marginal cost is equal to the global marginal willingness to pay. b) The marginal benefits from pollution reduction are equal to the marginal cost of pollution, so global damages are given by the area under the total marginal benefits curve pictured above, which is just the vertical sum of the two regional marginal willingness to pay curves. Since polluters have to pay full compensation for the pollution they cause, they will set Q = 5 to maximize net profits. (The total compensation paid out is just the area under the Total MB curve, marked A in the graph above, which is equal to 33.) The compensation received by region R is 1 (area below their marginal willingness to pay curve between Q = 5 and Q = 6) and by region O is 32 (area below their marginal willingness to pay curve between Q = 5 and Q = 13). From an efficiency point of view, it does not matter who receives the payments. c) Setting marginal cost equal to marginal willingness to pay separately for each region, we find that region R polluters would reduce pollution by 1 and region O producers would reduce it by 3. The total reduction of 4 is less than in parts (a) and (b) because each region s negotiations do not take into account the benefit to the other region. (However, note that this is an out-of-equilibrium outcome, because the assumption that the other region will not undertake pollution reductions is not fulfilled. In equilibrium, there would be even less pollution reduction as region R free-rides on region O s pollution reduction.)

5 5. a) The beekeeper would maximize his own profits by setting H = 5. b) The socially efficient number of hives maximizes total profits and is H = 10. c) The farmer would pay between $25 and $50 to the beekeeper in return for him keeping ten hives instead of five. d) Total profits increase by $25 with ten hives instead of five, so transaction costs of $25 and above would erase the gains from bargaining. 6. a) $ 12 MB to Maggie A 8 MC to Sam B 8 24 Pollution The decreasing marginal benefit to pollution for Maggie means that the more you reduce pollution, the more expensive it becomes to reduce it further. b) The efficient amount of pollution maximizes aggregate income and is c = 8. The aggregate income is YT = 268, with YM = 112 and YS = 156. c) Without an agreement, c = 0, YM = 32, YS = 220, and YT = 252. In the presence of an agreement, we d have c = 8, YM between 32 and 48, YS between 220 and 236, and YT = 268. That is, Maggie would pay between 64 and 80 to Sam in return for being allowed to pollute c = 8. An agreement is possible because a little more pollution benefits Maggie more than it hurts Sam this is true as long as c is less than eight. The gains from a voluntary agreement correspond to the triangle A in the graph above.

6 d) Now, without an agreement, c = 24, YM = 176, YS = 28, and YT = 204. With an agreement, we d have c = 8, YM between 176 and 240, YS between 28 and 92, and YT = 268. That is, Sam pays Maggie between 64 and 128 to reduce pollution to c = 8. The gains from the agreement correspond to the triangle B in the graph above. e) With this technology, Maggie can use detergent at will without polluting, so she would set c = 24 and have profits equal to 176. Since her profits in part (c) were between 32 and 48, she would be willing to pay between 128 and 144 for the new process it depends on how good a deal she would have gotten in the negotiation.