Chapter 18/Externalities, Commons, and Public Goods chapter 18 Externalities, Commons, and Public Goods
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Figure 18.4 
9) Figure 18.4 shows the payoff matrix for two firms. A chemical firm must choose between a low level of production which yields one ton of pollution into a nearby lake and a high level of production which yields two tons of pollution into the nearby lake. A private beach on the lake must decide whether to operate or not. Increased pollution reduces the number of people who wish to visit the beach. Determine the Nash equilibrium without property rights. Answer: Without property rights, operating is a dominant strategy for the beach owner and 2 tons of pollution is a dominant strategy for the chemical firm. Diff: 0
Topic: Allocating Property Rights to Reduce Externalities 10) Figure 18.4 shows the payoff matrix for two firms. A chemical firm must choose between a low level of production which yields one ton of pollution into a nearby lake and a high level of production which yields two tons of pollution into the nearby lake. A private beach on the lake must decide whether to operate or not. Increased pollution reduces the number of people who wish to visit the beach. If the chemical firm owns the lake and the beach owner must pay the chemical firm $10 to produce only one ton of pollution, what is the outcome? If the beach owner owns the lake and the chemical firm must pay $10 per ton of pollution, what is the outcome? Compare this result to the case where nobody owns the lake. Answer: If the chemical firm owns the lake, the bottom two cells do not change, the top cells change from (15, 0) and (15, 25) to (25, -10) and (25, 15). Producing just 1 ton of pollution is the firm's dominant strategy. The beach will operate, and both enjoy joint profits of 40. If the beach owner owns the lake, the top cells become (5, 10) and (5, 35). The bottom cells become (0, 0) and (0, 10). Producing 1 ton of pollution is a dominant strategy for the firm. The beach operates and they enjoy joint profits of 40. Without property rights, the dominant strategy for the chemical firm is to produce 2 tons of pollution. Diff: 2
Topic: Allocating Property Rights to Reduce Externalities 11) Explain the externality generated when a shepherd grazes sheep in a field which is common property that several other shepherds use. Answer: The shepherd allows his sheep to graze in the field until the marginal benefit of grazing there equals the marginal cost to the shepherd. However, by grazing his sheep in the field, the shepherd increases the cost of grazing to all the other shepherds. This occurs because less grass is available for all other sheep. Each shepherd's grazing decision affects the costs to all the others, but the shepherds do not consider the effects on others when making their own decisions. Diff: 1
Topic: Common Property 12) Explain why the social demand curve for a public good is the vertical sum of the demand curves of each individual. Answer: A public good lacks rivalry, so many people can get pleasure from the same unit of output. Thus, for each unit of public good, the total willingness to pay is the sum of everyone's willingness to pay because everyone can consume the good. Diff: 1
Topic: Public Goods. 13) Suppose three neighbors must vote on the installation of a traffic light that costs $210. The cost of the light will shared by all three. Voter A values the light at $50; voter B values the light at $50; and voter C (who drives the most) values the light at $200. If the voting rule is that the majority wins, does the light get purchased? Is it efficient to purchase the light? Answer: The cost of the light to each voter is $70. Since MC > MB for two of them, the light does not get purchased. It is efficient to purchase the light since SMB = 300 which exceeds the MC of 210. Diff: 1
Topic: Public Goods 14) Suppose 100 citizens each derive marginal benefit from submarines according to the function MB = 10 - Q. If subs cost $100 each to produce, what is the efficient quantity of submarines? Answer: The market demand is SMB = 1000 - 100Q. Setting this equal to the MC of 100 yields a quantity of 9. If the cost is shared equally, each citizen pays $1 for the ninth submarine, which they each value at $1. Diff: 1
Topic: Public Goods Figure 18.5 
15) Two neighboring farmers must each decide whether to contribute to a fence that separates their properties. The fence costs a total of $20. Both farmers currently have a profit of $30 each. With a fence to keep each farmer's animals from wandering onto the other's property, both farmers would experience a $15 rise in profits. Draw the payoff matrix and discuss the possible outcomes. Answer: See Figure 18.5. This is a prisoners' dilemma. The dominant strategy for each is to not contribute—to be a free rider. Yet, both farmers are better off contributing. The dilemma can resolved through compulsion—for example a tax—or, since there are only two of them, social agreement. Cooperation and trust are required to get the fence built. Good fences make good neighbors, and good neighbors make good fences. Diff: 2
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