ECP 3451 Homework 1 – Module 2 – Property
Dr. Bull
1. Suppose there is a society with two people who have the following valuations of level y of a public good: v1(y) = 1210√y and v2(y) = 410√y so their marginal benefits are given by 605/√y and 205/√y, respectively. The cost of providing the public good is given by c(y) = 10y. So we have MC(y) = 10. Suppose that their utility is given by u1 = x1 +v1(y) and u2 = x2 +v2(y) , where xi denotes person i’s money (that is not spent on the public good). Further, suppose their wealth/income levels are given by w1 = 500 and w2 = 800.
(a) What is the socially optimal level of the public good? (b) Suppose that it is proposed that y = 4 be implemented, and that this or y = 0 are the only two options. The two people vote on this proposal, and approval requires a majority vote. Suppose that, if it is approved, each will be required to pay a tax equal to half of the cost. Will this proposal be approved.
2. On the weekend days during the summer, people in a large metropolitan area like to go to the beach. Assume the population is 100,000 Suppose that going to the beach yields a payoff of 15− k 1000, where k is the number of people who choose to go to the beach. Suppose that the other option, staying at home, yields a payoff of zero. In equilibrium, how many people choose to go to the beach? If there is more than one equilibrium, report all equilibria.
3. Suppose that a cattle rancher (R) and a corn farmer (F) are located next to each other. Currently, there is no fence between the ranch and the farm so R’s cattle enter F’s field and destroy some of F’s corn. This results in a loss of 500 to F. Under the current situation, the value of production for R is 1000, and the value of production for F is 1200 (including the loss of 500). A fence that will keep the cattle out of the cornfield would cost 200 for R to build (assume that only R can build the fence). Suppose that R is not legally required to prevent his cattle from entering F’s cornfield. Assume R and F can negotiate costlessly and the outcome of their negotiation is given by the standard bargaining solution with equal bargaining weights. Describe the payoffs of F and R, and any payments made.
4. Herb’s Dog Walking Service and Kurt’s Scenic Pacific Beach Walking Tours operate in the same neighborhood. The dogs Herb walks relieve themselves in the same areas where Kurt’s customers walk and this imposes a cost on Kurt. Assume that Herb does not “curb” (clean up the waste of the dogs he walks).
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Herb’s units of dog walks is given by x, and his cost of producing x units is x2 and his marginal cost is 2x. Herb can sell as many units as he wishes at a price of $60 per unit. Kurt can produce w units of waking tours at a cost of w2 + 20x. So his marginal cost of production is 2w. Kurt can sell as many units as he wishes at a price of $60 per unit. Since Herb’s production imposes a cost on Kurt, the social marginal cost of dog walks is given by 2x+20. Note that Kurt’s production does not impose a cost on anyone else. Assume that Herb and Kurt are the only relevant parties to this problem.
(a) Assume the externality is allowed and no steps are taken to avoid it. What is the profit-maximizing quantity of x that Herb produces, and what are his profits? What is the profit-maximizing quantity of w that Kurt produces, and what are his profits? (b) What are the socially optimal levels of x and w? (c) Now suppose that Herb has the right to pollute with his dog walking. Assume that Herb and Kurt are not able to sort out a way to reduce/limit the pollution (perhaps Herb has a bad back and is unable to pick up after the dogs). Assume it is costless for them to negotiate (assume the Coase Theorem applies) and the outcome of their negotiation is given by the standard bargaining solution with equal bargaining weights. What is the outcome of the bargaining? Describe the output of each and any transfers. (d) Now suppose that Herb discovers that he can carry a bag with him and pick up after the dogs he walks at a cost of 2x. That is, cleaning up after the dogs implies a cost for Herb of x2 + 2x and a marginal cost of 2x + 2. Now what is the socially optimal outcome? (e) Again assume that Herb has the right to pollute with his dog walking, but that Herb is able to clean up after the dogs as in part (d). Assume it is costless for them to negotiate (assume the Coase Theorem applies) and the outcome of their negotiation is given by the standard bargaining solution with equal bargaining weights. What is the outcome of the bargaining? Describe the output of each and any transfers.
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