1.Suppose you live in downtown Pavement City and you would enjoy walking, having picnics, playing basketball, and basically chilling-out in a local city park, if one were available. Suppose your annual marginal benefit from having access to such a park is:
MB = 20 - (1/20000)X, where X is the size of the park in square feet.
The City estimates that the marginal cost of building and maintaining such a park would be MC = $25 per square foot.
(i)If you had to pay for the construction of the park all by yourself, what size park would you build? Explain why very briefly.
(ii)If there are 979 additional people (in addition to yourself, for a total of 980 people) living in the vicinity of the park who would all receive about the same annual marginal benefit from having access to the park as yourself, what is the efficient size of park to build, from society's perspective?
(iii)What is the name of the market failure occurring in this situation?
(iv)If this market failure is not corrected (say, by a city park construction project), graph and calculate an area that will be equal to the annual deadweight loss suffered by the honorable citizens of the city. SHOW YOUR WORK!!
2.Al regularly rehearses his Iggy and the Stooges cover band on his back deck. Practicing on his deck saves him the $500 per year it would take to rent a rehearsal space. Unfortunately, practicing on his deck keeps his neighbor, Marcy, awake at night. The value of Marcy’s lost sleep is $600 per year.
a.Is it efficient for Al to rehearse on his back deck? Explain your answer.
b.If the law says that it is illegal for Al to rehearse on his back deck, will Al end up practicing there? What might Marcy do to try to stop him?
c.Suppose that the law says it is legal for Al to rehearse on his back deck.
i.How much is Marcy willing to pay to get him to stop?
ii.What is the minimum amount of money Al is willing to accept in exchange for his silence?
iii.If possible, craft a bargain between Marcy and Al that results in his silence. Show that the bargain (if possible) makes both parties better off.
d.Given your answers to (b) and (c), does the outcome of this conflict depend on the law? Is the outcome consistent with your answer to (a)?
e.Suppose that instead of doing $600 damage to one neighbor, Al does $1 damage to 600 neighbors. Are those 600 neighbors as likely to be able to convince him to stop as easily as Marcy can? Explain.
3.A steel factory has the right to discharge waste into a river. The waste reduces the number of individuals willing to swim in the river. Let X denote the quantity of waste dumped.
The marginal damage (MD) imposed on the swimmers is given by the equation:
MD = 2 + 5X.
The factory’s marginal benefit (MB) of dumping waste is given by the equation:
MB = 34 – 3X.
a.Calculate the efficient quantity (from society’s perspective) of waste the factor should dump.
b.What is the efficient fee, in dollars per unit of waste, that would cause the firm to dump only an efficient quantity of waste?
c.What would be the quantity dumped if the firm did not care about the swimmers?
4.There are two proposed uses for a natural area located close to a city – as a park or open pit limestone mine. A set of costs and benefits is given for a 10-year period for each of the two possible projects. Calculate the net present value for each of the projects using a 10% discount rate.