3. An airport (A) is located next to a piece of land owned by a developer (D), and the noise from the planes reduces the value of land. If A has x planes flying per day and D builds y houses, total profit of A is m4 = 48z 22 and total profit for D is mp = 60y y?> ry, both measured in dollars. a) How many airplanes should fly, and how many houses should be built from an efficiency point of view? b) (Free to choose). Suppose first A chooses = to maximize its profits, ignoring the negative external effect on D. Calculate the profits maximizing number of planes r per day. Knowing z, D chooses y to maximize wp. Calculate the optimal number of houses y for D. What is total surplus/profit? c) (Strict Prohibition). Suppose local authorities make it illegal to land or start planes at the airport. How many houses will D built, and what is total surplus? 3 Econ 302 Anke Kessler Q) ) h ~ * g)" (Lawyer's Paradise). Suppose a law is passed that makes A liable to all damage to D's property values. If = planes fly and y houses are built, D is awarded damages that equal the actual external cost, xy. A's profit is thus 74 = 482 z2 zy while D makes mp = 60y y? (including the damage payments). How many houses & will D choose to built? And how many planes will A fly, knowing that D chose 2?7 What is total surplus? (The Conglomerate). Suppose A and D merged to a single firm that maximized joint profits. Give the profit maximizing amounts of x and y. (Government Intervention, optional). The government levies a tax t on A for each airplane that landed/started at the airport. How high should the government set t to restore efficiency? Can the tax revenue be distributed to make both A and D better off relative to b) ) and d)? (Bargaining, optional). Suppose that A and D remain independent, but D can negotiate with A about reducing noise pollution. Let be the agreed upon number of flights. Give Coasian solution to the problem. 4. Suppose five families share a common stretch of beach and they are considering a program of improvements, including a stairway and a play structure for children. All families have quasi-linear utility functions. If they spend an amount of $ = in total for the improvements, their (gross) values are vy(z) = va(z) = 5z iz 2 for families # 1 and #2, v3(z) = 13z 32? for family #3, and vs(z) = v(zs) = 2r %:\\.:2 for families #4 and # 5. Let t; be family #i's contribution to the cost of the measure and assume each family has the same income = 10. Everything is measured in 100 $ units. a) b)* Calculate the Pareto efficient level * of expenditure on beach improvements. How much should each family optimally contribute? Now suppose the cost of beach improvements are shared equally among the families. Show that, under this cost sharing rule, families # 4 and # 5 would prefer not have any improvements at all (xr = 0) rather than the efficient level (z*). If the families agreed to vote by majority vote on the level of beach improvements, with 3 alternatives on the ballot which equal their most preferred expenditures, what alternative will be the winner of the election? 1. Consider a firm whose output of x leads to a detrimental externality (pollution) for firm 2, e(x). Suppose e(x) = 4x. Assume that the price of x is px = 16 and that the firm's total cost function is cx(x) = 2x2. Assume that there is no market for the pollution itself and that a negotiated agreement between the firms is impossible. a) What is the Pareto efficient level of output, x? b) What level of output, x; would firm 1 produce? c) Compare your answers in part a) and part b) and explain. d) Find the (Pigouvian) tax rate that would lead firm 1 to produce the Pareto efficient level of output. 2. Let the marginal cost of producing a product be MC(Q) = 30 + Q, where Q is the industry's output of the product. The production of Q releases a toxic effluent into the water supply, creating a marginal external cost of MEC = Q. The inverse market demand for the product is P(Q) = 300 - Q, where Q is the market output of the product. a. How does the competitive equilibrium output in this market differ from the socially efficient level of output? b. Draw a diagram and show on your diagram the welfare loss that occurs at the competitive equilibrium. c. Is the socially optimal amount of pollution zero or positive? Why? d. lllustrate how a per-unit tax on output can be used to achieve the level of pollution