Econ 450 Autumn 2015 HW Solutions with Graphs - Econ 450 Autumn 2015 HW I Assuming no government intervention or provision briefly discuss why public

Econ 450 Autumn 2015 HW Solutions with Graphs - Econ 450...

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Unformatted text preview: Econ 450 Autumn 2015 HW I . Assuming no government intervention or provision, briefly discuss why public education may be underprovided if financed exclusively by private contributions. 5 points. If education has positive externalities, or aspect of a public good, the social marginal benefit Will lie above the private marginal benefit, and the quantity provided in a market will be less than the optimal quan— tity. . Define and explain the Cease Theorem, and relate it to the First Welfare Theorem. 5 points. The Coase theorem states that in the absence of transaction costs, and With fully specified property rights, private bargaining will lead to ef- ficient outcomes even in the presence of externalities; essentially pri- vate bargaining will internalize the externality. This is equivalent to the efficiency requirement in the First Welfare Theorem that markets exist for every good. . Define and explain what a Pareto improvement is, using an Edgeworth Box. 5 points. A Pareto improvement is an alternative to the status quo that leaves at least one person better off and no one worse off; in a two-good exchange economy, as depicted by an edgeworth box (see attached), the set of pareto improvements is the shaded lens area. . Consider the following market for a private good, where Anne and Beverly's inverse demand curves are given by PA = 500 e Q PB m 500 — 262 The marginal cost of this good is M C = 2Q (a) Calculate the market demand curve 2 points. For a private good we sum quantities to get the market demand curve. 50 we sum 500 — p Qa-l-Qs =500np+ 2 QM m500-10+250——.510 QM 2750—151; (b) (C) (d) (e) (0 Solving for p, we get the inverse market demand curve: P,” 2 750— mm?» = 500 m go. Depict this market graphically. 3 points. See attached. Calculate the market price and quantity that will be produced, assuming this market is perfectly competitive. 3 points. Setting the inverse market demand equal to inverse supply, we Solve for the market quantity: 500 w = 2Q Q“ : 187.5 and the market price is 375. Argue that this outcome is Pareto Efficient. 2 points. At the price of 375, the quantities consumed by A and B are 375 = 500“ QA => (2,4 = 125 and 375 = 500m 2623 => Q3 2 62.5. At these quantities their marginal utilities are M UA 500 — QA 2 375, M U B = 500 — ZQB = 375, so marginal util— ities are equal, so no further pareto improvements via trading are possible. Furthermore, when the market quantity is 187.5, the marginal cost of another unit is MC = 2 * 187.5 x 375, so marginal utilities are equal to marginai cost, so no further pareto improvements via production are possible. Therefore the out- come is efficient. Suppose instead that this good is a pure public good. Costs and utilities are the same. What wouid the outcome of private pro- vision of this good be in that case? 5 points. In this case, B would free-ride on A, since A demands more of the good. A would purchase 500 — q = 2r] => Q* : 166% units. What would the efficient level of production be in that case? 5 points. In this case the social marginal benefit is the sum of the marginal utilities, or Sit/I B = 1000 — 3Q. This is equal to marginal cost when 1000 —- 3Q = 262 => Q8 = 200. 5. Arturo, Bashir, and Carl share a house in Fremont, and each has his own bedroom. They heat the house with a shared wood—burning stove. Arturo values one hour of heating at 6.5 dollars, Bashir at 8 dollars, and Carl at 10 dollars (with one hour of heating being as vaiuable as the next). Suppose heat from the stove is a pure public good that can be produced at a constant marginal cost of 20 dollars per hour of heating (a) What is the efficient quantity of hours (H) of heating per day (of course, there are 24 hours in a day)? 5 points. The sum of the marginal benefits is 6.5 + 8 + 10 = 24.5 > 20 = M (3’. Since benefits exceed costs for all hours of the day, the efficient number of hours to provide is 24. Now assume that each of the housemates must choose between three options. Option 1: Continue to fuel the wood-burning stove. All of the housemates who choose Option 1 will split the stove heating bill equally. Option 2: Each housemate may bring in his own electric heater (costiessly) from his parent’s house. An electric heater pro- vides heat only for the bedroom of the housemate who brought it. If he turns it on, he will have to privately pay 7 dollars per hour to op- erate it. Under this option, they make no contribution to the common stove. Option 3: Neither; they can choose to neither fuel the stove, nor use their owner heater. (b) Which of the three options will each of the housemates choose in equilibrium? 10 points. Suppose all three choose to participate in the cost sharing scheme. This cannot be an equilibrium. To see why, note that the cost of of Arturo Wili be > 6.5, so that costs exceed his benefits. So he will opt out. If only two participate , cost shares Wili rise, so Arturo cannot be one of the two. So it can only be Bashir and Cari. Their shares will be § 2 10 > 8, so Bashir will opt out. If only one participates, he bears the entire cost, and 20 > 10, so Carl will not participate on his own. So the furnace will not be turned on in equilibrium. The cost of private heating is 7, Carl and Bashir wiil opt for private heating, since their benefits exceed this cost, while Arturo will buy nothing and receive no benefits, and pay no costs. (c) Is this equilibrium allocation Pareto efficient? Explain why or why not. 10 points. This is not pareto efficient. You can see this in a number of ways; first, Arturo receives no heat, an in an efficient outcome he would. Therefore it is no efficient. Another way to see it is that total welfare under this outcome is 10 + 8 —— 7 — 7 = 4, While total welfare under an outcome where heat is provided by the heater is is 10 + 8 + 6.5 — 20 2 4.5. Therefore the private out- come does not maximize welfare. Yet another way is to specify a pareto improvement; Here is one: let the furnace be turned on. Arturo is to be charged 6 doilars, While Bashir and Carl are each charged 7. Bashir and Carl and equally well off under this alternative, while Aturo is strictly better off. Thus it is a pareto improvement, so the previous arrangement was not efficient. 6. For each of the examples below, please answer the following: (a) (b) (C) Does an externality exist? If so, classify the externality as posi- tive/ negative (or both). 2 points. If an externality exists, determine whether the Coase theorem applies (i.e. is it possible to assign property rights and solve the problem?) 2 points. If an extenality exists and the Coase theorem does not apply, ar- gue which of the government’s tools are best suited to address the issue: quantity regulation, taxes/ subsidies, tradeable per- mits, or something else. 1 point. Consider the foilowing examples: (a) (b) British Petroleum drills for oil in the gulf coast If there is environmental damage BP does not pay for, there is an externality. IF the damage is so widespread or outside the jurisdiction of any one government, private bargaining will not work, due to high transaction costs and unclear property rights. A good way to address this would be a tax on oil equal to the marginal damage. Carbon emissions from vehicles The externality is the pollution and climate effects from car emis- sions. These damages are committed by drivers, of whom there are many, and experienced globally. The Coase theorem will probably not apply in this case. An effective response would probably be a Carbon tax, rather than requiring drivers to pur— chased permits, or mandated emissions goals. (c) Your upstairs neighbors throwing an awesome, but loud party They are bothering you, and your unhappiness is the external- ity. The coase theorem probably applies here; noise regulations give you the right to call police, so you have the property right to the "noise environment" and bargaining with your neighbor is easy. Social norms Culture can also help address this prob lem. Government intervention beyond property rights is proba~ bly not necessary. ((21) Buying a car with added safety features that prevent the driver’s and passengers death’ 5 in the event of an accident. The externality is the benefit to passengers who did not decide on which safety features you purchased with your car. The ben~ eficiaries are in the future and difficult to barging with; most people aren’t about to prey their friends to buy safer cars. An apropriate response would be to subsidize safer cars. (e) Bringing crying babies on a plane The externality is the unhap~ piness experienced by others on the plan due to your decision to bring the baby. The Coase theorem pay not apply here; it is not clear who has the property right here — your right to a quiet plane or their right to bring their baby? Bargaining may also not be possible, if it is not possible to make arrangements ahead of time to purchase quiet flights. The amount of inefficiency may be small, however. It is not clear that any regulatory scheme will be worth it. 7. Suppose that the agricultural production of hogs (pigs) create wa— ter pollution that results in serious health conditions for both hu~ mans / animals that rely on those water scurces. Specifically, assume that the market supply function is given by H3261) where H3 is the quantity of hogs supplied to the market and P is the market price for hogs. Similarly, assume that the market demand function is given by H D 2: 300 — 3P Further, assume that hog production imposes total external medical costs (M) on nearby communities, quantied as M=2H where M is measured in dollars and H is the number of hogs pro— duced. (a) Identify the relevant externality (consumer or producer, positive or negative). 5 points. This is a negative production externality. (b) Sketch the market for hog production and identify the corre- sponding DWL in the market resulting from the externality iden- tified in part (a). (Do not calculate.) 5 points. See Attached. (c) Suppose that property rights to clean drinking water are assigned to the neighboring communities. Further assume that hog pro— duction is common on numerous small farms in the area. i. Briey discuss the potential Coasian outcome. 2 points. ii. Determine whether or not the private market solution is likely to succeed in this context. 3 points. The Coasian outcome is for the communities to agree on a payment from the hog farmers to compensate them for their harm. This may be difficult; if there are many farms it may be difficult to assign the harm to a particular farmer and compel their agreement to a bargain. (d) If imposing a price controi, what corrective Pigouvian tax T in the hog market will lead to the socially optimal level of hog pro— duction? 5 points. In this case the marginal damage is constant, so a tax T : 2 could achieve the optimal level of hog production. ...
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