# Spring 2017 Environmental Economics/EEP 101/ECON 125 EEP 101/ECON 125 Problem Set 2

Spring 2017 Environmental Economics/EEP 101/ECON 125 EEP 101/ECON 125 Environmental Economics:Problem Set 2This handout includes the questions for Problem Set 2. Note that the answers need tobe turned in via bCourses, where you will be prompted to enter your answers. For mostquestions, you will just enter your answer. Questions marked with an asterisk * here willallow you to enter an explanation, and will be graded for partial credit. 1. Monopoly and Public GoodAn internet service company is considering providing full wifi connectivity to a city. Theyplan to charge a fee for access to the internet per month. The total cost of setting upinfrastructure for wifi is T C = 1000s where s is the speed of the network. Suppose thetotal benefit for each consumer is T B = 10s ? s2 and there are 500 consumers in the city.a) What is the socially efficient level of s? (1 point)b) What fee does the company charge each consumer? Is the socially efficient level of sprovided? (1 point)A new college opens, leading to more students in the city. Suppose now we have 100 students living in the city in addition to the original 500 inhabitants. College students have ahigher demand for faster internet and their total benefit for each student is T B = 20s?s2 .The company recognizes that it can charge a higher price to college students, howeverthis would entail losing all other business. So the company has two options: (A) chargea high fee and have only college students as customers, or (B) charge a low fee and haveeveryone in the city (including college students) as customers. If the monopolist chargesa lower price and gets everyone in the market, they wonât be capturing all of the benefitsof the college students. (Assume they have to charge all customers the same priceânoprice discrimination is possible.)c) What is the profit for the monopoly under scenario A? What is the profit for themonopoly under scenario B? (Note: you need to find the profit-maximizing s under eachscenario.) (2 point)d) What s does the monopoly produce? What is the socially efficient level of s? (1 point) 1 Spring 2017 Environmental Economics/EEP 101/ECON 125 2. (Voluntary provision of a public good) This question continues the example inLecture 10, slide 10. The cost of building a park is C(g) = 10g 2 , where g is size of apark in square miles. Total benefits from the park for each individual is: B = 3g ? 2g 2 .There are 10 identical individuals in the community. In class, we showed that undervoluntary contribution, it will not be an equilibrium for the 10 people to provide theefficient amount of the public good (because of free riding). In this problem, we are goingto walk you through steps to find what is the equilibrium level of contribution. Beforeyou do this, take 10 minutes and ask yourself how you would find the outcome assumingeveryone was making the same contribution. Then, see how we suggest you proceed.* a) Show that everyone contributing 0 will not be the equilibrium. (Hint: use reasoningsimilar to what we did in class.) (1 point) To proceed, letâs introduce some notation: let g1 be the amount of park that person 1provides. Note that the cost of providing this amount of park will depend on the quantity in equilibrium. It is easiest to describe contributions in terms of units of the good.Let G?1 = g2 + g3 + Â· Â· Â· + g10 be the combined contribution of everyone else. Thus, byconstruction, we have g = g1 + G?1 . In a voluntary provision equilibrium, we want toconsider how person 1 will choose their level of provision, taking as given the amountthat others are giving. That is, we want to figure out the optimal g1 as a function ofG?1 , which is taken as fixed by person 1. (For those of you who know the term, we arefinding a Nash Equilibrium.) b) Person 1 will choose g1 taking into account their own benefits, but ignoring everyoneelseâs. Write down the marginal benefit function that they use to make decisions, andsubstitute our definition of g = g1 + G?1 so you have marginal benefits as a function ofg1 (which is a choice) and G?1 , which person 1 takes as fixed. Write down the relevantmarginal cost curve as well, using the g1 and G?1 notation. (1 point) c) We are going to find the symmetric equilibrium, where all 10 people make identicalcontributions. Symmetric contribution implies something about the relationship betweeng1 and G?1 . Specifically, G?1 = ?g1 . What is ?? (1 point) * d) If you set the marginal benefit equal to the marginal cost (which defines the optimalg1 ) from part b), and you use the equation from part c), you should be able to solve forthe equilibrium quantity. What is the total amount of the public good provided in thesymmetric voluntary contribution equilibrium? (That is, what is g (rather than g1 )?) (1point) 2 Spring 2017 Environmental Economics/EEP 101/ECON 125 3. (Samuelson condition) A Cal student (denoted by C) is sharing an apartment witha student from the second best school in the Bay area (denoted by S). They are planningto invest in a public good for the apartment: a couch. Let Q denote the size of the couch.Demand of the two students are given by: PC = 10 ? Q and PS = 6 ? Q respectively.The total cost of a couch is T C = aQ2 /2, where a is parameter to be determined.* a) What is the aggregate demand from the two students? Note that because we donâtallow negative demand, you will need to describe this function using a piecewise functionthat has two linear segments. Write out the equation and draw a graph to show demand.(2 points) b) Suppose a = 6, then what is the size of the socially optimal couch? Suppose thetwo students share the cost evenly, how much will each one pay for the socially optimalcouch? (1 point) c) Suppose a = 0.6, then what is the size of the socially optimal couch? Pay attentionto which part of the piecewise linear demand function you are on. (1 point) 3 Spring 2017 Environmental Economics/EEP 101/ECON 125 4. (P vs. Q) Suppose the marginal benefit of controlling air pollution in Beijing isM B(q) = 12 ? q, where q is the amount of pollution controlled. Beijing EnvironmentalProtection Bureau (BEPB) estimated that the total cost of controlling the pollution isT C = q 2 + rq. The value of parameter r is unknown to BEPB. All they know is that itcould take the value of either r = 0 or r = 6, and with equal probability.a) What is BEPBâs expected marginal cost of pollution control? (Average the twopossibilities.) (1 point) b) Given that BEPB does not know for sure what true cost is, what q should they choose?(1 point) c) Instead of using a quantity mandate, BEPB could choose a tax on emissions. Whattax rate t would they choose, given uncertainty? (Hint: just find the tax rate thatcorresponds to the q you found in part b), assuming that the MC is the expected costfrom part a).) (1 point) d) According to the Weitzman theory, which policy instrument will be better in thissituation? (1 point) * e) Suppose that r=0. In a graph, show the deadweight losses from the quantity policyand from the tax policy. Calculate these deadweight losses. (Your calculation shouldconfirm your answer in part d)!) (2 points) To enter your answer, we will need youto upload a PDF image of your graph. Feel free to draw this by hand, take aphoto and turn it into a PDF. 4 Spring 2017 Environmental Economics/EEP 101/ECON 125 5. (Congestion) UC Berkeley is planing to offer a new class, Advanced EnvironmentalEconomics, in Fall 2017. The university has to choose the size of the class (that is, howmany students can enroll in this class, denoted by N ) and the number of units/credits(denoted by X) assigned to this course. After some research, the university finds thatstudents who are potentially interested in registering for the class are very similar. Moreover, benefit to an individual student is represented by the function B = 800X ? 40N ,where benefits are measured in dollars. Total cost of offering this course is C = 32, 000Xdollars.a) Suppose the universityâs goal is to maximize social welfare. Find the optimal classsize N ? and the optimal number of units/credits assigned to this class X ? . (1 point) b) Suppose the university offered the class at social optimal N ? and X ? . If the universitywanted to recover the total cost of offering the class, then how much would the universityneed to charge each student for tuition fees? (1 point) c) What is the maximum tuition fee that the university could charge each student thatthey would actually be willing to pay? (assuming the class size is still at N ? and thenumber of units is still at X ? .) (1 point) * d) Compare your answer to part c) to the results you got from part b). You shouldhave found that the the university cannot offer the course at the social optimum andrecover costs. Does this mean that it is not socially optimal to offer the class at all?Briefly explain why or why not? (1 point) 5

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