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PS1 Soln - EEP 101/Econ 125 Spring 2010 GSIs Biswo Diana...

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Unformatted text preview: EEP 101/Econ 125 Spring 2010 GSIs: Biswo, Diana Problem Set 1 Due on Tuesday, February 161th at lecture. Late assignments will not be accepted. Numerical Questions 1. (40 Points) Suppose the industry for rambutans (a fruit) has a demand curve given by Q = 60 — %P, where P is the price in dollars, and Q is the quantity. The marginal private cost (MP0) of production is MP0 2 20 + Q, and the marginal external cost of production (MEC) is given by MEC = 2Q. (a) Determine the socially optimal level of output (Q*). Calculate the total external cost (TEC*), consumer surplus (08*), producer surplus (PS*), and total social welfare (SW*) at this level of output. Figure not drawn to scale The socially optimal quantity occurs where MSC=MSB. MSC=MEC+MPC=20+3Q MSB=MEB+MPB=0+MPB Rearranging demand, we have MPB=120-2Q 120—2Q220—l—3Q Q*=20 P*=80 TEC* = 09* MECdQ = ff" 2QdQ = Q2 30 = 400 *=f0Q( 62* (—MPB 13*) Mg) 2 f0Q*(120 — 2Q — 80)dQ — CSfoQ( (-40 262) dc): (4062 — Q2)|3° = 40(20) — 202 = 800 — 400 = 400 *=ff( Q*( —)MPC )dQ = fOQ‘(80 _ (20 + Q))dQ _ PS‘MO (—60 P)Q )dQ: (60Q — Q72”? 2 1200 — 200 = 1000 SW" 203* + PS* — TEC* = 400 + 1000 — 400 = 1000 Calculate the quantity produced if the market is in perfect competition and only private costs are accounted for (the externality associated with production is NOT taken into account). What is the quantity produced (QC)? Calculate the total external cost (TECC), consumer surplus (CSC), producer surplus (PSC), total social welfare (SW6) and dead—weight loss (DWLC) at this level of output. Figure not drawn to scale The optimal quantity under perfect competition occurs where MPCrMSB. 120—2Q= 20+Q Qpc = M— — 33. 3 P116 2 fi— _ 53 3 100 TECpc ==f0rMECdQ f032QdQ—Q2|0_030:%:1111,1 CSpc :f0(1’c (—MPB Ppc) dQ: f0(1"° 1(20—2Q—1—g°)dQ c 2 _ _0Qp (3_60_2Q_1_60)d=Q (2_00Q_ Q2)|0—003 _m.m_ (100) = w = w = 1111.1 Pspc :f0 PC( (Ppc — MPC)dQ= f0(1c(1—g0 (—20 + Q))dQ 00 =(f0 pc (@___ ))dQ_ (1—30Q_%3)|0—3 szgz5555 5ch : cspc + Pspc — TECPC : 1—0300 + w — —1Og°°: T115110 : 555.5 DWLPC : SW* — 5ch : 444.4 Now assume that this industry is operate by a middleman who buys up all the rambutans from local farmers and packages them, and she is the only source of rambutans to consumers. What is the quantity produced (Qmm)? Calculate the total external cost (TECm), consumer surplus (CSm), producer surplus (PSm), total social welfare (SWm) and dead-weight loss (DWLm) under a middleman. Figure not drawn to scale The optimal quantity under a middleman occurs where M OzMR. 120—4Q220+2Q Qmm = 1—30_ — 16 6 Pmmseu— _ 612—0 2 *—1—g° :36°;1°° : 86.6 Pmmbuy— _ 20 + 1_00_ _6120—é—100 : 36.6 100 TECPC :fOQmm MECdQ= foe 2QdQ: Q2|0—3° : w 2277:; cspc :f0 mm (MPB— Pmmseu) dQ: f0 mm1(20— 2Q— 2—g°)dQ 3 :fg mm (3—60 _2Q_2g—O)dQ: (1_00Q_ Q2)|0—006 : 100 _1_gO (120)2 : 1010800_ 1%%0()_ _ 1030600_ _ 277- 7 PSpc =f0 mm( Pmmbuy _ MP0) )ZdQ foQ mm (L20 _(20 + Q))dQ (1_00 =5 W <— — — — c2» d=c2 <1—2°c2— %)l 6 = = — = 138-8 :PQmm( mmsell _ Pmmbuy) : 1_g0 ' 50 2 833-3 SWmm = 05mm + PSmm + 7rmm — TECmm = 277.7 + 138.8 + 833.3 — 277.7 2 972.2 DWme 2 SW* — SWmm = 1000 — 972.2 2 27.7 Now suppose that the government wants to fix the externality problem using a price mechanism (tax or subsidy). Calculate the optimal tax or subsidy under a competitive market (part b) and under a middleman (part c). Graphically, show how this tax or subsidy (choose one) is chosen under both cases. Perfect competition: From the graph we see that we need to push MPC up to the point where it crosses MPB at 62*. Therefore, we need to institute a tax equal to MPB(Q*) — MPC(Q*) = (120 — 2 - 20) — (20 + 20) = 80 — 40 = 40 Middleman: Uner the middleman, we see that we need to institute a subsidy to lower MO so that it crosses MR at 62*. Therefore, the subsidy is equal to MO(Q*) — MR(Q*) = (20 + 2 - 20) — (120 — 4-20) 2 60 — 40 = 20 Note: you were given full credit if you noted that we would not want to subsidize the middleman, since it is a negative externality and he is producing less externality. It might be more optimal to introduce competition of some sort. Assume that the market is perfectly competitive, and the government imposes the appropriate tax or subsidy (calculated in part d). Be sure that you clearly indicate which one you are using! Compared to (part b), how do the government’s finances change? What is the change in consumer surplus, producer surplus, total external costs, and social welfare? What is the level of dead—weight loss? Government revenue: G = t - Q* = 40 - 20 = 800 A08 2 08mm — C'S'pC = 08* — CS“ 2 400 — 1111.1 2 —711.1 A2PS= Pam—PS“: fOQ"( —(MPC+t)dQ— 555 5— _ 020(80— (20+Q+40)dQ—555.5 = 020(20 + Q)dQ — 555 5— _ (20Q + %)30 — 555. 5— _ 400—200—555 5— _ —355. 5 ATEC : TECm — TECZ,c : TEC* — TECpc : 400 — 111.1 : 711.1 ASW = SVVW, — SW1,C 2 05th + PStam + G — TECtaw — 555.5 2 400 + 200 + 800 — 400 — 555.5 2 444.4 DWL = SW* — SW,” = 1000 — 1000 = 0 2. (30 Points) Suppose the Oakland School of Art and Music (OSAM) is run with private funds and it has net costs of schooling, MPC=100+4Q since schooling is costly and the monetary returns are low. (Q represents a unit of schooling.) On the other hand, many people argue that art and music enrich the public culture and therefore provide an external benefit associated with schooling given by MEB=400—Q. (a) What is the optimal amount of schooling provided by OSAM? What is the optimal amount of schooling from the public point of View (those experiencing the external benefits)? What 1s the optimal amount of schooling from the societal point of view? Explain your answers. Since OSAM is always running with positive net costs, this means that for any unit they provide, the costs outweight the benefits. Thus, their optimal amount would be to provide Qomm : 0 units of schooling. For those experiencing the external benefits, they do not face any costs. This means they would want schooling to be provided until their external benefits were no longer positive. This occurs where qublic = 400. Many people found this confusing. Think, for instance, that you get paid 100 dollars for every year that your friend goes to school. You would want your friend to get infinite schooling if possible. This is the same situation that the people experiencing the external benefits are in { except their marginal benefit is decreasing). The societal point of view cares about both the private costs (faced by the school) and the external benefits. Thus, the optimal occurs where MPCzMEB, Q* = 60. (b) What is the dead—weight loss under the OSAM’s optimal choice? What is the dead—weight loss under the public’s optimal choice? Recall that DWL is the difference between the social welfare in the current situation and the social welfare under the optimal situation. So, we first calculate social welfare in each situation. Social welfare is usually given by consumer plus producer surplus, subtracting off any additional costs. It is equivalent to taking the integral below the MSB and above the MSC' from 0 to Q. In our case, MPB=0, and MEC=0, so MSBzMEB and MSCzMPC'. OSAM: Optimal quantity is zero, so there is nothing to integrate over. Public: f04°°(400 — Q— [100 + 4Q] )dQ= [040% 300— 5Q) dQ— [300Q — gQ2]|300 = 120000 — E 160000— — —280000 Alternatively, total benefit is given by the triangle with area §400 >1: 400 = 80000 and total cost is given by the sum of the rectangle 100 * 400— — 40000 and the triangle $—(1600)(400) — 320000. Again, the social welfare is given by 80000— 40000— 320000— — —280, 000 Note: the negative social welfare indicates that the costs largely outweigh the benefits, which makes sense because we are very far past the social optimum in this case. Society: 060(400—62— [100+4Q]) dQ— f0°( (300— 562) dc): [300Q— 362210": 18000 — g - 3000 — 9 000 Thus, the deadweight loss in OSAM’S case is 9000 — 0 = 9, 000, and in the public ’3 case it is 9000 — (—280000) 2 289, 000 (0) Suppose some people were interested in running a second school of art and music with the same net costs as OSAM. Calculate the new optimum from the societal point of View. Compare the total welfare under one school with that under two schools. With a second school, the cost curves are changing but the benefit curves are not. This is because the external benefits are only a function of the total schooling provided and thus does not depend on whether or not it is provided by one or many different schools. To find the new cost curve, we add the MPO horizontally. Intuitively, the two schools can now provide twice the units of schooling at the same price as before. Rearranging, we have 100 + 462 = P => Q = 25 — g Q2schools : 50 _ g 2} MPCZschools : 100 + 2Q Qaschools : 100 + 2Q : 400 _ Q => Qaschools : 100 SW* 2schools= “100(400 Q_ 3l100 + 2Q] )ZdQ f0(100 300— 3Q) ($le [300Q— gQ2]|(1,°°— _ 30000 — — 10000_ — 15 000 Thus, under two schools, there is an additional 6,000 units of total surplus. (d) Return to the case of one school. Calculate the total amount of revenue that would have to be raised for OSAM under the social optimal case for the school to break—even. The break—even point is when the school exactly covers its costs. To cover its costs, it must be given the total cost of providing the optimal quantity. The total cost is f06°(100 + 4Q)dQ = (100Q + 2Q2)|8° = 6000 + 2-3600 2 13200 Essay Question Write a brief typed essay (less than one page) on the topic described below. Be sure to write your answer in the form of an essay; don’t just answer the questions listed below. Please relate your essay to what we have discussed in class and try to hit on what you believe are the few relevant key points. (30 Points) Under the international agreement laid out by the Kyoto Protocol, the participant countries committed to reach binding targets for green house gas emissions. They also laid out three market based mechanisms to promote the achievement of these targets: emissions trading, clean development mechanism, and joint implementation. The emissions trading mechanism created a market for carbon using the idea of tradable permits. The clean development mechanism allows industrialized countries to earn credits toward their targets by implementing emission-reduction projects in developing countries, while the joint implementation mechanism allows the countries to earn credits with emission—reduction projects in other paricipant countries. Discuss the benefits and drawbacks of the emissions trading mechanism and one of the two credit—earning mechanisms. Comment on the likely advocates of each policy, and compare the mechanism with a carbon tax and and an untransferrable carbon quota. (http: //unfccc.int/kyotopr0tocol/items/2830.php) Points were awarded for the following key points: 0 Tradable permits (10 points): — Benefits: No deadweight loss, economically preferred because producers don’t suffer — Drawbacks: Difiicult to determine allocation. Outcome depends on market. Dirty technologies may still exist as long as they are still profitable. — Advocates: Free-market economists who are against strong interventions and companies which are not very clean but still efficient enough to be able to purchase permits and still make a profit. 0 Credit-earning mechanism (10 points): — Benefits: Promotes clean—technology use in developing/ partner countries. — Drawbacks: Countries can get away with not reducing their own pollution very much as long as they implement projects in other countries. — Advocates: Similar to advocates of tradable permits. Countries (developing and partner) which get the project benefits from the member countries. Companies which do not want to overhaul their dirty technology and can benefit from the positive public relations from doing an external project. 0 Taxes (5 points) — Benefits: Governments take in revenues. Outcome is certain. — Drawbacks: Deadweight loss and producers suffer. o Quota (5 points) — Benefits: outcome is certain, governments can tell each company exactly what they can produce. — Drawbacks: Requires more monitoring and is therefore likely more expensive. ...
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