Spring 2012Important Terms and concepts Mid-term #1 Review and Practice testKnow definition and how concept is used.Lindahl pricesPigouvian taxPareto efficientFree rider problemFirst Fundamental Theorem of Welfare EconomicsSocial welfare functionMedian Voter theorem and assumptionsDeadweight loss of a subsidyMeans testedCoase theoremCharacteristics of Public and Private goodsExternalities1. Externalities A steel factory has a MC function (supply curve) of 2+5x. The waste reduces the number of fish, causing damage for swimmers. Let X denote the quantity of waste dumped. The marginal damage, denoted MD, is given by the equation MD = 2X. The marginal benefit (MB) of dumping waste is given by the equation MB = 42 − 3X.(a) Calculate the efficient quantity of waste.Set SMC = MB and solve for X. X=4(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?Insert 4 into MD Fee=22(c) What would be the quantity dumped if the firm did not care about the fishery?Set MB equal to MC and solve for X. x=5Depict the situation graphically.You could make this a little more interesting by including a MPC = to sy 4Then MSC = MPC+MD  = 4+2+5X34-3X = 4 + 2+5x X=3.52. (18 pts) Andrew, Beth, and Cathy live in Durant. Andrew’s demand for bike paths, a public good, is given by Qa= 12 – 2P. Beth’s demand is Qb= 18-P and Cathy is Qc= 8-P/3 where Q= miles of bike paths. The marginal cost of building the bike path is $21, a constant.a. What is the socially optimum number of miles of bike paths?Bike paths are a public good. The 3 WTPs need to be summed Andrew: 2P+ 12- Qa ; Pa = 6- .5QaBeth: Pb = 18 – QbCathy: P/3 = 8 –Qc; Pc = 24-3QcAggregate Willingness to Pay : Pa + Pb +Pc = MC  6-.5Q+18-Q+24-3Q  48-4.5Q=21 27=4.5Q Q = 6b. Given these demand preferences, if the city uses a Lindahl taxing scheme, what would be the tax bill for each individual?A: P = 6 - .5 (Q) 6 - .5(6); Pa = 3B: P = 18 – (6); Pb = 12C P= 24- 3(Q) = 24- 18 =6A=3/21 B= 12/21 C = 6/21c. If the city had taken a more egalitarian approach and taxed each individual equally (i.e. $7 each) to finance the bike path, would any of the bikers have a consumer surplus (MB> their tax share of $7)? Which one(s)?Yes, Beth3. Consider the case of two farmers, Tony and Hal, depicted in the figure below. Bothuse DDT (a chemical pesticide) for their crops. The use of DDT causes anexternality for swimmers down river from the farms.a. Show the amount of pesticides used if each uses the privately optimal levelof pesticides.b. Show the amount of pesticides used if they are socially concerned.c. Why is a reduction back to XH = HT not socially desired?3.a)THXX SMC(PMC+MB)PMCMBHMB/MCPesticidesMBTSMC(PMC+MB)PMCMBHMB/MCPesticidesMBT11HTXX b)c) Not socially optimal.SMC(PMC+MB)PMCMBHMB/MCPesticidesMBT11HTXX *HX*TX4. Consider two college roommates Tom and Jerry. They both demand thegood called ‘clean bathroom’ (as opposed to ‘not-so-clean bathroom’). Thequantity in this case is expressed in terms of ‘cleanness units’ that are common toboth Tom and Jerry. Instead of money the prices/costs are expressed in terms ofhours spent cleaning the bathroom. The (inverse) demand functions are given by:PT=100 – 2QT; PJ=150 – 3QJ;and the marginal cost is given by MC=90=const.depict graphicallya. First suppose that Tom and Jerry have separate bathrooms, i.e. the ‘cleanbathroom’ should be considered private good. What is the efficient amount of‘cleanness’ and hours spent cleaning in this case? Show all your work.First we have to find the total demand in this economy. In case of privategoods, we perform horizontal summation of individual demand curves. Wefirst invert both of the individual demand curvesQT=50-1/2PT, 0<= PT<=100; QJ=50-1/3PJ; 0<= PJ<=150Then we sum the two demands (we sum quantities for each level of price) togetQ= 100 – 5/6 P, if 0<=P<=100 (=50-1/2P+50-1/3P) = 50 – 1/3 P, if 100<P<=150.Now, to find the equilibrium in this market, we need to invert it back (to beable to equate it with supply, which is expressed in dollar terms)P = 120 – 6/5 Q, if 50/3<=Q<=100 = 150 – 3 Q, if 0<=Q<=50/3It’s easy to check that supply crosses demand where demand is P = 120 – 6/5 Q.So Supply = 90 = 120 – 6/5 Q=demand produces the following quantityQpr*=25, Ppr *=$90.We know that in private good case, competitive markets produce efficientresult.b. Now assume that Tom and Jerry share the same bathroom, so that now ‘cleanbathroom’ is public good. What is the efficient amount of ‘cleanness’ andhours spent cleaning in this case? Show all your work.Again, we have to find the total demand (valuation may be a better wordhere) in this economy. In case of public goods, we perform vertical summationof individual demand curves. This amounts to summing the inverse demandsgiven in the setup of the problem.Moreover, since for both Tom and Jerry quantity demanded fluctuatesbetween 0 and 50, there will be no kinks in the total demand.P=250-5Q (=100-2Q+150-3Q)Now, to find the efficient level of public good, we just set our total valuationschedule given above equal to supply (=90)So 90 = 250 – 5 QBy solving the equation above we get quantity Qpb*=160/5=32, Ppb*=$90.This is not an equilibrium because market doesn’t even exit in this case.c. Based on your results in part (b), comment if free-rider problem is present inthis dorm-room?The efficient production is 32 units whereas markets will only produce 25units. The reason for underprovision of cleaning by marker system is freeriderproblem. In this case free-rider problem means that both Tom andJerry have strong incentives to shirk when it comes to cleaning. Each hopesthat the other one wouldn’t be able to take it any more and would clean thebathroom. The other roommate would just enjoy the benefits without doinganything – would be able to get a free-ride. This incentive leads tounderprovision of cleaning compared to the efficient level of cleaning.5. Two firms are ordered by the federal government to reduce their pollution levels. Firm A’s marginal costs associated with pollution reduction are MC=20+4Q. Firm B’s marginal costs associated with pollution reduction are MC=10+8Q. The marginal benefit of pollution reduction is MB=400-4Q.What is the socially optimal level of each firm’s pollution reduction?Set MC=MB