1EEP101/Econ125 Spring `02Professor David ZilbermanGSIs: Alix, McKim, SchoengoldSUGGESTED SOLUTIONS FOR MIDTERM EXAM1. Suppose that farmers in Brazil grow coffee beans with MPC = 10 + 3/2Q. The coffee beans arebought by a middleman, who sells them to consumers with MB = 40 - Q. Modern production ofcoffee involves an environmental externality (soil erosion, loss of biodiversity, and chemical run-off).This externality has a cost of MEC = ½ Q.** Note – this question only requires that you calculate the answers numerically. It may help to drawa graph, but this is not required. Please show all work.(a) (8 points) Under the middleman, what is the output level (QMM), the price paid to producers(PPMM), and the price paid by consumers (PCMM)?The middleman will set marginal outlay (MO) equal to marginal revenue (MR) to determine the profitmaximizing quantity. Total outlay is the total quantity paid by the middleman (P*Q), while marginaloutlay is the additional amount the middleman has to pay if he buys one more unit. This is greater thansimply the MPC(Q), because the middleman will have to pay a higher price on EVERY unit that he buys,not just the last one.QQTOMOQQQMPCQTO310/)(2310)(*2+=∂∂=+==Marginal revenue is the additional amount that the middleman will make by selling one more unit, giventhat selling a larger quantity will reduce the price in the market.QQTRMRQQQMBQTR240/)(40)(*2−=∂∂=−==Setting MR = MO yields the following:6305240310=⇒=−=+MMMMMMMMQQQQThe middleman will pay the producers the MPC(QMM) = (10 + 3/2*6) = 19. So, PPMM = 19. Themiddleman will charge the consumers the MB(QMM) = 40 – 6 = 34. So, PCMM = 34. This yields thehighest profit to the middleman.(b) (8 points) Now the government of Brazil decides to intervene and establishes regulation thatleads to the competitive outcome. What is the price (PC) and quantity (QC)? What is the amount ofconsumer surplus (CSC), producer surplus (PSC), and the total environmental cost (TECC)?If regulation leads to the competitive outcome, then the price and quantity will be given by theintersection of MPC and MB. Solving this gives:281240122530231040=−==⇒=+=−CCcCCPQQQQConsumer surplus is the area under the MB curve and above the price. Using the formula for the area of atriangle (you could also use integration), CSC = ½ * 12 * 12 = 72. Producer surplus is the area below theprice and above the MC curve, so PSC = ½ * 18 * 12 = 108. Total externality cost is the area below theMEC curve, so TECC = ½ * 12 * 6 = 36. In summary:QC = 122PC = 28CSC = 72PSC = 108TECC = 36(c) (8 points) Lastly, assume that concerned citizens convince the government to pass regulation tolimit pollution and land degradation. What is the socially optimal level of price (P*) and quantity (Q*)?Suppose that the government uses a tax on producers to achieve the socially optimal outcome. What isthe optimal per-unit tax (t*)? What is social welfare (SW*) at this output level?At the social optimal level, the externality will get taken into account. We calculate the marginal socialcost (MSC) = MPC + MEC = 10 + 3/2Q + 1/2Q = 10 + 2Q. Setting MB = MSC gives the following:30*,10**330*210*40==⇒=+=−PQQQQTo calculate the optimal tax (t*), we need to set MPC(Q*) + t* = MSC(Q*). Subbing in Q* = 10 givesthe following:5*30*25*210*)10(2310=⇒=++=++ttQtTo calculate social welfare (SW*), we want to find the area between the MB curve and the MSC curve(up until Q*=10). This can be solved using the area of a triangle (or integration) - SW* = ½ * 10 * 30 =150. The other method would be to calculate CS*, PS*, GR*, and TEC*. If you do this, you’ll find thefollowing:CS* = ½ * 10 * 10 = 50PS* = ½ * 15 * 10 = 75GR* = 5 * 10 = 50TEC* = ½ * 5 * 10 = 25SW* = CS* + PS* + GR* - TEC* = 50 + 75 + 50 – 25 = 150(d) (6 points) Coffee can also be grown using a more traditional method – shade-grown coffee. Thisoption eliminates many of the environmental problems of modern production techniques. Listand briefly explain (this is not an essay, just list and briefly explain!) 3 policy options that thegovernment could use if it wants to encourage farmers to grow shade-grown coffee.There are lots of possible answers to this question, and anything that made sense was accepted. Here is alist of some of the possible answers (by no means is this list complete!) - One possibility is for the government to impose a tax on environmental damage. If the tax is largeenough, the cost difference could convince some farmers to switch to shade-grown coffee. - The government could also tax the fertilizer that is a necessary input into conventionally grown coffee. - The government could also subsidize the costs associated with switching from conventional to shade-grown coffee for farmers. - Another possibility is to educate farmers or consumers about the environmental destruction associatedwith conventionally grown coffee (awareness). This could create a market for shade-grown coffee wherethe farmers can sell their product for a higher price than conventionally grown coffee. This can be seen inthe market for Fair Trade certified coffee.32. Suppose that there are two electrical plants in our town. The total net benefits (benefitsminus private costs) that the firms derive from releasing emissions are as follows:2222211150B30Bxxxx−=−=The marginal externality cost of the emissions on health and well-being is defined by thefollowing expression:MEC = X, where X=x1+x2After spending three hours on the computer, you have made the following graph of therelevant information (the labeled points are to assist you later in the problem to identifyrelevant areas):10 20 30 40 501020304050BADCE G HILJ KMN O P QR S T UFirm 2'sdemandfor pollutionFirm 1'sdemand forpollutionFVUnits of Emissions(X)$MarginalexternalcostZa) (12 points) Mathematically derive the aggregate demand curve of the two firms foremissions. Please show your work- very few points (if any) will be given if you write theright answer without showing your work! (continue your answer on the next page)First, we find the two marginal benefit curves:mb1= 30 - 2x1; mb2= 50 - 2x2In order to add the two demand curves horizontally, we need to first take their inverses (solveeach the two equations for x1 and x2):x1= - .5mb1 + 15; x2 = -.5mb2 + 25We add the two equations to get aggregate amount of pollution demanded (X = x1 + x2):X = 40 - MB (where MB = mb1 + mb2)4Rearranging, and using the graph to determine