mid_key

# mid_key - EEP101/Econ125 Spring `02 Professor David...

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1 EEP101/Econ125 Spring `02 Professor David Zilberman GSIs: Alix, McKim, Schoengold SUGGESTED SOLUTIONS FOR MIDTERM EXAM 1. Suppose that farmers in Brazil grow coffee beans with MPC = 10 + 3/2Q. The coffee beans are bought by a middleman, who sells them to consumers with MB = 40 - Q. Modern production of coffee 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 draw a graph, but this is not required. Please show all work. (a) (8 points) Under the middleman, what is the output level (Q MM ), the price paid to producers (P PMM ), and the price paid by consumers (P CMM )? The middleman will set marginal outlay (MO) equal to marginal revenue (MR) to determine the profit maximizing quantity. Total outlay is the total quantity paid by the middleman (P*Q), while marginal outlay is the additional amount the middleman has to pay if he buys one more unit. This is greater than simply the MPC(Q), because the middleman will have to pay a higher price on EVERY unit that he buys, not just the last one. Q Q TO MO Q Q Q MPC Q TO 3 10 / ) ( 2 3 10 ) ( * 2 + = = + = = Marginal revenue is the additional amount that the middleman will make by selling one more unit, given that selling a larger quantity will reduce the price in the market. Q Q TR MR Q Q Q MB Q TR 2 40 / ) ( 40 ) ( * 2 - = = - = = Setting MR = MO yields the following: 6 30 5 2 40 3 10 = = - = + MM MM MM MM Q Q Q Q The middleman will pay the producers the MPC(Q MM ) = (10 + 3/2*6) = 19. So, P PMM = 19. The middleman will charge the consumers the MB(Q MM ) = 40 – 6 = 34. So, P CMM = 34. This yields the highest profit to the middleman. (b) (8 points) Now the government of Brazil decides to intervene and establishes regulation that leads to the competitive outcome. What is the price (P C ) and quantity (Q C )? What is the amount of consumer surplus (CS C ), producer surplus (PS C ), and the total environmental cost (TEC C )? If regulation leads to the competitive outcome, then the price and quantity will be given by the intersection of MPC and MB. Solving this gives: 28 12 40 12 2 5 30 2 3 10 40 = - = = = + = - C C c C C P Q Q Q Q Consumer surplus is the area under the MB curve and above the price. Using the formula for the area of a triangle (you could also use integration), CS C = ½ * 12 * 12 = 72. Producer surplus is the area below the price and above the MC curve, so PS C = ½ * 18 * 12 = 108. Total externality cost is the area below the MEC curve, so TEC C = ½ * 12 * 6 = 36. In summary: Q C = 12

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2 P C = 28 CS C = 72 PS C = 108 TEC C = 36 (c) (8 points) Lastly, assume that concerned citizens convince the government to pass regulation to limit 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.
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mid_key - EEP101/Econ125 Spring `02 Professor David...

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