Fall 2022
\nProblem Set
\nPlease submit through canvas (if you face any technical issue, email your solution also to the graders)<\/p>\n
1. A small town is trying to decide whether to build a new water filtration system for its public water
\nsupply. There are two districts in the town and the willingness to pay for the system differs between the
\ntwo districts. The WTP curves are given by:
\nDistrict 1: WTP1 = 8 – .05Q
\nDistrict 2: WTP2 = 12 – .2Q
\nwhere Q is the percent of water filtered by the system, a public good.
\nA) Based on these WTP curves, determine the town\u2019s marginal social benefit (MSB) for this
\npublic good. Provide a graphical and algebraic answer. Remember, that WTP cannot go
\nbelow zero.
\nB) If the market supply for the system were MC = 6 + 0.15 Q, what is the allocatively
\nefficient level of the public good to provide? Provide a graphical and algebraic answer.
\nC) Using your graph from part B), explain why the individual districts will not provide the
\nallocatively efficient level of water filtration.
\n2. The supply curve and demand curve for bottled water given by:
\nSupply: Q = -100 + 400P
\nDemand: Q= 1150 \u2013 100P
\nA) Find the competitive equilibrium price and quantity, PC and QC say.
\nB) Suppose that this water was drawn from an underground acquifer by the water bottling company.
\nThe production of this bottled water imposed an external cost on other users of the water supply. For
\nexample, farmers that drew water from the same acquifer faced higher costs to pump water for
\nirrigation. Suppose that the marginal external cost (MC) imposed by the bottling company was
\nMC = .001Q. Derive the allocatively efficient level of bottled water when this cost externality is present.
\nC) Calculate the change in welfare that will occur if the town could move from the competitive
\noutput level to the allocatively efficient level. That is, you have to calculate the area of the triangle
\nshaded in orange in the doc-cam lecture notes V, pages 7\/8. Also show your answer in a clearly
\nlabeled graph.
\nD) Suppose now that the MC was constant for each unit of output, not increasing with Q, and
\ngiven by MC = .5. Recalculate your answers to parts B and C using this constant MC curve.
\nE) Explain how a Pigouvian tax on bottled water could be used to achieve the allocatively
\nefficient output level. Calculate the tax. (You have to wait until Tuesday\u2019s lecture on 9\/13 to be able to
\nsolve this last part).<\/p>\n","protected":false},"excerpt":{"rendered":"
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