Posted: September 23rd, 2022

A small town is trying to decide whether to build

Fall 2022
Problem Set
Please submit through canvas (if you face any technical issue, email your solution also to the graders)

1. A small town is trying to decide whether to build a new water filtration system for its public water
supply. There are two districts in the town and the willingness to pay for the system differs between the
two districts. The WTP curves are given by:
District 1: WTP1 = 8 – .05Q
District 2: WTP2 = 12 – .2Q
where Q is the percent of water filtered by the system, a public good.
A) Based on these WTP curves, determine the town’s marginal social benefit (MSB) for this
public good. Provide a graphical and algebraic answer. Remember, that WTP cannot go
below zero.
B) If the market supply for the system were MC = 6 + 0.15 Q, what is the allocatively
efficient level of the public good to provide? Provide a graphical and algebraic answer.
C) Using your graph from part B), explain why the individual districts will not provide the
allocatively efficient level of water filtration.
2. The supply curve and demand curve for bottled water given by:
Supply: Q = -100 + 400P
Demand: Q= 1150 – 100P
A) Find the competitive equilibrium price and quantity, PC and QC say.
B) Suppose that this water was drawn from an underground acquifer by the water bottling company.
The production of this bottled water imposed an external cost on other users of the water supply. For
example, farmers that drew water from the same acquifer faced higher costs to pump water for
irrigation. Suppose that the marginal external cost (MC) imposed by the bottling company was
MC = .001Q. Derive the allocatively efficient level of bottled water when this cost externality is present.
C) Calculate the change in welfare that will occur if the town could move from the competitive
output level to the allocatively efficient level. That is, you have to calculate the area of the triangle
shaded in orange in the doc-cam lecture notes V, pages 7/8. Also show your answer in a clearly
labeled graph.
D) Suppose now that the MC was constant for each unit of output, not increasing with Q, and
given by MC = .5. Recalculate your answers to parts B and C using this constant MC curve.
E) Explain how a Pigouvian tax on bottled water could be used to achieve the allocatively
efficient output level. Calculate the tax. (You have to wait until Tuesday’s lecture on 9/13 to be able to
solve this last part).

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