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A small town is trying to decide whether to build a new water filtration system for its public watersupply

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A small town is trying to decide whether to build a new water filtration system for its public watersupply.  There are two districts in the town and the willingness to pay for the system differs between thetwo 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 thispublic good.  Provide a graphical and algebraic answer.  Remember, that WTP cannot gobelow zero. 

  B) If the market supply for the system were MC = 6 + 0.15 Q, what is the allocativelyefficient 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 theallocatively 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

(Notice these are direct, not inverse, supply and demand curves).  The competitive equilibrium price andquantity are:  PC = $2.50 and  QC=900 

 A) Suppose that this water was drawn from an underground acquifer by the water bottlingcompany.  The production of this bottled water imposed an external cost on other users of the watersupply.  For example, farmers that drew water from the same acquifer faced higher costs to pump waterfor irrigation.  Suppose that the marginal external cost (MEC) imposed by the bottling company was  MEC = .001Q.  Derive the allocatively efficient level of bottled water when this cost externality ispresent.

B)  Calculate the change in welfare that will occur if the town could move from the competitiveoutput level to the allocatively efficient level.   Show your answer in a clearly labeled graph.

C)  Suppose that the MEC was constant for each unit of output, not increasing with Q, and givenby MEC = .5.  Recalculate your answers to part A and B using this constant MEC curve.   

 D)  Explain how a Pigouvian tax on bottled water could be used to achieve the allocativelyefficient output level.

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