Assume that a small town uses a referendum to overcome the free-ridership proble

Question

Assume that a small town uses a referendum to overcome the free-ridership problem and determine how its residents might value a new water filtration system for its public water supply. The voting results are aggregated by the town's two districts, yielding the following dend estimates: District 1: Q 160-20P District 2: Q60-5P2 where Q is the expected percent of copper to be filtered by the system and P is the price in millions of dollars. a) Based on these estimates, determine the town's market demand for this public good, the new filtration system. Provide a graphical and algebraic answer b) If the market supply for the system were P60.15 Q, what would bet the equilibrium price and quantity for the town? Provide a graphical and algebraic answer. c) Calculate total welfare from the provision of the public good.

Explanation / Answer

Yes, you guessed it right. You have to first get the inverse demand functions expressed in terms of price and then add these two demand functions to get the market demand function. We need to get the inverse demand functions as it is a case of public good in which the demanding residents are expressing their willingness to pay for the same goods. Now, for district 1:

Q = 160 -20P1

or, 20P1 = 160 – Q

or, P1 = 8 – 0.05Q

For District 2:

Q = 60 -5P2

or, 5P2 = 60 – Q

or, P2 = 12 – 0.2Q

(a) Let us add these two demand functions to get the following market demand function:

P1 + P2 = 8 – 0.05Q + 12 – 0.2Q

or, P = 20 – 0.25Q

a) Now, let us equate the market demand and market supply to get equilibrium price and quantity. Market supply is given by P = 6 + 0.15Q

Therefore, at equilibrium:

20 – 0.25Q = 6 + 0.15Q

or, 0.4 Q =14

or, Q = 14/0.4 = 35

Now, let us put the value of Q in the market demand function to get the equilibrium price:

P = 20 – 0.25Q = 20 – 0.25 × 35 = 20 – 8.75 = $11.25 million

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