3. Suppose the state is trying to decide how many miles of a senic river it shou

Question

3. Suppose the state is trying to decide how many miles of a senic river it should preserve. There are 100 people in the community, each of whom has an identical demand function given by P = 10 Q, where Q is the number of miles preserved and P is the price in dollars each person is willing to pay for Q miles of preserved river. (a) If the cost of preserving Q miles is C(Q) = 500×Q dollars, how many miles would be preserved in a socially efficient allocation? (b) How large is the consumer surplus?

Explanation / Answer

The good in discussion is a public good so we must have a demand function in the form of marginal benefit curve. For 100 consumers, we have the MB curve as

MB = 1000 - 100Q

MC is 500

Find socially efficient quantity

MB = MC

1000 - 100Q = 500

Q* = 5

P* = 500

a) A total of 5 miles would be preserved in a socially efficient allocation

b) Consumer surplus is CS = 0.5*(Max price - eq price)*eq quantity = 0.5*(1000 - 500)*5 = $1250

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