2. Suppose the state is trying to decide how many miles of a very scenic river i

Question

2. Suppose the state is trying to decide how many miles of a very scenic river it should preserve There are 100 people in the community, each of whom has an identical inverse demand function given by p = 10-g, where q is the number of miles preserved and p is the per mile price he or she is willing to pay for q miles of preserved river. (a) If the marginal cost of preservation $500 per miles, how many miles would be preserved in an efficient allocation? (b) How arge are the net benefits? 1210/17 Econ 434 112% 4265

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) here meet benefits are equal to consumer surplus CS = 0.5*(Max price - eq price)*eq quantity = 0.5*(1000 - 500)*5 = $1250

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