Consider a two-good economy with one private and one public good. There are four consumers in this economy who contribute to public good provision. The price of the private good is $1 and the demand function of the public good for each consumer is as follows: p1 = 20 - 2G, p2 = 30-(5/10)G, p3 = 100-(G/2) and p4 = 60-G where G is the number of units of the public good and p^i is the price of each unit for consumer i in dollars. The cost of providing one extra unit of the public good is (alpha).

(a) With 170 < alpha < 210, what is the optimal level of provision of the public good? Show the optimal point on a graph.

(b) Is there a possibility that the public good is not supplied at all? Why?

(c) If the public good is not supplied at all, what is the size of the deadweight loss due to this market failure?

(d) If at least one person contributes, for what values of the public good will be supplied?