(30 points) Assume we have a small economy with two consumers, con sumer 1 and consumer 2. The functions, G = 32 (pl /5) + 4alog(101/') and G = 14a p2 (7a/2)log(1002) + 60 are demand functions for con sumer 1 and 2 respectively. a is a positive constant, G is the level of public good provision and p,- is the price that consumer i e {1, 2} is Willing to pay for each unit of public good. (a) If the marginal cost of the public good is $36, which level of public good is the optimal level? Show the optimal point and demand func tions on a graph. If at least one consumer participate is there any chance that the public good will not be provided at all? Is there any chance for free-riding? (15 pts) (b) If a new technology decreases the marginal cost of the public good to $18, how much the optimal level changes? Has any consumer an intensive to misreport her demand function? (8 pts) (c) Now assume although the new teclmology has decreased the marginal cost, an explosion in the pipeline has forced the ofcials to deliver the fuel by train. This adds $225 to the marginal cost of the public good. How much is the optimal level of G? (7 pts)