Consider an economy with population N. There is a club which is providing a level of provision G. When the cost of the club is shared equally and paid by members as a membership fee, the obtain utility is: U i = (1/2)log(G2 ) (n 2/2d) + M (G/n), where M is the individual income and d > 0 is a positive constant.

(a) If the utility of each member is maximized, what is the optimal level of membership, n, for the club? (5 pts)

(b) Now assume that the club chooses G optimally while its size is given, calculate the loss due to membership of a club with non-optimal size.(5 pts)

(c) What club size maximizes total utility produced by the club? If log(n) = while > 3/2 then contrast your result to the answer for part a. What happens to each member utility? (5 pts)

(d) Find the optimal club membership n which maximizes each member's utility when there are 2 identical clubs? What if there are 3 clubs? What you can say about increasing the number of clubs? (