Consider a population of consumers. When a consumer is a member of a club providing a level of provision G and having n members, they obtain utility
Where k is a positive constant and G n is the charge for club membership.
a. Derive the optimal membership for the club if it maximizes the utility of each member.
b. Assuming the club chooses G optimally given its member ship; calculate the loss due to membership of a club with suboptimal size.
c. Assume that the total population is of size m, with k
d. What club size maximizes total utility produced by the club? Contrast to the answer for part a.