1. Consider a population of consumers. When a consumer is a member of a club providing a level G of club goods and having n members, they observe utility: U=M- % + log(G) %, where k is a positive constant and% is the charge for club membership. a) Derive the optimal membership for the club, if it maximizes the utility of each member b) Assuming that the club chooses G optimally given its membership, calculate the loss in membership of a club with suboptimal size