題組內容

六、Consider a population of consumers. When a consumer is a member of a club providing a level of club good G and having n members, they obtain utility \( U = M - \frac{G}{n} + \ln G - \frac{n}{k} \), where k is a positive constant and \( \frac{G}{n} \) is the charge for club membership.

1. Derive the optimal membership for the club if it maximizes the utility of each member. (5 分)