3. Using the solution to part 2, construct the contract curve for an economy with 2 units of good 1 and 3 units of good 2. (5 分)

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 - G/n + ln G - n/k, where k is a positive constant and 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)

2. Assuming the club chooses G optimally given its membership, calculate the loss due to membership of a club with suboptimal size. (5 分)

3. What club size maximizes total utility produced by the club? Contrast to the answer for part 1. (5 分)

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