_ _ Consider an economy with 246 identical consumers. Each individual i of this economy is a member of only one club and the clubs are identical. Let us assume n is the number of members in one club and the cost of the club is shared equally between the members. If U i = n 1 forn8: (a) Draw the utility function of the consumers in a graph. (b) If each individual is maximizing her utility, What is the optimal size of the club? (c) What is the minimum number of clubs needed to allocate the whole population optimally? With an optimal allocation what is the specic size of each club? (d) What is the minimum number for N which guarantees the optimal allocation beyond that number? (5 pts) (e) Now assume the utility function of consumers has changed as follows: U\" = n 1 for n S 8.5, U1 = 24.5 2n for n 2 8.5. What is the optimal club size? What is the maximum utility for each member? (5 NS)