(20 pts) Consider a local Badminton club which is under construction. The owner has the possibility to buy the nearby lands and construct more Badminton courts. The good that the club wants to provide is the Bad- minton court so if the club provision level is G, then G is the number of courts. The cost of the club is shared equally between the members and they pay their share as a membership fee. The utility of each member 3' is: U; = n3/16 + Kr/Z + (3G4) (G/(3k + f)), where G is the club good provision, Y, is the individual's income, as is the club size and k and f are positive constants related to the possibility of buying the nearby lands. (a) If the owner's objective is to maximize the utility of each member, what is the optimal level of membership, n, for the club? What is the optimal value for the courts, (G), to be built by the owner? (5 W) (b) If the objective of the club owner is to maximize the total utility produced by the club, then what is the optimal level of 'n. and G if 711/3 = 0:. (5 pts) (0) Now assume that the club owner cannot buy the nearby lands and he can only provide a given number of courts. Calculate the utility loss for each member due to this limitation. (5 pts) ((1) Now assume another identical Badminton club is under construction in the area. Both clubs have the possibility of buying the nearby lands and both will be ready to open at the same time. What is the total number of members of these two clubs if they maximize the individual utility of their members? Compare the amount of optimal G and as between the two clubs if the k and f for the second club are less than the k and f for the rst club. (5 pts)