Look at the attached question.

Consider a town with N residents. The town has been selected to receive either a new swimming pool (S) or a new bridge (B) and must decide which it wants. Therefore, there are two possible allocations: S or B. Each individual i has private information about his or her value for a pool or a bridge. Specically, given individual i's type 0,, his value for the pool is u,(S, 6,) = 6,- + 5 and his value for the bridge is u,(B, 19,-) : 26,-. The type 6,- is drawn from the set 8 = {1, 2, ..., 9} with equal probability of each number, and types are drawn independently across residents. An individual observes his own type but not the types of other residents. (a) For which possible types does the individual strictly prefer the pool over the bridge? How about the bridge over the pool? Ex ante (i.e. before the type is drawn), is an individual more likely to strictly prefer the bridge, more likely to strictly prefer the pool, or equally likely to strictly prefer each option? (b) What is an efcient allocation rule? Recall that an allocation rule maps each possible vector of types to an allocation (in this case, B or S). Your answer will depend on the utility functions given above. (c ) Using the VCG mechanism described 1n lecture, describe the transfer payments of each resident for a town of N 3 and the following reported type vectors. (i) (61, 62, (93): (1, 7, 8), (11) (031,032,083): (1, 3, 4), (111) (91,02,63) (5, 6, 9)