5. (30 points) "Logrolling" is a phenomenon in which elected representatives trade votes with one another. For instance, Representative A may be willing to vote for Representative B's prefered policy, even if A doesn't like it, provided that B will vote for Representative A's prefered policy, even if B doesn't like it. Suppose we have the follwing three projects up for vote: A naval ship, a hospital, and a park. There are three representatives who will individually vote on the projects. The net social benefits to the constituents of each representative are given in the table below. Note these benefits may be negative, meaning that the policy actually does harm to the constituents of the representative. Project John Dennis Susan Naval Ship -75 -40 Hospital -40 150 -25 Park -100 -80 360 a) What are the total benefits from each project? b) If a vote were held for each project, what would be the result for each project? Is this socially optimal? c) If these representatives were to logroll (trade votes) to get their prefered policy to pass, what would be the result? (Hint: one of these representatives will be disappointed.) d) Is the final result from c) an improvement over the outcome of b)? Is it optimal? e) As hinted, one of the representatives will be left out of the logrolling. In principal, is there anything else that representative can do to get his/her prefered policy passed? Now suppose the benefits looked like this: Project John Dennis Susan Naval Ship 200 -170 -90 Hospital 100 150 80 Park -250 -130 360 f) What are the total benefits from each project? g) If a vote were held for each project, what would be the result for each project? Is this socially optimal? h) If these reperesentatives were to logroll (trade votes) to get their prefered policy to pass, what would be the result? i) Is the final result from h) an improvement over the outcome of g)? j) What conclusions, if any, can we make about the practice of logrolling from these examples