The mayor of Keukenhof would like to build a new public park, if he can raise taxes enough to cover the cost, which is 950 euros. There are four families in the town. The families' benefits from a public park are as follows: v = 100, V = 200, V3 = 300, and 14 = 400. The mayor wants to use a version of the demand-revealing tax mechanism, as described in Section 18.6 above. (a) Indicate whether or not it is efficient to build the park. (b) If each family reports its true benefit vi, how much will the demand-revealing tax T; paid by family i be? (c) Suppose family 4 misreports its benefit as 500, while the other families report their true benefits. Does the park get built? If so, how much does family 4 have to pay? Is family 4's net benefit different from its net benefit in part (b)? (d) Suppose family 4 misreports its benefit as 300, while the other families report their true benefits. Does the park get built? If so, how much does family 4 have to pay? Is family 4's net benefit different from its net benefit in part (b)? (e) The final touch to the mayor's proposed mechanism is that, in addition to the demand-revealing taxes as calculated in part (b), each family will be charged a fixed lump-sum fee K. Find a K so that, with the demand-revealing taxes and the K fees, the town's park budget is exactly balanced.