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Pollutoville is a small town interested in improving its air quality. To do this, they are considering building a public park, whose size will be denoted by r. There are n + 1 consumers in town. One of them, whose name is Mr. Sukker, has preferences over the park and money spent on all other private goods represented by the utility function u;(r, y;) = 100vr + y; The other n people feel neutral towards the public good, and hence, their preferences are represented by uj (r, y,) = y; for each person j in that group. Suppose the individual income of each person in town is 10, 000. (a) The Town Hall has found a firm that could build the park, and the mayor is insisting that the firm should not charge any mark-up over marginal cost. It is known that the firm's technology transforms input into output at a one-to-one rate, i.e., its production function is x = y -y here denotes the money put into this productive process, and a the size of the park built. Graph the marginal cost curve as a function of the output r. As part of a market equilibrium, what would the unit price of park services be?(b) Complete the market equilibrium that you have begun to describe. That is, determine the size of the park built in equilibrium, and how much each person in town contributes towards it. Detail also the money that each consumer wants to spend on all other goods. To do this, draw the budget constraint for each consumer, finding the point at which they maximize their utility. (Recall that each person may contribute some amount towards the park, but is fully aware that she will be enjoying the total amount contributed by all - the public good feature.) (c) Evaluate the efficiency of this equilibrium, using the Samuelson condition. Is there anything peculiar about your finding? In particular, how would it be affected if some of the n neutral consumers started to display a little bit of interest in the public good, so that their utility function would be u;(x, y;) = ex + y; for a tiny e > 0