Suppose that a town is considering investing money into making a public show in a park that can be enjoyed by families during a weekend. This show requires an investment of $950. Assume that there are 150 families, each of which is willing to pay up to $6 for the show. Furthermore, there are 50 families each of which is willing to pay $5. If the money is invested, there is a large capacity so that the enjoyment of the show is unchanged regardless of how many actually attend.

(i)  Should the money be invested according to the utilitarian criterion? Assume now that the city is considering installing gates to charge tickets at a price of P per person for access to the park in order to repay the investment.

(ii)  Can the city finance the investment by charging appropriate entrance fees?

(iii)  What are all the prices P that are sufficient to repay the investment? Which one maximizes revenue?

(iv)  Which if any of the prices you found in (iii) lead to the (utilitarian) efficient outcome?

Assume now that there are 10,000 additional families who are only willing to pay $1 for the show.

(v)  How does this change your answers to parts (i), (ii), (iii), and (iv)?