Suppose four families share a common stretch of beach and they are considering a program of improvements, including a stairway and a play structure for children. The value of spending y in total for the improvements is 5y - 1y for families 1 and 2, 7y - y for family 3, and 4y y for family 4. Assume quasilinear utility (linear in family i's money spending x; and nonlinear in the value of the project y) and hence no wealth effects. (a) What is the efficient level of expenditure y on beach improvements? (b) Suppose that the families plan on sharing the costs equally, and that, to implement the improvements, each of the families has to agree, otherwise no improvements will be made. i. Show that the improvements will not be implemented. ii. What is the highest possible improvement that the families can implement this way? iii. Demonstrate that the resulting expenditure is inefficiently low by finding an alternative level of expenditure and pattern of cost sharing that the families unanimously prefer.