Consider the following: Suppose that two neighbours with identical preferences derive utility from the number of water fountains in their shared community lot, y, and on the number of figs that they eat from their own fig trees, x. The specific form of the utility function is given by:

(,) =n+ 2n

The price of one water fountain is $3 and the price of a fig tree is $1. Each neighbour has a budget of $10.

a)If each neighbour lived in a community that did not have a shared community lot (i.e. had to individually purchase and own both water fountains and fig trees), what portion of their income would they spend on flower and vegetable gardens, respectively? Allow for mixed numbers (fractions) of each good.

b)What utility would they each receive from the allocation in a) above?

c)Now, assume the neighbours do, in fact, live in the shared community such that both share and enjoy the number of water fountains that are available. If neighbour #1 assumes that neighbour #2 will not pay for any water fountains, what will be each neighbour's utility if neighbour #1 buys the least whole number of water fountain(s) such that he derives utility from the water fountain(s)?

d)Assume that each neighbour buys 3 water fountains and uses the remaining amount on fig trees. What utility will each neighbour receive, and is this a Pareto superior solution than your answer in c)? Explain why or why not.