Suppose that two neighbors with identical preferences derive utility from the number of flower gardens in their shared community lot, x, and on the number of tomatoes that they eat from their own vegetable gardens, y. The specific form of the utility function is given by:

U_i(x,y_i) = 1/4 lnx + 3/4 lny

The price of one flower garden is $1 and the price of a vegetable garden is $2. Each neighbor has a budget of $12.

a) If each neighbor lived in a community that did not have a shared community lot (i.e had to individually purchase and own both flower and vegetable gardens), what portion of their income would they spend on flower and vegetable gardens, respectively?

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

c) What is the marginal rate of substitution (MRS) for this utility function?

Part 2

d) Now, assume the neighbors do, in fact, live in the shared community such that both share and enjoy the number of flower gardens that are available. If neighbor #1 assumes that neighbor #2 will not pay for any flower garden, what will be each neighbor's utility if neighbor #1 buys the least whole number of flower garden(s) such that he derives utility from the flower garden(s)?

e) Explain why the allocations in d) are inefficient.

f) Calculate the efficient level of flower garden purchases and that of vegetable gardens.

g) Assume that neighbor's split (e.i 50/50) the cost of efficient number of flower gardens obtained in f) and use the remaining funds to purchase vegetable gardens. What utility will each neighbor receive, and is this a Pareto superior solution that your answer in b)? Explain