Consider the following: Suppose that two neighbours with identical nonhomothetic 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: Ui(x,yi)=x+lny

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

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 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? Interpret the meaning of the MRS. Is MRS diminishing?

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

e)Show that the allocations described in d) are inefficient.

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

g)Assume that the neighbour's split (i.e. 50/50) the cost of efficient number of flower gardens obtained in f) and use the remaining funds to purchase vegetable gardens. Can the neighbours derive any utility from vegetable gardens given nonhomothetic preferences? What utility will each neighbour receive, and is this a Pareto superior solution than your answer in b)? Explain why or why not.