2. Shella, Dorian and Thom live in the same house, and are considering growing vegetables in their garden. If they spend an amount x in total for the seeds, dirt, etc..., the gross utility of Shella and Dorian is uS(x) = uD(x) = x 1 2 x 2 each whereas Thom gets a gross utility uT (x) = 2 x x. Let ti , i = S, D, T be the contribution of each member respectively. For this exercise, round o your nal results at two decimal places. (a) Find the Pareto ecient amount of money to spend in the garden. Call it x . (b) Individually, how much does each want to be spent on the garden if the cost is split evenly? Call the amounts xT , xD and xS. (c) Does Thom prefer x or xS to be spent under the even split rule? If a vote between the three is cast about spending x or xS, which amount will be chosen? (d) Thom has heard about Lindhal, who proposed personalized contributions. Let T , S and D be the individual share of the expense each has to pay. Those shares are determined by equating the marginal utility (with respect to x) of each with their respective share. Under this rule, nd the individual shares and the spending amount x L (don't forget shares add up to 1). Compare your answer with x . (e) In practice, the rule proposed by Lindhal requires each agent to report their preferences (i.e. their utility function), so that the contributions can be computed for each agen