Consider a situation of two farmers who grow different kinds of plants. Depending on the climate, there are two states, $ and 52. Farmer 1 grows a plant that harvests much in state si but does not so in state s2. In contrast, Farmer 2's harvest will be better in state s2 but not in state s. To be precise, denote by (e,e) the income Farmer i can obtain from their harvest and suppose that (el,el) = (3,1) (e. e) = (1,3) Let 3 1 0 1 3 X 45 be farmers' (common) utility function from the consumption plan (x,x) of farmer i for each state. In particular, the utility function is characterized with indifference curves convex toward the origin. Indifference curves. x the direction of increase utility (a) Compute the utility levels for the farmers without any trade between them. (b) Now suppose that there is a financial market that issues two kinds of fi- nancial securities. Security 1 pays one unit of good in state s and pays nothing in state s2. Security 2, in contrast, pays one unit of good in state $2 and pays nothing in state $. The prices of the two securities are set to be 1. The farmers can buy and sell the securities to manage the risks of their consumption plans. Let a be farmer i's holding of security t (note that a may be negative). Then the flow budget constraints for farmer i is given by Initial period: a + a = 0 State s: x= + a State S: x2= 2 + a Draw the budget line on (x,x)-space. (c) Derive the optimal consumption plan in the case with financial markets. (d) Compute the utility level in the case of financial markets.