2. Consider the following economy with two agents and two consumpti which is used to produce the other. Let Household h's consumption be denoted r, and , respectively, where h = 1, 2. Preferences: Household h has preferences given by: Un(r,, r,) = Inc, + 2lna, h=1,2. Endowments: Both households are endowed with 2 units of good one (ie. w;). There of good two. Technology: Let Yz denote the total amount of good two available to the econom using good one, by means of the following technology: Y2 = = [4 - (x] + 2:3)] where the term in brackets on the right-hand side of the equation ab of good one that is used as an input to production of good two rathe Consider the problem of a "social planner" who maximizes an equa of agents' utilities subject to the feasibility constraints. a. Write down the social welfare maximization problem that the pla b. Use this problem to derive necessary conditions for an allocat efficient in this economy