4. Consider an economy with two altruistic agents 1, 2 and two goods r, y. Normalize the total supply of each good to 1 and assume that each agent derives material utility u;(I;, y;) from consumption. Their total satisfaction depends on the material welfare of both agents so that U.(X1, 12, U1, 92) = vi(1 (21, y1), u2(x2, 92)). Assume that U, is strictly increasing in both components for i c {1, 2}. (a) Define Pareto-efficiency with respect to total satisfaction and show that all Pareto-efficient allocations are Pareto efficient for non-altruistic economies as well (i.e. the standard ones where each agent cares about her own welfare only). (b) Suppose the agents have an initial endowment and that they can buy and sell the two goods in a competitive market. Note that they cannot affect the other agent's consumption choices. De- fine the competitive equilibrium with respect to total satisfaction preferences. Are the two welfare theorems valid for this altruistic economy