1. (General Bilateral Exchange) Consider a bilateral exchange economy in which there are two individuals, labeled by i E {1, 2}. There are two goods in the economy, each of them perfectly divisible. The quantity of the rst good is denoted by q and the quantity of the second good by m. The individuals are initially endowed with bundles (1.13m?) 6 R1 and (g3, mg) 6 n1, reSpec- tively. The preferences of individual 1' are given by an ordinal utility function [Ii-(q, m). (a) Draw the initial aggregate endowment in (q,m)-Space. Also draw the endowment of individual 1 in the same space. (b) Consider the rectangle whose c0rners are (0,0) and (q'f + gam'f + mg), reSpectively, and let the point ([1,0] denote the origin for individual 1, and (q'f + gang? + mg) the origin for individual 2. Thus if individual 1 receives the aggregate endowment for each good, individual 2 receives a zero quantity of each good. Illustrate how the aggregate endowment can be split between the two individuals in this space, i.e. illustrate feasibility of an allocation. (c) Shade the areas in (q,m) space that are individually rational for both traders. Indicate the set of all feasible and individually rati0nal allocatiOns. (d) Find the set of all Pareto Optimal allocations in (ql,Q2)-space that are also individu- ally rational. (HINT: maximize individual 1's utility subject to the requirement that individual 2"s utility is no lower than 11.2). What equation characterizes Pareto Optimal allocations