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' . mesa, ,"iyi' donuts do; person B) gods (good 1 and good 2). Initial endowments are W} = 6, w} = 3, w; = 6, and WE, = 3. . \"Individual income (equal to the total value of each person's endowment) is mA and mg. 2 1 1 2 Individual utility functions are uA(x}1, xi) = (xj)(x) and ug (36%, 96%) == (x)3(x). a. Find the expressions for the individual demand functions xj (131, p2, mA), , xi (P1: P2: ma), xii; (P1: P2; 1713), 311d x (P1: 392, m3)- (4P1) 'b, Set :22 == 1 and replace mA and ms witiI the values of the initial endowments to derive the expressions for the individual demand functions xi (pl, 1), xi (pl, 1), x(p1, 1), and xpl, 1). Make sure to plug in W} = 6, w} = 3, w; = 6, and w}, = 3! ' (4pt) c. Using the above functions and the initial endowments, derive the market-clearing conditions in the markets for goods 1 and 2. Again, make sure to plug in W} = 6, w} = 3, w; = 6, and w; = 3. (Zpt) d. Use the market-clearing condition in either one of the two markets to calculate the competitive equilibrium price pi. (1101') e. Using the value of pi, derived above, and setting p2 = 1, calculate the consumPtion quantities x3, xi, xii}, and x in equilibrium. (4 pt) f. Find a Pareto efcient allocation in this economy. State the quantities of goods 1 and 2 consumed by each individual under this allocation. _ (1 pt)