l. Homework 5 Consider an exchange economy with 2 individuals (person A and person B) and 2 goods (good 1 and good 2). Initial endowments are wi = 5, wi = 2, WE{ = 1, and wi = 10. Individual income (equal to the total value of each person's endowment) is mi and 1113. 1 2 2 1 Individual utility mctions are uA (xi, xi) = (xi)(xi) and uB (xi, xi) = (x)(xi). a. Find the expressions for the individual demand functions xi (p1, p2, mi), xii (P1: P2; 771A): x; (P1: P2: 1113), and 35134191: 392- mB)- (41\") b. Set p2 = 1 and replace m A and m B with the values of the initial endowments to derive the expressions for the individual demand functions xi (pl, 1), xi (pl, 1), x; (pl, 1), and xi(p1,1). Make sure to plug in wi = 5, wi = 2, \"7% = 1, and wi, = 10: (4 pt) 0. 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 wi = 5, wi = 2, w; = 1, and wi = 10! (Zpt) d. Use the market-clearing condition in either one of the two markets to calculate the competitive equilibrium price pf. (1 pt) e. Using the value of pi, derived above, and setting p2 = 1, calculate the consumption quantities xi, xi, xi, and xi 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)