Question 4 An economy with three goods has total endowments e1 = 1; e2 =1; e3 = 1 The market demand functions (not excess demand) are: X1(P1, P2, p3) _ Pit P2 + P3. X2(P1, P2, p3) = Pit P2 + P3 . 23(P1, P2, p3) = Pi + 2 + p3 2p1 4p2 4p3 1. Write down the excess demand functions and simplify them. Z1 (P1, P2, P3) = Z2 (P1, P2, P3) = 23 (P1, P2, P3) = 2 For each good i = 1, 2,3, write down the configurations of prices for which zi (P1, P2, P3) 2 0 Each of these will be an inequality involving all three prices.] 21 (P1, P2, p3) 20 Z2 (P1, P2, p3) 2 0 23 (P1, P2, P3) 2 0Now recall the mapping from the price simplex to itself that we used in order to generate a xed point which would correspond to the equilibrium. In part 3 below, you will map a particular price vector p into its value p). Please be careful with your arithmetic. 3 Let p = (7i, 7i, %). Answer parts A and B below for these prices. A. Find m(p) given by mdp) = pi + min{eg, max{0,z.(p)}}. W5101') E 53.. 3.5, | | B. Find the vector f(p) in the simplex which p maps into, by normalising the price-vector m(p) that you just found. 4. Remember that a price-vector is an equilibrium if each excess demand is zero. Using your answers to part 2, nd a price vector in the simplex that is an equilibrium [remember Walras' Law and what it implies for the solution]