Question 4 An economy with three goods has total endowments -=1; a=1 9=1 The market demand functions (not excess demand) are: II (PI, P2, pa) = Pitpapa. T2(PI, P2,p3) = PITRTR. 2p1 x3(p1, pa, pa) = Pi f P2 + p3 4p2 Apa 1. Write down the excess dernand functions and simplify them. (PP.P) = =2(PI.P.P) = =(PI.P.P) = 2 For each good i = 1, 2,3, write down the configurations of prices for which s;(pi, pa, pa) 2 0 Each of these will be an inequality involving all three prices.] = (p1, pz, pa) 20 # =2(p1, pz, pa) 20 # 23(p1, pa, pa) 2 0Now recall the mapping from the price simplex to itself that we used in order to generate a fixed point which would correspond to the equilibrium. In part 3 below, you will map a particular price vector p into its value f(p). Please be careful with your arithmetic. 3 Let p = (7. 7, ). Answer parts A and B below for these prices. A. Find m(p) given by mi(p) = pi + minfei, max[0, s;(p)}}. mi(p) = my(p) = ms(P) = B. Find the vector /(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, find a price vector in the simplex that is an equilibrium [remember Walras' Law and what it implies for the solution