Question

Question v) to question viii)

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An economy has three agents, A. B and C, and three goods 1, 2 and 3. The endowments of the three consumers are as follows e (3,0,0); e (i) Write down the total endowment vector of the economy. (0,5,0); (1,1,1) Given a price vector p (p,P2 Pa), the demand functions of the three agents for cach of the three goods are as follows (I am giving these to you rather than ask you to solve the optimisation problems): Pi P) 1: P2 f(p)2 p) P2 2: Pt Ps Pi +P2 -1 PS P3 (P) = P2 (ii) Find the aggregate demand functions for the three goods in this economy, and simplify them (p) 2(p) ra(p) (iii) Write down the aggregate excess demand functions for the three goods 1(p) zg(p) za(p) Now 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. Below, you will map a particular price vector p into its value (p). Please be careful with your arithmetic. Answer the question below for these prices. Let p (iv) Find the excess demand for each good at this price vector: 1(P) 22(P) zs(p) (v) Find the vecetor m(p), where mip) is given by m, (p) pminfe,, max(0, ,(p)}). m(p) m2(p)= m3(P) f(P) which the price p ( maps into, by normalising the price-vector m(p) (vi) Find the yector that you just found. (vii) Recall the excess demand functions that you found in part (i). For each ggood i the configurations of prices for which (p) 1,2,3, write down 0 [Each of these will involve all three prices (Pi P Ps) #1(p) = 0 22lp) 0 s(p)= 0 (viii) Using your answers to part (vii) above, find a price vector in the simplex that is an equilibrium [Hint: you can't solve for the three equilibrium prices from the three excess demand equations Walras Lawl Total endowment vector ot D Do vectox the economy endowment vectors of all three addition of Comsumers- (3,0,0) +(05,0) + (1,L1) (4,6,1) + e e= eA Aagreaate demand functions fox the three goods economy in this A X,CP) +2 P2 + P. XCP) t2 X2 CP)= P,+2 PtP P2 Pa +2 11 TA A + CP2 + P2 P3 + - P3 P3 2CPtPe)-Ps Pa geads Agpregate excess demand functions fox the thxee e. X,CP) ZiCP) 2 P2tPa P,+2P tP3 3 4 22CP)-e2 P,+2P2+P3-6 P2 4 11 - P2 Z3CP) X3CP2-es 2 (PtPe)-Pa 2 (Pt Pe 2 Aggregate subhracting supply of that goodin the economy Lwhich ialven by endouoment in the a9 greaate clemand of that good gead is given by excess demand of a case) from in the eco nomy oux 2 4 Let + 2 2. 4 3 2 4 4 4 Z3CP)-2 2 2

Answer 1

ma -3win, max (o, min , max min,o} ,max (o, ,(F) 3(F)F2* min mim 5 vil) vii) Aseuming P,'' from f 2p24 P3 a 3 eani ubiwm Pice vector a