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Question 2 An economy has two agents, A and B, and three goods 1, 2 and 3. The endowments of the two consumers are: 6A = (13231); EB = (2} 112) Given a price vector p = (p1, 102,103), the demand functions of the three agents for each of the three goods are as follows: A _ p1+2p2+p3_ A _ p1+2p2+p3_ #4 _ p1+2p2+p3 551(1)) _ 2P1 1 272(1)) _ 4P2 1 3(1)) _ 4P3 2103 103 2101 +102 951309) = ; I23(1)) = ; $3131?) = -1 P1 P2 303 (i) Write down the total endowment vector of the economy, 6. (ii) Find the aggregate demand functions for the three goods in this economy, and simplify them. $1 (P) 332(1)) = $30?) (iii) Write down the aggregate excess demand functions for the three goods. 21 (P) 22 (P) 23(1)) Now 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. Below, you will map a particular price vector p into its value f (p) Please be careful with your arithmetic. Let 13 = (:7, i, i). Answer the question below for these prices. (iv) Find the numerical value of the excess demand for each good at this price vector: 21 (27) 22 (15) 2:3 (15) (v) Find the vector mi), where ma) is given by mia) = p,- + mtn{ei, Inax{0, again}. ml (13) = m2 (P) ms (13) (vi) Find the vector fa?) which the price p = (:7, vector m(;5) that you just found. , %) maps into, by normalising the price- Hilll (vii) Recall the excess demand functions that you found in part (iii). For each good i = 1, 2, 3, write down the congurations of prices for which 21(1)) = 0 [Each of these will involve all three prices (131,102: P3) -l 21 (P) 22 (P) 23(2)) 0 4: 0 er 0 4: (viii) Using your answers to part (vii) above, nd a price vector in the simplex that is an equilibrium