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3. Exchange Economy (33 marks) Consider an exchange economy with two consumers 1 and 2, and two goods :1: and 3;. Consumer 1's initial endowment is: :09 : 4, and y? : 7. Consumer 2's initial endowment is $9 = 6 and y3 = 3. Their preferences are given by the utility functions U1(x1,y1) I 551 +10g(y1)a and (120527 92) I log(x2) 'l' 92- Remember that the derivative of log(m) is given by 1/:1:. (a) ( 8 marks) Draw an Edgeworth box for this economy with the initial endowment, the indifference curves of the two consumers at their initial endowment, and the set of allocations that Pareto dominate the initial allocation. (b) ( 5 marks) Compute the marginal rates of substitution for both consumers. (c) ( 5 marks) Characterize the efficient allocations in this economy. On the Edgeworth box from question (a), draw the set of efficient allocations that dominate the initial allocation (this is called the contract curve). (d) (7 marks) Denoting by p the price of good :1: and normalizing the price of good y to 1, compute the demands of the two consumers for both goods as a function of p. (e) (5 marks) Characterize the competitive equilibrium for this economy. Find the equilib rium price p, and the equilibrium allocation? (f) (3 marks ) Show that the market equilibrium is efficient