Question 1 Part (d)

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Question 1 In an exchange economy with two consumers and two goods, consumer A's utility function is U(xA,yA) = xA 2yA and consumer B's utility function is U(xB, 313) = xByB. A is endowed with is 6 units of x and 4 units of y and B is endowed with 10 units of x and 8 units of y. a) Is the endowment allocation Pareto efcient? If yes, why? If not, suggest a Pareto improvement over the endowment allocation. b) Is the allocation (xA = 2, yA = 0, x3 = 14, 323 = 12) Pareto efficient? If not, suggest a Pareto improvement over this allocation. c) Draw an Edgeworth box with x on the horizontal axis and y on the vertical axis. Measure goods for consumer A by the distance from the lower left corner of the box. Draw the contract curve in your graph. Label your graph clearly. (N o explanation is needed.) d) Set y as a numeraire. Find the equilibrium price of x and the equilibrium allocation. For simplicity, assume the equilibrium allocation is a tangency point between the budget line and consumer B's indifference curve