Question 3 30 Marks Consider A Pure Exchange Economy Consisting Of 2 Consumers Albert And Brandon And 2 Goods Z And 1 (57.5 KiB) Viewed 13 times
Question 3 (30 marks) Consider a pure-exchange economy consisting of 2 consumers, Albert and Brandon, and 2 goods, z and y. Suppose that each consumer i has the same Cobb-Douglas utility function: u₁(x₁, y₁) = x²yº where 0 < a < 1. In addition, Albert is endowed with WA = (1,2), and Brandon is endowed with WB = (2,1). (a) (5 marks) Draw an Edgeworth box diagram indicating the endowment bundles, each consumer's indifference curve at the endowment, and the direction in which the utility increases for each consumer. Do not forget to label the total endowments and y. (b) (5 marks) Redraw the Edgeworth box diagram without the indifference curves. Draw the budget sets for Albert and Brandon when p₁ = 3 and Py = 9 within the Edgeworth box diagram. Do not forget to label all the intercepts for both Albert's and Brandon's budget line (refer to the instructions at the beginning of the exam).
(c) (10 marks) Find the competitive equilibrium. (d) (5 marks) Based on your answer in part (c), who sells good? Who sells good y? [Hint: compare the competitive equilibrium allocations to the endowments.] (e) (5 marks) Draw the Edgeworth box diagram including the endowment bundles and the competitive equilibrium you found in part (c). Draw the indifference curves of both consumers at both the endowments and competitive equilibrium allocations. Draw the budget line representing the equilibrium prices. Draw the set of Pareto Optimal allocations. Label appropriately.
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