Describe the contract curve, i.e., the set of Pareto e¢ cient allocations preferred to the endowment point, graphically in the Edgeworth box.
Ann has utility function uA (xA1; xA2) = xA1 + xA2 over consumption this year (xA1) and consumption next year (xA2), where 2 (0; 1). Bob has utility function uB (xB1; xB2) = ln (xB1) + ln (xB2) over the consumption this year (xB1) and consumption next year (xB2). Ann has $100k this year, but no income next year. Bob has $50k this year and $200k next year. (a) Describe this exchange economy in an “Edgeworth box”. Carefully label all the graph and all of its components. (b) Describe the Pareto e¢ cient allocations in this economy (give an analytic answer and illustrate your answer in the Edgeworth box). (c) Describe the competitive equilibrium interest rate and allocations (give an analytic answer and illustrate your answer in an Edgeworth box). The interest rate r is determined by the ratio of the price between consumption next year, p2 and this year, p1 : 1 + r = p2 p1 ; (where you may normalize the price level of this year by setting p1 = 1:) (d) Describe the contract curve, i.e., the set of Pareto e¢ cient allocations preferred to the endowment point, graphically in the Edgeworth box.
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