9. Consider an exchange economy, consisting of two consumers, denoted by i = A, B, who trade two commodities, denoted by j = 1,2. = (a) Assuming that consumers A and B's endowments are e (1, 2) and eB = (2, 1) respectively, construct the Edgeworth Box diagram relative to this econ- omy. With reference to the same economy, define the following notions: com- petitive equilibrium, Pareto-efficient allocation, contract curve. (b) Assume that consumers A and B's preferences are represented by the following utility functions: u(x, x) = x u³ (x, x) = x + In x + 2ln x Find the equation for the contract curve; then, taking commodity 1 as the numeraire, hence positing p₁ = 1 and denoting p2 = p, find the competitive equilibrium allocation and price. (c) State and verify the first theorem of welfare economics.
9. Consider an exchange economy, consisting of two consumers, denoted by i = A, B, who trade two commodities, denoted by j = 1,2. = (a) Assuming that consumers A and B's endowments are e (1, 2) and eB = (2, 1) respectively, construct the Edgeworth Box diagram relative to this econ- omy. With reference to the same economy, define the following notions: com- petitive equilibrium, Pareto-efficient allocation, contract curve. (b) Assume that consumers A and B's preferences are represented by the following utility functions: u(x, x) = x u³ (x, x) = x + In x + 2ln x Find the equation for the contract curve; then, taking commodity 1 as the numeraire, hence positing p₁ = 1 and denoting p2 = p, find the competitive equilibrium allocation and price. (c) State and verify the first theorem of welfare economics.
Chapter13: General Equilibrium And Welfare
Section: Chapter Questions
Problem 13.1P
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Transcribed Image Text:9. Consider an exchange economy, consisting of two consumers, denoted by i = A, B,
who trade two commodities, denoted by j = 1,2.
=
(a) Assuming that consumers A and B's endowments are e (1, 2) and eB =
(2, 1) respectively, construct the Edgeworth Box diagram relative to this econ-
omy. With reference to the same economy, define the following notions: com-
petitive equilibrium, Pareto-efficient allocation, contract curve.
(b) Assume that consumers A and B's preferences are represented by the following
utility functions:
u(x, x) = x
u³ (x, x) = x
+ In x
+ 2ln x
Find the equation for the contract curve; then, taking commodity 1 as the
numeraire, hence positing p₁ = 1 and denoting p2 = p, find the competitive
equilibrium allocation and price.
(c) State and verify the first theorem of welfare economics.
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