Assume that there is two-person two-commodity pure exchange economy. A's utility function is u¹(x,x) = x + ln x2 and his endowment is w4 = (1,4). B's utility function is u²(x,x) = x + 2 In x2 and his endowment is w³ = (3,2). (a) Determine and draw the set of Pareto efficient allocations in an Edgeworth box for this economy (b) The price p₂ is normalized to 1; for simplicity we write p₁ as just p. Calculate the Walras equilibrium price p and Walras allocation [(₁,2), (,)]. Check that the Walras allocation is Pareto efficient graphically and algebraically.
Assume that there is two-person two-commodity pure exchange economy. A's utility function is u¹(x,x) = x + ln x2 and his endowment is w4 = (1,4). B's utility function is u²(x,x) = x + 2 In x2 and his endowment is w³ = (3,2). (a) Determine and draw the set of Pareto efficient allocations in an Edgeworth box for this economy (b) The price p₂ is normalized to 1; for simplicity we write p₁ as just p. Calculate the Walras equilibrium price p and Walras allocation [(₁,2), (,)]. Check that the Walras allocation is Pareto efficient graphically and algebraically.
Chapter13: General Equilibrium And Welfare
Section: Chapter Questions
Problem 13.5P
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![Assume that there is two-person two-commodity pure exchange economy. A's utility
function is u^ (x,x) = x + ln x2 and his endowment is w4 = (1,4). B's utility function is
u²(x,x) = x + 2 In x2 and his endowment is w = (3,2).
(a) Determine and draw the set of Pareto efficient allocations in an Edgeworth box for this
economy
(b) The price p₂ is normalized to 1; for simplicity we write p, as just p. Calculate the Walras
equilibrium pricep and Walras allocation [(4,2), (2)]. Check that the Walras
allocation is Pareto efficient graphically and algebraically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64e22897-7393-441c-a03b-d6c25465272e%2F70cc5427-5343-428c-83ef-a31e3156e769%2F4pqn0omu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Assume that there is two-person two-commodity pure exchange economy. A's utility
function is u^ (x,x) = x + ln x2 and his endowment is w4 = (1,4). B's utility function is
u²(x,x) = x + 2 In x2 and his endowment is w = (3,2).
(a) Determine and draw the set of Pareto efficient allocations in an Edgeworth box for this
economy
(b) The price p₂ is normalized to 1; for simplicity we write p, as just p. Calculate the Walras
equilibrium pricep and Walras allocation [(4,2), (2)]. Check that the Walras
allocation is Pareto efficient graphically and algebraically.
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