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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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(5) A has utility function u4(x4) = x4 + x and initial endowment w4 = (3,6). Consumer B has utility function uB (xB) = xf · x% and initial endowment wB = (3,6). Consider an exchange economy with two consumers and two goods. Consumer (a) Is the initial endowment a Pareto efficient allocation? Justify your answer. (b) Find a competitive equilibrium (p, xª, x³) for the economy. (c) Construct the contract curve. A picture here is not a complete answer; you need to specify analytically the set of points that are in the contract curve.
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Consider a 2-good, 2-agent pure exchange economy where the initial endowment is eд = (5, 5), eß = (5, 5) and preferences are represented by UA, UB: R → R where UA (XA) UB (XB) = X₁X2 and Which 2 of the following 8 options are false: For all B [0, 1], the initial endowment is a Walrasian Equilibrium allocation. If B<1 then at prices p = (1,1) there will be excess demand of good 2 and excess supply of good 1. O For all B € [0, 1], every Pareto efficient allocation can be supported as a Walrasian Equilibrium for some reallocation of resources. O For any prices p = (1, 1), the budget sets of both players leave the Edgeworth box. For all B € [0, 1], the bottom left and top right corners of the Edgeworth box (0A and Og) are both Pareto efficient. For all B [0, 1], the Walrasian Equilibrium will be Pareto efficient. For all 8 [0, 1], Bob's preferences are strictly convex. For ß = 1/2, the Pareto Set is the straight line joining OA and Og.
(1) Consider a small exchange economy with two consumers, A and B, and two commodities, ₁ and 2. Consumer A's initial endowment is 3 units of ₁ and 2 unit of 2. Consumer B's initial endowment has 5 units of 2₁ and 4 units of r2. Consumer A's utility function is given by U(₁, ₁) = x^x^. Consumer B's utility function is given by U(x,x) = 2x² + x2. Note that and are the amounts of the two goods for Consumer A, and rf and are amounts of the two goods for Consumer B. (a) Draw an Edgeworth box, showing the initial allocation. Label it as E. Measure Consumer A's consumption from the lower left and Consumer B's from the upper right. Also measure the number of ₁ on the horizontal axis and the number of r2 on the vertical axis. (b) Draw Consumer A's indifference curve (ICA) going through E. (c) Draw Consumer B's indifference curve (ICB) going through E.
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