Consider a 2-good, 2-agent pure exchange economy where the initial endowment is eA = (5, 5), eg = (5, 5) and preferences are represented by UA, UB: Ro UA (XA) = XA1XÁ2 and UB (XB) = x²₁x2. where Which 2 of the following 8 options are false: ********** For all ß [0, 1], the initial endowment is a Walrasian Equilibrium allocation. If ß < 1 then at prices p = (1,1) there will be excess demand of good 2 and excess supply of good 1. For all ß [0, 1], every Pareto efficient allocation can be supported as a Walrasian Equilibrium for some reallocation of resources. For any prices p (1, 1), the budget sets of both players leave the Edgeworth box. For all ß [0, 1], the bottom left and top right corners of the Edgeworth box (0A and Og) are both Pareto efficient.

Consider a 2-good, 2-agent pure exchange economy where the initial endowment is eA = (5, 5), eg = (5, 5) and preferences are represented by UA, UB: Ro UA (XA) = XA1XÁ2 and UB (XB) = x²₁x2. where Which 2 of the following 8 options are false: ********** For all ß [0, 1], the initial endowment is a Walrasian Equilibrium allocation. If ß < 1 then at prices p = (1,1) there will be excess demand of good 2 and excess supply of good 1. For all ß [0, 1], every Pareto efficient allocation can be supported as a Walrasian Equilibrium for some reallocation of resources. For any prices p (1, 1), the budget sets of both players leave the Edgeworth box. For all ß [0, 1], the bottom left and top right corners of the Edgeworth box (0A and Og) are both Pareto efficient.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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7. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo = Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (a) The conditions require that A and B consume at a point on their budget lines where their indifference curves have the same marginal rate of substitution, and equilibrium for the market as a whole requires that the sum of the individuals' demands for each commodity must equal the totals (Xo and Yo) available. Mathematically express the point of equilibrium, that is, express the above statement with equations in relating each endowments, equilibrium points (Xa, Xb, Ya, Yb), and totals ((Xo, Yo). (b) Suppose MRSa = Ya/Xa, MRSB = Yb/Xb, Xa = 10, Ya, = 100, Xb = 50, Yb = 20, and let good Y be the numeraire (Py =1). Verify that the competitive…
4. Aaron and Burris have the following utility functions over two goods, x and y. Aaron’s utility function: UA(xA, yA) = min{xA/3, yA} Burris’s utility function: UB(xB, yB) = 9xB + 3yB Aaron’s endowment is eA = (2, 4). Burris’ endowment is eB = (10, 8). In an Edgeworth Box diagram, show which allocations are in the core. Solve for the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram. Let good y be the numeraire (i.e. set py = 1 and let px = p). Solve for the Walrasian competitive equilibrium allocation and price ratio.
Suppose that Romeo in Problem 8 has the utility function U= S° RS2, and Juliet has the utility function U= S2RS5, where SRis Romeo's spaghetti consumption and Sj is Juliet's. They have 42 units of spaghetti to divide between them. Juliet would want to give Romeo some spaghetti if she has more than 28 a) units. Romeo would want to give Juliet some spaghetti if he has more than 26 units of spaghetti. C) Romeo and Juliet would never disagree about how to divide the spaghetti. d) Romeo would want to give Juliet some spaghetti if he had more than 21 units of spaghetti. Juliet would want to give Romeo some spaghetti if she has more than 30 units e) of spaghetti.
6. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and d Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo = Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (a) The conditions require that A and B consume at a point on their budget lines where their indifference curves have the same marginal rate of substitution. and equilibrium for the market as a whole requires that the sum of the individuals' demands for each commodity must equal the totals (Xo and Yo) available. Mathematically express the point of equilibrium, that is, express the above statement with equations in relating each endowments, equilibrium points (Xa, Xb, Ya, Yb), and totals ((Xo, Yo).
5.18 In a two-good, two-consumer economy, utility functions are u¹ (x₁, x₂) = x₁(x₂)², u² (x₁, x₂) = (x₁)²x₂. Total endowments are (10, 20). (a) A social planner wants to allocate goods to maximise consumer 1's utility while holding con- sumer 2's utility at u² = 8000/27. Find the assignment of goods to consumers that solves the planner's problem and show that the solution is Pareto efficient. (b) Suppose, instead, that the planner just divides the endowments so that e¹ = (10, 0) and e² = (0, 20) and then lets the consumers transact through perfectly competitive markets. Find the Walrasian equilibrium and show that the WEAs are the same as the solution in part (a).
Consider a pure exchange economy with two goods k = 1,2 and two households i = A, B. The total available amount of good 1 and 2 is 9 and 12 units, respectively. Utility functions for households A and B are UA (TA1, A2) = TA1TA2 and UB(B1, B2) = XB1T32. (a) Find an expression for the Pareto optimal set. (b) Assume e A = (4,4) and eg (5,8) are A and B endowments, respectively. Find the competitive equilibrium. (c) Is the competitive equilibrium allocation in the Pareto Optimal set? Why this result should not surprise us?
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6. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and d Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo = Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (b) Suppose MRSa = Ya/Xa, MRSb = Yb/Xb, Xa = 10, Ya, = 100, Xb= 50, Yb = 20, and let good Y be the numeraire (Py = 1). Verify that the competitive equilibrium price is Px = 2.
9. Consider an exchange economy with two individuals, a and b, and two goods, x and y. Individual a has utility function U"(x, y) = x?y, and individual 6 has utility function U(x, y) = 3x+4y. What condition will hold at all Pareto efficient allocations in the interior of the Edgeworth box? A. ***8yª = 3r" B. yº = { C. 8y = 3.xb D. y" = 2x"