2(b)There are three people and two goods in an economy. The utility functions and the initial bundles aregiven below:U₁ = X11 X 12Uz = 2X zi+ X 22W₁ = (0,8)W=(2,2)W3= (8,0)U3 = x 31 x 32+X 32Suppose it is suggested that the three traders move to the allocation x given by x₁= (1,2), x₂= (8,4),X3= (1,4)b. Show that x makes no one worse off than the original allocation.c. Show that x is not in the core.

Utility function can be defined as the measure for a group of goods and services preferred by…

2(b)There are three people and two goods in an economy. The utility functions and the given below: U₁ = X11 X 12 W₁ = (0,8) W>=(2,2) U, = 2X zi+ X zz U₂ = X 32 X 32+X 32 W;= (8,0) Suppose it is suggested that the three traders move to the allocation x given by x₁= (1,2), x₂= (8,4), X₁= (1,4) b. Show that x makes no one worse off than the original allocation. c. Show that x is not in the core.

2(b)There are three people and two goods in an economy. The utility functions and the given below: U₁ = X11 X 12 W₁ = (0,8) W>=(2,2) U, = 2X zi+ X zz U₂ = X 32 X 32+X 32 W;= (8,0) Suppose it is suggested that the three traders move to the allocation x given by x₁= (1,2), x₂= (8,4), X₁= (1,4) b. Show that x makes no one worse off than the original allocation. c. Show that x is not in the core.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. The consumers have the following utility functions: UA(X1A,X2A)=X1A+3x2A; UB(X1B,X2B)=x1B +X2B. Consumer A is initially endowed with 4 units of good A and no unit of good 2, that is, consumer A's initial endowment is (W1A,W2A)=(4,0). Consumer B is initially endowed with 3 units of good 2 and no unit of good 1, that is, (WIB,W2B)=(0,3). In order to implement the allocation (x1A,X2A)=(0,1), (x1B,X2B)=(4,2) as a Walrasian equilibrium, what transfer of wealth should we make between the consumers if good 1 is the numeraire, that is, if p1 =1? O a. An amount 7 of wealth should be transferred from consumer A to consumer B. O b. None of the other answers. An amount 3 of wealth should be transferred from consumer A to consumer B. O c. d. An amount 3 of wealth should be transferred from consumer B to consumer A. An amount 7 of wealth should be transferred from consumer B to consumer…
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?
Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. The consumers have the following utility functions: UA(X1A,X2A)=X1A+3X2A; UB(X1B,X2B)=X1B +X2B. Consumer A is initially endowed with 4 units of good A and no unit of good 2, that is, consumer A's initial endowment is (w1A,W2A)=(4,0). Consumer B is initially endowed with 3 units of good 2 and no unit of good 1, that is, (w1B,W2B)=(0,3). In order to implement the allocation (x1A,X2A)=(0,1), (x1B,X2B)=(4,2) as a Walrasian equilibrium, what transfer of wealth should we make between the consumers if good 1 is the numeraire, that is, if p1 =1? An amount 7 of wealth should be transferred from consumer A to consumer B. O a. O b. None of the other answers. O c. An amount 3 of wealth should be transferred from consumer A to consumer B. O d. An amount 3 of wealth should be transferred from consumer B to consumer A. e. An amount 7 of wealth should be transferred from consumer B to…
2(b)There are three people and two goods in an economy. The utility functions and the initial bundles are given below: U1 = X11X 12 U = 2x 21+ X 22 U3 = X 31 X 3z+X 32 W; = (0,8) W;= (2,2) Wy= (8,0) Suppose it is suggested that the three traders move to the allocation x given by x;= (1,2), x2= (8,4), X3= (1,4) b. Show that x makes no one worse off than the original allocation.
For the case of two goods, give examples of different two utility functions that satisfy all of the following properties: (i) one utility is strictly concave in good 1 and the other is strictly convex in good 2; (ii) they represent the same preferences; and (iii) one utility function is homogeneous of degree 2.
Q. It is possible to have a Pareto efficient allocation where everyone is worse off than they are at an allocation that is not Pareto efficient?