8. (a) Prove that competitive equilibria are always Pareto efficient.(b) Consider two-persons, two-goods exchange economy. Person A has an endowment of(1, 0) and preferences U^ =Cf C$. Person B has an endowment of (1, 2) and preferencesU* = Min [2Cf 3C ]. Using an Edgeworth Box draw their offer curves. Find competitiveequilibrium prices and quantities.

Pareto efficiency describes a situation in which no one can be helped without harming someone else.…

(a) Prove that competitive equilibria are always Pareto efficient. (b) Consider two-persons, two-goods exchange economy. Person A has an endowment of (1, 0) and preferences UA =CACA. Person B has an endowment of (1, 2) and preferences U³ = Min [2C3C]. Using an Edgeworth Box draw their offer curves. Find competitive equilibrium prices and quantities.

(a) Prove that competitive equilibria are always Pareto efficient. (b) Consider two-persons, two-goods exchange economy. Person A has an endowment of (1, 0) and preferences UA =CACA. Person B has an endowment of (1, 2) and preferences U³ = Min [2C3C]. Using an Edgeworth Box draw their offer curves. Find competitive equilibrium prices and quantities.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

(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.
!
Consider a two-agents, two goods economy, in which both agents, A and B, are represented by the following utility function: UA(1, 22) = rr2 UB(y1, Y2) = Y1y% There are w units of each good in the economy. 1. Characterize the set of Pareto optimal allocations and represent it in the Edgeworth box. The 3 units of each goods are initially share as follows: A has w units of good 1 and zero unit of good 2; B has zero unit of good 1 and w units of good 2. 2. Determine the Walrasian equilibrium 3. Represent the economy in the Edgeworth box.
Ma1. Please give only typed answer.
please if you can teach explain
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.
iii) Define "Free Good" in a general equilibrium framework. Explain whether the goods are free goods in the following context after determining the equilibrium price. Consider an exchange economy. There are two consumers A and B and two goods X and Y. A has lexicographic preference over good X and B also has the same type of preference. Their endowment is (5,5) each.
B4
(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.
9
!
A small exchange economy is comprised of two of individuals, A and B, and two types of goods, x, ,x,. The individuals' preferences over two goods are can be represented by the following utility functions: U*(x;,.x; ) = min (2.x,x; ) and U* (x;,x;) = min(x;.2x, ). Initial endowments are 10 x, (individual A), and 10 x, (individual B). Calculate the price ratio which yields an equilibrium in the exchange market.