General Equilibrium 1 Consider, U1(21, y1) = 2(x11)* + 20 U2(2, Y2) = 10lnx2 + 4lny2 W1 (2, 1) and W2 = (1,2) 1.1 Characterize the Pareto efficient allocations and contract curve. %3D 1.2 Which allocations are in the core? 1.3 Find the Competitive/Walrasian equilibrium for this problem. 1.4 Is the answer of 1.3 in the core?

General Equilibrium 1 Consider, U1(21, y1) = 2(x11)* + 20 U2(2, Y2) = 10lnx2 + 4lny2 W1 (2, 1) and W2 = (1,2) 1.1 Characterize the Pareto efficient allocations and contract curve. %3D 1.2 Which allocations are in the core? 1.3 Find the Competitive/Walrasian equilibrium for this problem. 1.4 Is the answer of 1.3 in the core?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.12P

See similar textbooks

Similar questions

General Equilibrium Consider, U1(x1, y1) = 5(x1y1) 3 + 12 U2(x2, y2) = 3lnx2 + 25lny2 + 10 W1 = (7, 3) and W2 = (4, 6) a. Characterize the Pareto efficient allocations and contract curve b. Which allocations are in the core ? c. Find the Competitive/Walrasian equilibrium for this problem . d. Is the allocation found in c in the core? Why?
Consider, U1(x1, y1) = 2(x1y1) 4 + 20 U2(x2, y2) = 10lnx2 + 4lny2 W1 = (2, 1) and W2 = (1, 2) 1.1 Characterize the Pareto efficient allocations and contract curve. 1.2 Which allocations are in the core? 1.3 Find the Competitive/Walrasian equilibrium for this problem. 1.4 Is the answer of 1.3 in the core?
4. Consider a two-consumer, two-good exchange economy. Utility functions and endowments are u'(x1, x2) = (x1x2)² and e' = (18, 4),u²cx1, x2) = In(x1) + 2 In(x2) and e? = (3, 6). (a) Characterize the set of Pareto-efficient allocations as completely as possible. (b) Characterize the core of this economy. (c) Find a Walrasian equilibrium and compute the WEA. (d) Verify that the WEA you found in part (c) is in the core.
2. Consider a two person pure exchange economy with two divisible goods: : a consumer can consume any positive amount of any good The goods are; x1 and x2. The utility function are u' (x1, x2) = x1+Vx2, and u?(x1, x2) = x1 + x2, and the initial endowments are el Pi = 1, compute the competitive equilibrium for this economy. It is to say that you need to find the vector of prices, and allocations that sustain the Walrasian equilibrium. (25, 75) and e? = (75, 25). Assuming
Consider an economy inhabited by George and Harriet, whose utility functions are Ug : (ac)² (bc)2 Он тан + 2bн The total quantities of ale and bread that can be produced by the economy are a and b, and they are constrained by the production function b = 2(10 – a)/2 There are infinitely many Pareto optimal allocations. In one of them, Harriet's utility is 8. a) An allocation in this economy is described by a list of four variables. What are these variables? b) What four equations describe the Pareto optimal allocation in which Harriet's utility is 8? c) Find this Pareto optimal allocation.
Consider trade between two consumers (1 and 2) and two goods, X and Y. Suppose the total quantities of each good are 100 units. Each consumer has Cobb-Douglas preferences given by: U(X,Y) = XY Denoting by X1 the first consumer's consumption of X and by Y1 the first consumer's consumption of Y, the contract curve consists of all allocations where A. X1 = 0.5Y1 B. X1 = 2Y1 C. X1 = Y1 square D. X1 = Y1
5. Consider an exchange economy with 2 agents and 2 goods. a) In an Edgeworth-Bowley diagram, show and illustrate that if both agents have the same preferences, the contract curve is a straight line from the bottom left-hand corner to the top right-hand corner. Explain. b) Does it follow that if the agents do not have the same preferences, the contract curve is not a straight line? Explain. c) Suppose the two agents have the same endowments and the same preferences. Is mutually beneficial trade possible? Illustrate in an Edgeworth Bowley diagram. Explain.
Derive a Co 5. Consider a two-consumer economy in which wA = (1,2), wB=(2, 2), u^(x₁,x) = x₁³x₂ and u²(x,x) = x, ³x₂² (a) Illustrate this economy in an Edgeworth box. (b) Derive a competitive equilibrium for this economy. 11_JJ)
Throughout this problem set, we will look at exchange economies with two goods and two agents. Let X = R², let u denote agent i's utility, and let wie X denote agent i's endowment. 1. Suppose u¹(x¹) = min{ri, 2} and wi = (4,8) for both agents i. (a) Argue that every Pareto optimal allocation has r≥r for both agents i. (b) Argue that every allocation z with r≥r for both agents i is Pareto optimal. (c) Draw an Edgeworth box, with a picture depicting every Pareto-optimal allocation. In this picture, also draw the endowment allocation, and draw each agent's indifference curve through the endowment. (d) Argue that, in any competitive equilibrium, the price of good 2 must be zero. (e) Find all competitive equilibria.
Alice can produce goods X and Y. It takes her 1 hour of labor to produce 2 units of X. It takes 2 hours of labor to produce three units of Y. If Alice divides four hours of her time between the two tasks, which of the following (X, Y) allocations are efficient? Could be more then one answer. (3, 4) (8, 0) (4, 3) (5, 1)
Question [1]: For each of the following pure exchange economies with 2 goods and 2 consumers, draw a well labelled representation of the Edgeworth Box and clearly indicate and/or describe the Pareto Set, i.e. the set of Pareto optimal allocations. Indicate the set of allocations that are only weakly Pareto optimal if there are such allocations. 1. u4(x, y) = r + Vy; uB (x, y) = 8x + y; Total endowment (10, 20) 2. u4(x, y) = min{x, y}; u² (x, y) = x + 2/ỹ; Total endowment (10, 15)
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.