4) Consider a two agent and two good exchange economy where agent 1 has preferences represented by U, (x11, X21) = x11X21. Agent 2 has preferences represented by utility function U2(x12, X22) = x12X22. The initial endowments are w = (1,3) and w2 = (3,1). Show directly that every interior Pareto optimal allocation in this economy is a price equilibrium with transfers by finding the associated prices and transfers.

4) Consider a two agent and two good exchange economy where agent 1 has preferences represented by U, (x11, X21) = x11X21. Agent 2 has preferences represented by utility function U2(x12, X22) = x12X22. The initial endowments are w = (1,3) and w2 = (3,1). Show directly that every interior Pareto optimal allocation in this economy is a price equilibrium with transfers by finding the associated prices and transfers.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.5P

See similar textbooks

Similar questions

consider an exchange economy with 2 goods (1 and 2) and 2 consumer (A and B). a bundle with x units of good 1 and y units of good 2 is written as (x,y). consumer A has an endowment (4,0) and consumer B has an endowment (12,12). the 2 goods are perfect substitutes for each consumer. consider an allocation in which A receives (1,9) and B receives (15,3) if we can redistribute endowments suitably, it is possible to obtain this allocation as the outcome of a competitive equilibrium. is this true or false? explain carefully
Bluth’s preferences for paper and houses can be expressed as Ub(p, h) = 2pb + hb, while Scott’s preferences can be expressed as Us(p, h) = ps + 2bs. Bluth begins with no paper and 10 houses, whereas Scott begins with 10 units of paper and no houses. 1. Is the starting endowment Pareto efficient? Justify your answer using an Edgeworth box? Determine whether each of the following price pairs is consistent with a competitive equilibrium. If yes, determine the resulting allocation of goods, sketching that equi- librium in your Edgeworth box. If not, explain why not (for what good is there a shortage, for what good is there a surplus?) pp =$3 and ph =$1 along with pp =$1 and ph =$1 Assume that the price of houses is $1. Given that price, determine the highest price pp that is consistent with a competitive equilibrium.
1.) In an endowment economy with market exchange, let two consumers have preferences given by the utility function U^{h}=(x_{1}^{h})^{a}*(x_{2}^{h})^{1-a}for consumer h (1,2) with endowments given by\omega _{1}^{1}=6, \omega _{2}^{1}=4, \omega_{1}^{2}=4, and \omega_{2}^{2}=6. a.) Calculate the consumers' demand functions. b. Selecting good 2 as the measure of value (i.e. p2=1) and with alpha=1/4, find the equilibrium price of good 1 which implies equilibrium levels of consumption of both goods for both consumers. c. Demonstrate whether both consumers' indifference curves are tangential at the equilibrium. Demonstrate whether both consumers' indifference curves are tangential at the initial endowment.
Persons 1 and 2 have the following utility functions over goods x and y: Person 1: U1(x1, y1) = min{2x1, y1} Person 2: U2(x2, y2) = x2 + y2 Person 1 has an endowment of e1 = (2, 1). Betty’s endowment is e2 = (1, 2). Graph the Edgeworth Box for this economy. Draw each person’s indifference curve through the endowment point. Are there allocations that Pareto dominate the endowment? If so, show them on the diagram. Also, identify which allocations are Pareto optimal relative to the endowment point. Solve for the contact curve for this economy. Illustrate it in the Edgeworth Box.
I need help with this homework problem. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = (X^1/2)*(Y^1/2) UB(X,Y) = X + Y The initial endowments are: A: X = 8; Y = 3 B: X = 4; Y = 5 What is the marginal rate of substitution for consumer A at the initial allocation? What is the marginal rate of substitution for consumer B at the initial allocation? Is the initial allocation Pareto Efficient?
Please draw its diagram Consider the following pure exchange economy with two consumers and two goods. Consumer 1 has utility given by U1 = min {4x1, 2x2} Consumer 2 has utility given by U2 = 2x1 + x2 The initial endowment has consumer 1 starting with 200 units of x1 and 200 units of x2. Consumer 2 starts with 300 units of x1 and 300 units of x2. Draw an Edgeworth box diagram for this initial endowment complete with the indifference curves for each individual.
Chris and Dana live in an exchange economy with two goods: good Q and good R. Chris starts off with an endowment of 6 units of Q and 10 units of R. Dana starts off with an endowment of 8 units of Q and 8 units of R. Suppose that the price of good R is pR=1 and the price of good Q is pQ=2. a )At these prices, does the market clear? Yes or no? Explain your answer. b) What relationship must hold between the consumption of each agent and the price of the two goods at the market clearing equilibrium? Write the equation
Consider an economy with 2 goods and 30 agents. There are 10 agentseach with the utility function u (x1; x2) = ln x1 + 2 ln x2 and endowments e = (3; 1).Also, the other 20 agents each have the utility function u (z1; z2) = 2 ln z1 + ln z2 andendowments e = (1; 2). Normalize p2 = 1. Calculate the Walrasian equilibrium pricep1*
Two individuals, Fred and Helen, are in an economy with no production, and each have the utility function U = 10XY. Prices of both X and Y are set at $1. Initial endowments for Fred are 10 units of X and 6 units of Y. Helen has 8 units of X and 12 units of Y. Find the general equilibrium prices and allocation, then show that the G.E. allocation is Pareto efficient.
Consider an Edgeworth box economy, where preferences and endowments are given by. ( attached below ) In the following, use the normalization p2 = 1.(a) Find all the Pareto optimal allocations (use x1 to parameterize thePO allocations). (b) Suppose the government wants individual 1 to have the bundle x1 = (5, 9). Show whether the government can induce this outcome an equilib- rium with transfers. Find the supporting prices and transfers if possible. (c) State the Second Fundamental Theorem of Welfare and explain how the result in part (b) relates to that theorem. (d) Suppose the government does not care what bundle individual 1 gets and only wants to ensure that the individual 1 receives utility level equal to 45. Show whether this can be achieved as an equilibrium with transfers. Find the supporting prices and transfers if possible.
If an allocation is Pareto optimal and if indifference curves between the two goods have no kinks, then (Select all that applies) Group of answer choices a. two consumers who consume both goods must have the same MRS between them, but consumers may consume the goods in different ratios. b. two consumers with the same income who consume both goods must have the same MRS, but if their incomes differ, their MRSs may differ. c. any two consumers who consume both goods must consume them in the same ratio. d. for any two consumers who consume both goods, neither will prefer the other consumer’s bundle to his own. e. all consumers receive the bundle that they prefer to any other bundle the economy could produce for them.
Consider a market with M= 2 consumers and L = 2 goods. The preferences of each consumer are u₁(x₁) = min (x₁, x2} (6) U₂(x2) = X1X2 (7) Draw the Edgeworth box for this economy, where endowments are ₁ = (0,1) and ₂ = (1,0). Be sure to label the budget constraint, endowment point, equilibrium price ratio, equilibrium allocation, and the indifference curves of each consumer. Please do fast ASAP fast