Consider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation? a. always, for any consumers' preferences b. only if consumers' preferences are exactly the same c. Never d. None of the above

Consider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation? a. always, for any consumers' preferences b. only if consumers' preferences are exactly the same c. Never d. None of the above

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.5P

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Consider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation. a. always for any consumers' preferences b.only if consumers' preferences are exactly the same c. never d. non of the above
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.
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.
####### Consider the following pure exchange, Edgeworth box economy. There are 2 consumers and 2 goods. Consumer 1 has an endowment of 3 units of good Y, while consumer 2 has an endowment of 3 units of good X. For both consumers the utility function is given by: U (x, v) = x^2y, where x and y denote the respective quantities of goods X and Y. Find the Walrasian equilibrium price ratio P/Pr and the Walrasian allocations. Does trade take place in equilibrium? i want answer in 1 hour. if you provide solution within time, i will upvote. thanks in advance
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?
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
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.
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A fixed amount of a good has to be allocated between two individuals, h = 1; 2 with utility functions Where xh is the amount of the good allocated to consumer h. a. How should be allocated to maximize a utilitarian SWF? Illustrate the answer graphically. How do the optimal values of x1 and x2 change among the cases a1 2, a1 = a2, and a1 > a2? b. What is the allocation maximizing the Bernoulli-Nash SWF ? Illustrate graphically. How do the optimal values of x1 and x2 change with the preference parameters a1 and a2? c. What is the allocation maximizing the maxim in-Rawlins SWF? Illustrate graphically. How does the allocation change with preference parameters a1 and a2?
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.