N=7 4. Carl and Linda are the only people living in a village. Theyconsume only two goods, apples (A) and bananas (B). Carl has aninitial endowment of 10 apples and 60 bananas. Leyla has an initialendowment of 50 apples and 20 bananas. Carl's utility function isUc(Ac, Bc) = AcBc, where Ac and Bc represent his consumption ofapples and bananas, respectively. Leyla's utility function is UL(AL,BL) = min{(N+2)AL, BL}, where AL and B₁ denote her consumption ofapples and bananas, respectively.40a)=,40) and LeylaN+2'Is the allocation where Carl gets (Ac, Bc):gets the rest of both goods a Pareto efficient allocation? Explain.Find the equation for the contract curve. Draw both that allocationand the contract curve in an Edgeworth box. Be precise in yourdrawing.b) Find the competitive equilibrium prices (pA, PB). Find theresulting Walrasian Equilibrium Allocation and represent it in theEdgeworth box. Again, be precise in your drawing.c) Can you find a new initial endowment allocation such thatthe resulting competitive equilibrium is the egalitarian allocationof goods, i.e. (Ac,AL) = (30,40) = (AL,BL)?

Pareto Efficiency: Pareto optimality (also known as Pareto efficiency) is a common economic…

4. Carl and Linda are the only people living in a village. They consume only two goods, apples (A) and bananas (B). Carl has an initial endowment of 10 apples and 60 bananas. Leyla has an initial endowment of 50 apples and 20 bananas. Carl's utility function is Uc(Ac, Bc) = AcBc, where Ac and Bc represent his consumption of apples and bananas, respectively. Leyla's utility function is UL(AL, BL) = min{(N+2)AL, BL}, where AL and BL denote her consumption of apples and bananas, respectively. 40 N+2 a) Is the allocation where Carl gets (Ac, Bc) = ,40) and Leyla gets the rest of both goods a Pareto efficient allocation? Explain. Find the equation for the contract curve. Draw both that allocation and the contract curve in an Edgeworth box. Be precise in your drawing. b) Find the competitive equilibrium prices (PA, PB). Find the resulting Walrasian Equilibrium Allocation and represent it in the Edgeworth box. Again, be precise in your drawing. c) Can you find a new initial endowment allocation such that the resulting competitive equilibrium is the egalitarian allocation of goods, i.e. (Ac,AL) = (30,40) = (AL,BL)?

4. Carl and Linda are the only people living in a village. They consume only two goods, apples (A) and bananas (B). Carl has an initial endowment of 10 apples and 60 bananas. Leyla has an initial endowment of 50 apples and 20 bananas. Carl's utility function is Uc(Ac, Bc) = AcBc, where Ac and Bc represent his consumption of apples and bananas, respectively. Leyla's utility function is UL(AL, BL) = min{(N+2)AL, BL}, where AL and BL denote her consumption of apples and bananas, respectively. 40 N+2 a) Is the allocation where Carl gets (Ac, Bc) = ,40) and Leyla gets the rest of both goods a Pareto efficient allocation? Explain. Find the equation for the contract curve. Draw both that allocation and the contract curve in an Edgeworth box. Be precise in your drawing. b) Find the competitive equilibrium prices (PA, PB). Find the resulting Walrasian Equilibrium Allocation and represent it in the Edgeworth box. Again, be precise in your drawing. c) Can you find a new initial endowment allocation such that the resulting competitive equilibrium is the egalitarian allocation of goods, i.e. (Ac,AL) = (30,40) = (AL,BL)?

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 an economy with 2 goods and 2 identical agents, each of whom has the following utility function, u (x1; x2) = ln x1 + 2 ln x2. The aggregate endowments of the 2 goods are given by (1; 2). Suppose there is a social planner who cares about agents equally.(a) Set up the plannerís problem.(b) Calculate the first-best outcome 2. Consider an economy with 2 goods and 2 identical agents, each of whom has thefollowing utility function, 11(31, 3:2) = In 3:; + 2111332. The aggregate endowments ofthe 2 goods are given by (1, 2). Suppose there is a. social planner who cares aboutagents equally. (a) Set up the planner’s problem.(b) Calculate the ﬁrst-best outcome (11.6., the social planner’s solution).
A possible explanation for the indecency might be the fact that the consumers are not all alive at the same time and therefore some mutually advantageous trades cannot occur. Consider an economy where consumer t receives an endowment of 1 unit of the single consumption good at time t and obtains utility only from consumption at times t and t + 1. All consumers meet at time 0 to trade. What is the equilibrium? Is exigency restored?
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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?
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