are Consider an economy inhabited by George and Harriet, whose utility functions UG= (ac)1/2 (bg) 1/2 Uнан+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)1/2 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.

are Consider an economy inhabited by George and Harriet, whose utility functions UG= (ac)1/2 (bg) 1/2 Uнан+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)1/2 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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.1P

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Q. It is possible to have a Pareto efficient allocation where everyone is worse off than they are at an allocation that is not Pareto efficient?
Suppose Zaharah (Z) and Quah (Q) are now at an allocation bundle where their marginal rates of substitution (MRS) are given by MRS₂ = 10 and MRSQ = 5, respectively. In general equilibrium analysis, this suggests that Andaikan Zaharah (Z) dan Quah (Q) kini berada pada sesuatu longgok alokasi di mana kadar penggantian marginal (MRS) masing-masing adalah MRS₂ = 10 dan MRSQ = 5. Dalam analisis keseimbangan am, ini menunjukkan bahawa a. both individuals have already engaged in voluntary exchange of resources kedua-dua individu telah pun terlibat dalam pertukaran sumber secara sukarela b. Zaharah's situation is better off than Quah situasi Zaharah adalah lebih baik daripada Quah there exists a basis for voluntary exchange for resources between both terdapat asas untuk pertukaran sumber secara sukarela antara kedua-duanya d. both of them are in equilibrium C.
1) Suppose that Abel and Eden spend their incomes on two goods, food (F) and clothing (C).Abel’s preferences are represented by the utility function U(F,C)=10FC, while Eden’spreferences are represented by the utility function U(F,C)= 0.20F2C2A) With food on the horizontal axis and clothing on the vertical axis, identify on a graph theset of points that give Abel the same level of utility as the bundle (10, 5). Do the same forEden on a separate graph.B) On the same two graphs, identify the set of bundles that give Abel and Eden the samelevel of utility as the bundle (15, 8).C) Do you think Abel and Eden have the same preferences or different preferences? Explain 2. Graphically show the effect of an increase in price of Coca Cola on the demand of PepsiCola 3. Assume a budget line is drawn for two commodities: X on the x-axis and Y on the y-axis. Ifthe income of the consumer is 120 Birr, the y-intercept is 3, and the slope of the budget lineis -0.5 then determined the price of commodity…
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Question 6: Transitivity There is only one consumption good in the world (cities). Karen is moving – suppose that her preferencesover cities are described as follows: she strictly prefers city A to city B if either (1) the average rent in cityA is cheaper than in city B, or (2) the average rent is the same in both cities, and there are more goodrestaurants in city A than in city B. Are these preferences transitive? Justify your answer.
Carol needs to decide how to spend her wealth on sh and chicken.For Carol, 1 lb of sh is equivalent to 2 lb of chicken. Her preferences2Intermediate Microeconomics NYUAD, Spring 2023can be represented by the utility functionu(x; y) = 2x + ywhere x is the quantity of sh (in lbs) and y is the quantity of chicken(in lbs). The consumption set is R2+.(a) Draw two typical indi erence curves for Carol, one correspondingto a utility level of u1 and one corresponding to a utility level u2,where 0 < u1 < u2. Make sure you label the slope of the indif-ference curves and the intercepts with the horizontal and verticalaxes.(b) Suppose the price of sh is $1:5 per lb and and the price of chickenis $1 per lb. Carol has $20 to spend on sh and chicken.(i) Draw Carol's budget set, labeling the slope and the interceptpoints clearly.(ii) How much sh and chicken will Carol choose to purchase?
Li's marginal rate of substitution of hamburger for steak is 1/4, and Zhang's marginal rate of substitution of hamburger for steak is 2. The allocation of hamburger and steak Pareto-efficient between Li and Zhang because is not; if Li traded some amount of hamburgers to Zhang for some steak, it is possible that each can be better off is; Zhang's MRS is exactly 8 times larger than Li's MRS is; no trade can make both Li and Zhang better off is not; if Li traded some amount of steak to Zhang for some hamburgers, it is possible that each can be better off
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Consider two commodities: toy cars and batteries. Each toy car takes three batteries to operate. Suppose Andy enjoys a toy car only if it moves and Andy has no other toy that needs battery. That is, one toy car and three batteries are a set of perfect complements to Andy. Task 1: Let x1 >= 0 be the quantity of toy cars and x2 >= 0 be the quantity of batteries. FindafunctionU(x1, x2)thatrepresentsthispreference. Task 2: Draw Andy's indifference curves going through bundles (2, 3), (4, 3) and (5, 5) in the commodity space in the same graph. How does Andy's preference order these 3 bundles in terms of > or ? Task 3: What mathematical expression describes the line formed by all the corners of the indifference curves?
Suppose the utility function of the two individuals in the economy is given by UA = 2XA0.5YA0.5 ; UB = XB0.5YB0.5 and X and Y are allocated equally between the two individuals. Compute for XA, YA ,XB ,YB Calculate the MRSXY of each individual Is the allocation efficient? How so?