Person A has a utility function of and person B has a utility function Agent A and agent B have identical endowments of (1/2,1/2). (a) Illustrate this situation in an Edgeworth box diagram. (b) What is the equilibrium relationship between p1and p2? (c) What is the equilibrium allocation
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Person A has a utility function of and person B has a utility function Agent A and agent B have identical endowments of (1/2,1/2).
(a) Illustrate this situation in an Edgeworth box diagram.
(b) What is the equilibrium relationship between p1and p2?
(c) What is the equilibrium allocation?
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- 3(b)Consider the following social choice problem in the setting of consumption of two goods by two consumers. The two goods are called tillip and quillip and the two consumers are called 1 and 2. Consumer 1 has utility function U; (t,g) =6+.4 In(t) + .6 In(q) (where t is the amount of tillip 1 consumes and q is the amount of quillip). Consumer 2 has utility function U; (t,q) = 8 + In (t) + In(q). The social endowment consists of 15 units of tillip and 20 units of quillip. a. Suppose that a social dictator has social welfare functional of the following form: social welfare, as afunction of (u",u") is a weighted sum with weight 2 on the lesser of u' and u' and weight 1 on the greater of the two. What will be the welfare optimum plan chosen by this social planner? b. What is the set of all feasible, Pareto efficient allocations of the consumption good for this society? %3DSuppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 8 units of X and a TOTAL of 8 units of Y. The consumers' utility functions are given by: UA(X,Y) = 2X + Y UB(X,Y) = X*Y2 Which of the following allocations is Pareto Efficient? None of the other answers are Pareto Efficient. Consumer A gets 3 units of X and 8 units of Y, and Consumer B gets 5 units of X and O units of Y. Consumer A gets 4 units of X and 4 units of Y, and Consumer B gets 4 units of X and 4 units of Y. Consumer A gets 1 units of X and 4 units of Y, and Consumer B gets 7 units of X and 4 units of Y. Consumer A gets 8 units of X and 8 units of Y, and Consumer B gets 0 units of X and O units of Y.2(b)There are three people and two goods in an economy. The utility functions and the initial bundles are given below: U; = X11X 12 Uz = 2x 21+ X 22 U3 = X 31 X 3z+X 32 W; = (0,8) W;F (2,2) Wy= (8,0) Suppose it is suggested that the three traders move to the allocation x given by X;= (1,2), x;= (8, 4), X3= (1,4) a. Calculate the MRS for the three at the allocation x. b. Show that x makes no one worse off than the original allocation. C. Show that x is not in the core.
- John and Belle consume only two goods, x and y. They have strictly convex preferences and no kinks in their indifference curves. At the initial endowment point, the ratio of John's marginal utility of x to his marginal utility of y is J and the ratio of Belle's marginal utility of x to her marginal utility of y is B, where J B. b. C < J. c. C = J. d. C = B. e. J2(b)There are three people and two goods in an economy. The utility functions and the initial bundles are given below: U1 = X11X 12 U = 2x 21+ X 22 U3 = X 31 X 3z+X 32 W; = (0,8) W;= (2,2) Wy= (8,0) Suppose it is suggested that the three traders move to the allocation x given by x;= (1,2), x2= (8,4), X3= (1,4) b. Show that x makes no one worse off than the original allocation.John and Belle consume only two goods, x and y. They have strictly convex preferences and no kinks in their indifference curves. At the initial endowment point, the ratio of John's marginal utility of x to his marginal utility of y is J and the ratio of Belle's marginal utility of x to her marginal utility of y is B, where ] B. b. C < J. c. C = J. d. C = B. e. JI 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?Q8. Person A has a utility function uA (X₁, X₂)X₁X₂ and person B has a utility function Agent A and B have identical endowments of (3, 3). 1/3, 2/3 UB (X1, X2)X1X₂ (a) Illustrate this situation in an Edgeworth box diagram. (b) What is the equilibrium relationship between p, and p₂? (c) What is the equilibrium allocation?2) Which of the following utility functions represent the same preferences? Explain. a) U (x₁, x₂) = X₁ X₂ b) W (x₁, x₂) = 5lnx₁ +5lnx₂ c) V (x₁, x₂) = x₁¹/3x₂ ¹/3 - 0.8 d) Z(x₁, x₂) = 0.5x₁ + 0.5x₂3. Anita (A), Ben (B) and Carlos (C) are housemates who have moved to a new house and must decide how to allocate rooms X, Y and Z. An 'allocation' is where each housemate is assigned to exactly one room. For example, Anita → Room Z, Ben → Room X and Carlos → Room Y is allocation (Z, X, Y). Utilities for each room are given below: Room X Utility for A 7 Utility for B 9 Utility for C 2 Room Y 4 3 7 Room Z 2 1 42(b)There are three people and two goods in an economy. The utility functions and the initial bundles are given below: U1 = X11X 12 U2 = 2x 21+ X 22 U3 =X 31 X 32+X 32 W; = (0,8) w (2,2) W3= (8,0) Suppose it is suggested that the three traders move to the allocation x given by x;= (1,2), x2= (8, 4), X3= (1,4) a. Calculate the MRS for the three at the allocation x. b. Show that x makes no one worse off than the original allocation. C. Show that x is not in the core.Problem 2. There are two consumers with the following utility functions: x² + √√√x/²2₂ u² (x1, x²) u? (r, rå) x ²2. Total endowment is e = (1,1). = = = (a) Calculate the set of Pareto optimal allocations (a convincing figure is enough). (b) Assume that the planner wants to implement some Pareto efficient allocation (x¹, x²) ((x1, x²), (x², x²)) where x½ ‡ 0, as an equilibrium with transfers. Prove that any price vector such that 0 < p1 < 2√√x½ can support that allocation (normalizing p2 = : 1). (c) What happens if the planner wants to implement precisely the allocation ((1,0), (0, 1))?SEE MORE QUESTIONSRecommended textbooks for youPrinciples of Economics (12th Edition)EconomicsISBN:9780134078779Author:Karl E. Case, Ray C. Fair, Sharon E. OsterPublisher:PEARSONEngineering Economy (17th Edition)EconomicsISBN:9780134870069Author:William G. Sullivan, Elin M. Wicks, C. Patrick KoellingPublisher:PEARSONPrinciples of Economics (MindTap Course List)EconomicsISBN:9781305585126Author:N. Gregory MankiwPublisher:Cengage LearningManagerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage LearningManagerial Economics & Business Strategy (Mcgraw-…EconomicsISBN:9781259290619Author:Michael Baye, Jeff PrincePublisher:McGraw-Hill EducationPrinciples of Economics (12th Edition)EconomicsISBN:9780134078779Author:Karl E. Case, Ray C. Fair, Sharon E. OsterPublisher:PEARSONEngineering Economy (17th Edition)EconomicsISBN:9780134870069Author:William G. Sullivan, Elin M. Wicks, C. Patrick KoellingPublisher:PEARSONPrinciples of Economics (MindTap Course List)EconomicsISBN:9781305585126Author:N. Gregory MankiwPublisher:Cengage LearningManagerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage LearningManagerial Economics & Business Strategy (Mcgraw-…EconomicsISBN:9781259290619Author:Michael Baye, Jeff PrincePublisher:McGraw-Hill Education