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2) Consider an Exchange economy composed of two individuals A and B and two goodsx1 and...
9) (10 points) Consider an exchange economy composed of two individuals A and B and two goods x1 and X2. A's utility function is given bỵ U,-2X1 + X2. Individual B's utility function is givenby u = xx2. In the economy, the total endowment of xņš 2 and the total endowment of x2 is 1. Normalize p2 to 1. We know that, in this economy eauilibrium price is given bypi-1. a. (6 points) Find the equilibrium allocation b. (4 points,...
4) (8 points) Consider an exchange economy composed of two individuals A and B and two goods xi and x2. Individual A has an endowment of wA2,4) and individual B has an endowment ofw (3,3). A's utility function is given bỵU,-x1 X2. Individual B's utility, function is giyen bỵ UB-X1 X22. Eind the equilibrium price and allocation.
2) This guestion is from Final 2016. Consider an Exchange economx composed of twO individuals A and B and two goods x1 and x2. Individual A has an endowment of WA-(3,5) and individual B has an endowment of Ws- (3,3). A's utility function is given by UA- Xx2 a. (3 points) Show that no matter what utility function B has, there exists a Pareto Efficient (PE) allocation. (i.e. Speciỵa Pareto efficient allocation and explain why it is efficient nomatter what...
3. Consider a general equilibrium model with two individuals (A and B) and two goods (zi and x2). Consumer A has utility function given by Consumer B has utility function given by Consumer A has endowment: 5and and wr = 2. 6, and Consumer B has endowment: (a) Draw the Edgeworth Box for this economy, where the origin for Consumer A is on the bottom-left corner (QA) and the origin for Consumer B is on the top-right corner (Op). Label...
Consider an exchange economy consisting of two people, A and B, endowed with two goods, 1 and 2. Person A is initially endowed with wA(4,8) and person B is initially endowed with w(4,0). Their preferences are given by UA(ri,r2)1 and UB(xi, r2) (a) Write the equation of the contract curve (express as a function of ) (b) Let P2 Find the cornpetitive equilibrium price, pi, and allocations, xA -(zl,r1) and B-B (c) Now suppose that person B's preferences are instead...
Consider a pure exchange economy with two individuals (A and B) and two goods (x and y). The utility functions are given by UA(xA, yA) = min[xA, yA] UB(xB, yB) = min[xB, yB], where xi and yi are the quantities of the two goods consumed by individual i = A, B. The total endowments are wx = 10 and wy = 5. (a) Represent the indifference curves of both individuals in the Edgeworth box and find the Pareto set. (b)...
Consider an exchange economy consisting of two people, A and B, endowed with two goods, 1 and 2. Person A is initially endowed with ωA= (10,0) and person B is initially endowed with ωB= (0,20),where the first component of each vector indicates the endowment of good 1.Their preferences are given by UA(x1, x2) =x10.6x20.4 and UB(x1, x2) = 3x1+x2. Which of the following choices represents the contract curve in this economy (in terms of A’s coordinates)? (a) x2A=(xA1)/3 (b) x2A=(2xA1)/9 ...
Description of the economy: For each of the following problems, consider a 2x2 Exchange Economy with two consumers A and B, and two goods X and Y . The preferences of consumer A can be represented by the utility function uA(xA, yA) = xAyA , where xA is the amount of good A consumed by consumer A, and yA is the amount of good Y consumed by consumer A. The preferences of consumer B can be represented by the utility...
Description of the economy: For each of the following problems, consider a 2x2 Exchange Economy with two consumers A and B, and two goods X and Y . The preferences of consumer A can be represented by the utility function uA(xA, yA) = xAyA , where xA is the amount of good A consumed by consumer A, and yA is the amount of good Y consumed by consumer A. The preferences of consumer B can be represented by the utility...
Consider a pure exchange economy with two consumers and two goods. Total endowments of the two goods are given by X̅=10 and Y̅=20. Consumer A’s utility function is given by UA(XA,YA)=sqrtXAYA.. Consumer B regards the two goods as perfect substitutes with MRS=2. (1) Find the contract curve for this economy. (2) Suppose the initial endowments are given as the following: 2,8), (XA, YA)=(2,8) (XB,YB)=(8,12). Find the set of Pareto efficient allocations that Pareto dominate the endowment poin