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- Consider a 2-good, 2-agent pure exchange economy where there are 10 units of each good and preferences are represented by UA, UB: R30 →R where UA (XA) = 2XA1 + XA2 and uB (XB) = XB1 + 2XB2- Which 2 of the following 8 options are true: (If you wish to change your response, please untick your selected answer before selecting another answer.) There are initial endowments from which we can have a Walrasian Equilibrium with prices p = (1, 0). O The only Pareto efficient allocation is XA = (10, 0), XB = (0, 10). Every Pareto efficient allocation can be supported as a Walrasian Equilibrium after some reallocation of resources. We cannot apply the First Welfare Theorem because preferences violate local non-satiation. The allocation XA = (5, 10), XB = (5, 0) is Pareto efficient. For all price vectors PER²0, we have p₁z₁ + P2z2 = 0 where z; is the excess demand of good i € {1, 2}. 0 Preferences of both players satisfy strict convexity. At initial endowment eд = (5, 5), eg = (5, 5), there is a…Problem 1: Exchange economy Consider an exchange economy with two consumers, A and B, and two goods, X and Y. Consumer A has an initial endowment TA = i >0 of good X, an initial endowment yA = 0 of good Y, and preferences over consumption bundles that can be represented by the Cobb-Douglas utility function uA(TA: YA) = ", where ra is the quantity of good X, yYA is the quantity of good Y, and a € (0, 1) is a preference parameter. Consumer B has an initial endowment ig = 0 of good X, an initial endow- ment js = j > 0 of good Y, and preferences over consumption bundles that can be represented by the Cobb-Douglas utility function up(rB, YB): B1-3 where rB is the quantity of good X, YB is the quantity of good Y, and BE (0, 1) is a preference parameter. (a) Find the set of Pareto optimal allocations in this economy. In appro- priate diagrams, illustrate the set of Pareto optimal allocations when (i) 3 = a, (ii) 3 > a, and (iii) 3 a.Problem 3: Consider a pure exchange economy with two consumers (4 and B) and two goods (X and Y). Suppose consumers A and B have the utility functions: UA (XA, YA) u³ (XB, YB) = a1-a 81-8 = XBYB a. Derive the equation of the contract curve. b. Let the endowments of the economy be 1 unit of X and 2 units of Y. Show that an equal division of goods (an egalitarian outcome) is not Pareto optimal. What condition on the parameters of the utility functions is required for equal division of goods to be Pareto optimal? 0 < a < 1 0 < 3 <1 3
- In an exchange economy, there are two people (Shadi and Nino) and two goods (x1 and x2). Their initial endowments are ωS = (2, 4) and ωN = (3, 6). Their utility is given by the following functions: US(x1,x2) = x12x23 and UN(x1,x2) = x1x24. Which of the following is the equation for the contract curve? Group of answer choices a. x2N = 96x1N / (15 + 4x1N) b. x2N = 47x1N / (8 + 4x1N) c. x2N = 91x1N / 5 d. x2N = 16x1N / (3 + x1N) e. x2N = 41x1N / (9 + x1N)Consider a pure-exchange economy of two individuals (A and B) and two goods (X and Y). Individual A is endowed with 5 units of good X and 3 units of good Y, while individual B with 3 and 4 units of goods X and Y, respectively. Assuming utility functions of individuals A and B to be UA=XA YA² and UB-XB² YB where Xi and Yi for i= {A, B} represent individual i's consumption of good X and Y respectively, what will be the set of Pareto optimal allocation in this economy?A small exchange economy is comprised of two of individuals, A and B, and two types of goods, x, ,x,. The individuals' preferences over two goods are can be represented by the following utility functions: U*(x;,.x; ) = min (2.x,x; ) and U* (x;,x;) = min(x;.2x, ). Initial endowments are 10 x, (individual A), and 10 x, (individual B). Calculate the price ratio which yields an equilibrium in the exchange market.
- In an exchange economy there are two people (A and B), and two goods (x and Y). Their respective utility functions and endowments are: UA(xA, YA) = 6xA + YA , UB(XB, YB) (10, 10). What is the minimum possible amounts of XA in the core? Round your answer to 2 = xB + 6yB; WA = WB = decimal points. Answer:Give typing answer with explanation and conclusion 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 = (0,10) and person B is initially endowed with ωB = (11,0). They have identical preferences, which are given by U^A(x1,x2) = U^B(x1,x2) = x1^2*x2. Suppose that p2 =1. Under the competitive equilibrium, what is p1? Round answers to two decimal places.4) Consider a pure exchange economy with two goods, (x, y), and two consumers, (1, 2). Consumers' endowments are e1 = (4, 2) and e? = (6, 6) And their preferences are represented by utility functions: u(x, y) = x³y and u(x,y) = x³y$ (d) Set up the utility maximization problem for each consumer and solve for their Marshallian demand functions. (e) Compute the market demand for each good. () State the Walrus law for this economy and explain its economic interpretation. (g) Assume the excess demand for good x is zero, i.e., EDx = 0, and calculate the ratio of prices, i.e., p Ipy . Then, use this ratio of prices to show that the excess demand for good Yis also zero, i.e., EDy= 0. Briefly explain how this relates to the Walrus' law. (h) Given the price ratio found above, calculate the equilibrium allocations and show that feasibility, individual rationality, and Pareto efficiency holds.
- Consider a 2-good, 2-agent pure exchange economy where there are 10 units of each good and preferences are represented by UA, UB: RR where uA (XA) = 2XA1 + XA2 and uB (XB) = XB1 + 2XB2- Which 2 of the following 8 options are true: There are initial endowments from which we can have a Walrasian Equilibrium with prices p = (1, 0). O The only Pareto efficient allocation is XA = (10, 0), XB = (0, 10). Every Pareto efficient allocation can be supported as a Walrasian Equilibrium after some reallocation of resources. We cannot apply the First Welfare Theorem because preferences violate local non-satiation. The allocation XA = (5, 10), XB = (5, 0) is Pareto efficient. For all price vectors PER3 we have p1z₁ + P2z2 = 0 where z; is the excess demand of good i € {1, 2}. O Preferences of both players satisfy strict convexity. At initial endowment eA= (5, 5), eg = (5, 5), there is a Walrasian Equilibrium with prices p = (1, 2).In an exchange economy there are two people (A and B), and two goods ( and ). Their respective utility functions and endowments are: , ; . What is the minimum possible amounts of in the core? Round your answer to 2 decimal points.Consider a pure exchange economy with two goods and two agents, A and B. Agents A and B have the same utility u (1, y) = /TY. Since the agents' initial allocations are given by eA = (4.2) and eB = (2.4), then the Walrasian equilibrium will be composed of the following consumption baskets: %3D O (XA,YA )=(2,2) e (Xg,Ye) = (4,4) (Xa, YA)=(1,0) e (Xg,Yg)=(5,6) (XA,YA)=(2,4) e (Xg,YB)=(4,2) (XA,YA)=(3,3) e (Xg,Ye)=(3,3) o (XA,YA)=(1,1) e (Xg,YB)=(5,5)