Consider a two-agents, two goods economy, in which both agents, A and B, are represented by the following utility function: UA(r1, 12) = rr2 UB(y1, 42) = Y1y There are w units of each good in the economy. 1. Characterize the set of Pareto optimal allocations and represent it in the Edgeworth box. The 3 units of each goods are initially share as follows: A has w units of good 1 and zero unit of good 2; B has zero unit of good 1 and w units of good 2. 2. Determine the Walrasian equilibrium
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- consider an exchange economy with 2 goods (1 and 2) and 2 consumer (A and B). a bundle with x units of good 1 and y units of good 2 is written as (x,y). consumer A has an endowment (4,0) and consumer B has an endowment (12,12). the 2 goods are perfect substitutes for each consumer. consider an allocation in which A receives (1,9) and B receives (15,3) if we can redistribute endowments suitably, it is possible to obtain this allocation as the outcome of a competitive equilibrium. is this true or false? explain carefullyPerson 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?If an allocation is Pareto optimal and if indifference curves between the two goods have no kinks, then (Select all that applies) Group of answer choices a. two consumers who consume both goods must have the same MRS between them, but consumers may consume the goods in different ratios. b. two consumers with the same income who consume both goods must have the same MRS, but if their incomes differ, their MRSs may differ. c. any two consumers who consume both goods must consume them in the same ratio. d. for any two consumers who consume both goods, neither will prefer the other consumer’s bundle to his own. e. all consumers receive the bundle that they prefer to any other bundle the economy could produce for them.
- Two individuals, Fred and Helen, are in an economy with no production, and each have the utility function U = 10XY. Prices of both X and Y are set at $1. Initial endowments for Fred are 10 units of X and 6 units of Y. Helen has 8 units of X and 12 units of Y. Find the general equilibrium prices and allocation, then show that the G.E. allocation is Pareto efficient.Consider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation. a. always for any consumers' preferences b.only if consumers' preferences are exactly the same c. never d. non of the aboveTwo consumers, Budi and Marry, together have 10 apples and 4 oranges. a. Draw the Edgeworth box that shows the set of feasible allocation for the two individuals and two goods b. Suppose Budi has 5 apples and 1 orange, while Marry has 5 apples and 3 oranges. Identify this allocation in the Edgeworth box c. Suppose Budi and Marry have identical utility functions and assume that this utility function exhibits positive marginal utilities for both apples and oranges and a diminishing marginal rate of substitution of apples and oranges. Could the allocation in part (b) be economically efficient?
- Consider a two-good exchange economy with two types of consumers. Type A have the utility function And an endowment of 3 units of good 1 and k units of good 2. Type B has the utility function And an endowment of 6 units of good 1 and 21 - k units of good 2. a. Find the competitive equilibrium outcome and show that the equilibrium price p* = p1/p2 of good 1 in terms of good 2 is p* = 21+k/15. b. Find the income levels (MA; MB) of both types in equilibrium as a function of k. c. Suppose that the government can make a lump-sum transfer of good 2, but it is impossible to transfer good 1. Use your answer to part b to describe the set of income distributions attainable through such transfers. Draw this in a diagram. d. Suppose that the government can affect the initial distribution of resources by varying k. Find the optimal distribution of income if (i) the SWF is W = log(MA) + log(MB) and (ii) W = MA + MB.1.) In an endowment economy with market exchange, let two consumers have preferences given by the utility function U^{h}=(x_{1}^{h})^{a}*(x_{2}^{h})^{1-a}for consumer h (1,2) with endowments given by\omega _{1}^{1}=6, \omega _{2}^{1}=4, \omega_{1}^{2}=4, and \omega_{2}^{2}=6. a.) Calculate the consumers' demand functions. b. Selecting good 2 as the measure of value (i.e. p2=1) and with alpha=1/4, find the equilibrium price of good 1 which implies equilibrium levels of consumption of both goods for both consumers. c. Demonstrate whether both consumers' indifference curves are tangential at the equilibrium. Demonstrate whether both consumers' indifference curves are tangential at the initial endowment.Bluth’s preferences for paper and houses can be expressed as Ub(p, h) = 2pb + hb, while Scott’s preferences can be expressed as Us(p, h) = ps + 2bs. Bluth begins with no paper and 10 houses, whereas Scott begins with 10 units of paper and no houses. 1. Is the starting endowment Pareto efficient? Justify your answer using an Edgeworth box? Determine whether each of the following price pairs is consistent with a competitive equilibrium. If yes, determine the resulting allocation of goods, sketching that equi- librium in your Edgeworth box. If not, explain why not (for what good is there a shortage, for what good is there a surplus?) pp =$3 and ph =$1 along with pp =$1 and ph =$1 Assume that the price of houses is $1. Given that price, determine the highest price pp that is consistent with a competitive equilibrium.
- Below is an edgeworth box of two individuals, Ross and Rosa, in the consumption of two goods, X and Y 1. Consider allocations b-f (meaning points a, b, and f). Which allocations(s)A. are better for Ross than “a” (ignoring Rosa)?B. are better for Rosa than “a” (ignoring Ross)?C. are worse for both Ross and Rosa than “a”?D. are better for both Ross and Rosa than “a”?E. are Pareto superior to “a”?2. Suppose that the initial allocation is point a between Ross and Rosa.A. Discuss how Ross’s condition be made better off without harming Rosa(i.e., Rosa maintains her level of utility).B. Illustrate this in a separate diagram and label point/s as necessary (also,if other point/s will have to be made or incorporated).3. Consider once again that the initial allocation is point a. A. Discuss (very briefly) how point d is reached as a Pareto efficientallocation between Ross and Rosa.B. illustrate this condition in a separate diagram.4. Consider points b, c, d, and e. Now plot the utility…An exchange economy consists of two individuals and two goods. The two individuals have the following Leontief utility functions: Person 1: U1(x1, y1) = 3x1 + y1 Person 2: U2(x2, y2) = x2 + 2y2 Person 1 has an endowment of e1 = (3, 2). Person 2’s endowment is e1 = (3, 4). In an Edgeworth Box diagram, show which allocations are in the core. Describe the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram. Let good y be the numeraire (i.e. set py = 1 and let px = p). What price ratio(s) P* will support a competitive equilibrium allocation for this economy?Consider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation? a. always, for any consumers' preferences b. only if consumers' preferences are exactly the same c. Never d. None of the above