wo 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.
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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.
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- Suppose 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.In this farmers market there are two goods, Apples and Oranges (1 and 2) and two consumers, Bill and Joel (A and B). Preferences and endowments are as follows: i) Depict above in an Edgeworth box, include autarkic allocation and indifference curves ii) Identify Pareto efficient allocations using Edgeworth box iii) Šuppose p1 = 6 and p2 =8. Find optimal consumption. u* (xf, x²) = 4rf + x u® (xf, a#) = af + 4r B 2'2 112Come up with an example with four agents and four items in which there is only one Pareto efficient allocation
- Extend the model of the jungle to the case in which the number of houses is smaller than the number of agents. In this case, an allocation is a function from the set of agents to the set H U {homeless} with the property that no two agents are assigned to the same house. Each agent has a preference ordering over H U {homeless}. Assume that this ordering is strict; assume also that every agent prefers to be allocated any house than to be homeless. Define an equilibrium for this extended model and show that it always exists.A small economy has only two consumers, Harold and Irene. Harold's utility function is U(x, y) = x + 50y1/2. Irene's utility function is U(x, y) = x + 5y. Harold is endowed with 500 units of x and 60 units of y. They make trades to reach a Pareto optimal allocation of resources in which both persons consume positive amounts. How much y does Harold consume? 50 units 25 units 28 units O 23 units There is not enough information to determine how much y he will consume.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. JThroughout this problem set, we will look at exchange economies with two goods and two agents. Let X = R², let u denote agent i's utility, and let wie X denote agent i's endowment. 1. Suppose u¹(x¹) = min{ri, 2} and wi = (4,8) for both agents i. (a) Argue that every Pareto optimal allocation has r≥r for both agents i. (b) Argue that every allocation z with r≥r for both agents i is Pareto optimal. (c) Draw an Edgeworth box, with a picture depicting every Pareto-optimal allocation. In this picture, also draw the endowment allocation, and draw each agent's indifference curve through the endowment. (d) Argue that, in any competitive equilibrium, the price of good 2 must be zero. (e) Find all competitive equilibria.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. JTrue/False (1) If the assumptions of the first theorem of welfare economics apply and if the economy is in a competitive equilibrium, then any reallocation that benefits someone must harm someone else.< (2) The second welfare theorem of economics states that if preferences are convex, then any Pareto optimal allocation could be achieved as a competitive equilibrium after some reallocation of initial endowments.<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?Consider a two-agents, two goods economy, in which both agents, A and B, are represented by the following utility function: UA(1, 22) = rr2 UB(y1, Y2) = 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 3. Represent the economy in the Edgeworth box.Bert has an initial endowment consisting of 10 units of food and 1o units of clothing. ernie’s initial endowment consists of 10 units of food and 20 units of clothing. Bert regards food and clothing as perfect 1-for-1 substitutes. Ernie regards them as perfect complements, always wanting to consume 3 units of clothing for every 2 units of food. 1. Describe the set of allocations that are Pareto preferred?2. What price ratio will be required to sustain an allocation on the contract curve?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. 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