Consider the following pure exchange,Edgeworth box economy. There are twoconsumers, Adam and Mark, and two goods.Adam has an endowment of 7 units of good 1and 3 units of good 2 (i.e. wadam = (7, 3)),while Mark has an endowment of 3 units ofgood 1 and 7 units of good2 (wmark$ = (3,7)).The consumers' utility functions are given by:Uadam = Xa1 + Xa2 and Umark = min{xm1,Xm2) where x¡1 is the consumption of good 1by consumer (i = adam, mark)(a) Find the set of Pareto optimal allocationsof this economy(b) Find the Walrasian equilibrium.

(a) pareto optimal allocations are all points where one consumer can not be better off without…

Answered: Consider the following pure exchange,…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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QUESTION 1 Alice (A) and Bob (B) have an endowment of goods 1 and 2, with Alice's endowment being (wt, w) = (1,2) and Bob's endowment equals (wf , w) = (1,3). Alice's utility is given by u4 (xf, xf) = 2 ln xf + In æ£ , while Bob's utility is uB(xf, x}) = ln xf + 2 ln x? . Suppose that the social planner considers it to be imperative that agent B consumes exactly one uni of good 1 and four units of good 2. Although the social planner can not force the individuals to a particular consumption, they can enforce transfers of good 1 between the consumers (transfers of good 2 are not enforceable by the social planner). What transfer of good 1 would guarantee that in the resulting competitive Walrasian equilibrium consumer B consumes one unit of good 1 and four units of good 2? Answer this please Select one: O a. One half unit of good 1 has to be transferred from agent A to agent B. O b. There is no endowment for which agent B would consume x = 1 and x = 4 in the corresponding competitive…
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Suppose there are two consumers A and B, and two goods x and y. A's utility function has the following form UA = XA - (XB)1. Which of the following is true? Consumer A's consumption of good x exhibits a negative externality. Consumer A's consumption of good x exhibits a positive externality. Consumer B's consumption of good x exhibits a negative externality. Consumer B's consumption of good x exhibits a positive externality.
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.
Two individuals A and B have utility functions defined over two goods, a private good 'x') and a public good, 'F. The utility function of an agent 'i' is defined by ui = 2 log xi + log F where F =FA + FB. Each agent has 200 units of private goods x, as his endowment and 1 unit of private good can be transformed into 1 public good F. Answer the following (a) Find the Nash equilibrium values of FA and FB? (b) What is the Pareto optimal level of F? (c) In what condition the Pareto optimal level of F will not depend on the number of private goods? (d) What would be the consumption of x by each agent if they contribute equally towards the public good (F)? (e) Would it change if an agent had a larger endowment of x to begin with?
(5) A has utility function u4(x4) = x4 + x and initial endowment w4 = (3,6). Consumer B has utility function uB (xB) = xf · x% and initial endowment wB = (3,6). Consider an exchange economy with two consumers and two goods. Consumer (a) Is the initial endowment a Pareto efficient allocation? Justify your answer. (b) Find a competitive equilibrium (p, xª, x³) for the economy. (c) Construct the contract curve. A picture here is not a complete answer; you need to specify analytically the set of points that are in the contract curve.
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(1) Consider a small exchange economy with two consumers, A and B, and two commodities, ₁ and 2. Consumer A's initial endowment is 3 units of ₁ and 2 unit of 2. Consumer B's initial endowment has 5 units of 2₁ and 4 units of r2. Consumer A's utility function is given by U(₁, ₁) = x^x^. Consumer B's utility function is given by U(x,x) = 2x² + x2. Note that and are the amounts of the two goods for Consumer A, and rf and are amounts of the two goods for Consumer B. (a) Draw an Edgeworth box, showing the initial allocation. Label it as E. Measure Consumer A's consumption from the lower left and Consumer B's from the upper right. Also measure the number of ₁ on the horizontal axis and the number of r2 on the vertical axis. (b) Draw Consumer A's indifference curve (ICA) going through E. (c) Draw Consumer B's indifference curve (ICB) going through E.
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