QUESTION 1Alice (A) and Bob (B) have an endowment of goods 1 and 2, with Alice's endowment being (wt, wg) = (1,2) and Bob's endowment equals(wf, wk) = (1,3). Alice's utility is given by u4(x4, x4) = 2 ln xt + In æf , while Bob's utility is up(af, æ}) = In xf + 2 ln æ. Find thecompetitive (Walrasian) equilibrium prices in this pure exchange economy.Select one:Pi = 5, p2 = 3O b. Pi = 3, p2 = 7О а.O c.Pi = 7, p2 = 3O d. Pi = 1, P2 = 4Assume the setting outlined in Question 1. Suppose that the social planner considers it to be imperative that agent B consumes exactly one unitof good 1 and four units of good 2. Although the social planner can not force the individuals to a particular consumption, they can enforcetransfers of good 1 between the consumers (transfers of good 2 are not enforceable by the social planner). What transfer of good 1 wouldguarantee that in the resulting competitive Walrasian equilibrium consumer B consumes one unit of good 1 and four units of good 2?Select one:One half unit of good 1 has to be transferred from agent A to agent B.Ob.There is no endowment for which agent B would consume xf = 1 and a = 4 in the corresponding competitive equilibrium.Therefore, no such transfers exist.Oc.One unit of good 1 has to be transferred from agent A to agent B.Od.Transferring good 1 is not sufficient. It is necessary to transfer one unit of good 2 from agent A to agent B.

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.
Two individuals (A and B) live on an island where they consume coconuts (good x) and bananas (good y) for survival. A owns the coconut producing part of the island and B owns the banana part. Their utility functions and endowments are given by UA (TA,YA) = A+YA +min {A, YA}, UB (TB, YB) = TB +YB + min {ïß, YB}, (ww) = (0, 12) B B Assume that the price of coconuts is p and that of bananas is 1, so relative prices are denoted by p. (ww) = (10,0) A 1. What are their respective budget constraints? 2. What are their individual demand functions? (Hint: you have to consider multiple cases for the value of p) 3. The individuals trade their endowments with each other. What is the competitive equilibrium price in the market? What are their respective utilities at equilibrium?
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Consider an economy with 2 goods and 2 agents. The Örst agent has the utilityfunction, u (x1; x2) = ln x1 + 2 ln x2, and the other one has u (y1; y2) = 2 ln y1 + ln y2.The aggregate endowments of the 2 goods are given by (50; 100). Suppose there is asocial planner who cares about agents equally.(a) Set up the plannerís problem b) Calculate the first-best outcome (i.e., the social plannerís solution).
(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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