In an exchange economy, there are two agents, A and B, and there are 330 total units of x and 330 total units of y. The two consumershave utility functions u(x, y) = x²y and u(x, y) = zy, respectively. The equation of the contract curve in terms of the allocationsof agent A can be written asУА330z AV-ZAwhere the value for V isV=

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Answered: In an exchange economy, there are two…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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Using the Slutsky Equation, show that if a good is inferior, then its (Marshallian) demand curve may or may not be negatively sloped.
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)
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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: 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).
5. Consider Paola willingness to pay to obtain a specific good and her willingness to accept to trade the same good. Let her utility function be given by 0.5 0.5 u(x, x) = x+x5. a) Briefly explain why the willingness to pay and the willingness to accept for the same person over the same good may diverge. b) Assume that her wealth is given by w = P2 = 2, so that x = 100, if the demand for good 1 is zero. Derive the maximum willingness to pay and the minimum willingness to accept for 25 units of good 1, and identify which measure of value is larger? 200 , and the price of good 2 is defined as c) How does your answer change if instead we considered only 1 unit of good 1? d) Under which scenario are the measures of value almost the same? Accurately motivate your answer.
General Equilibrium Consider, U1(x1, y1) = 5(x1y1) 3 + 12 U2(x2, y2) = 3lnx2 + 25lny2 + 10 W1 = (7, 3) and W2 = (4, 6) a. Characterize the Pareto efficient allocations and contract curve b. Which allocations are in the core ? c. Find the Competitive/Walrasian equilibrium for this problem . d. Is the allocation found in c in the core? Why?
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If the initial allocation of goods is not efficient, consumers will: be required to consume somewhere along their contract curve. buy and sell goods at market prices until the marginal rate of substitution is equalized across all consumers. change their tastes and preferences via their utility function to match the market's marginal rate of substitution. not be able to trade goods and achieve Pareto efficiency.
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Consider an exchange economy with two types of agents, A and B, and two goods, x and y. Preferences are given by UA (XA, YA) = = A + 6 ln(y₁) and UB(TB, YB) = ln(TBYB). Suppose the government wants to reach the goal of XB = 5 with the competitive equilibrium by setting a redistribution r such that w₁ = (10,r) and wB = (0,20 - r). 1. Find r reaches the government's goal. Round your answer to 2 decimal points. Let Py = Answer:
For the Robinson-Crusoe economy with one input and two outputs, provide a short essay in which you explain why a Walrasian Equilibrium Allocation exists and what properties it has.

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