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

Section: Chapter Questions

Problem 1QTC

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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.
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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.
Suppose you have the following indirect utility function: V(px, Py, I) = In ( PxPy What are marshallian demands for x and y? O(gx, gy) = (2p, 2p, 2px' 2py O(8x, 8y) = (In , In ) 2px 2py I O(gx, gy) = (exp(2p.Py ), exp( 2p.P, )) 2pxPy %D O(8x» 8y) = ( %3D 2p, +P,' Px+2p, What is the expenditure function for the associated expenditure minimization problem? OE(px, Py, U) = (px + Py) In(U) %3D OE(px, Py, U) = Vexp(U)PxPy %3D OE(Px, Py, U) = (p + p3) In(U) %3D OE(Px, Py, U) = exp(U) PxPy %3D
There are 40 people living in a village each having preference over apples andshirts represented by U(a,b) = a1/3s2/3, where a and s are amount of applesin pounds and shirts consumed, respectively. The price of a shirt is $10. Each villager has $300 income. Apples are supplied to the village by a farmer, whose supply function is S(pa) = 1000pa.Part a1What is the equilibrium price of apples? How many pounds of apples does eachvillager consume?Part a2What is the aggregate net consumer surplus at the equilibrium?Part a3What is the price elasticity of demand at the equilibrium?Part b1Suppose 50 more people move in to the village. What is the equilibrium pricenow? Part b2Are consumers better or worse off now? Why? If a consumer is worse off, byhow much additional income he/she needs to be compensated in order to be aswell off as in Part a.

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