ECONOMICS 001 Microeconomic Theory Summer Mid-semester Exam 2. There are two questions. Answer both. Marks are given in parentheses.
|
|
- Richard Riley
- 5 years ago
- Views:
Transcription
1 Microeconomic Theory Summer Mid-semester Exam 2 There are two questions. Answer both. Marks are given in parentheses.. Consider the following 2 2 economy. The utility functions are: u (.) = x x 2 and u 2 (.) = x 2 + 2x 2 2, where x i j denotes the quantity of jth good consumed by ith individual; i =, 2 and j =, 2. Let the initial endowments be e (.) = (3/4, 3/8) and e 2 (.) = (/4, 5/8), respectively. Assume that individuals act as price-takers. (a) Is (e (.), e 2 (.), as above, a Pareto optimum allocation? (b) Does there exist a Walrasian equilibrium for the above economy? (c) Is the Walrasian equilibrium unique? Prove your claims. ( ) 2. Consider two small and open economies; A and B. Each economy produces two goods f and c. A good is produced using two factors of production labour; l, and capital, t. There is free flow of outputs (goods) across countries. But, factors of production cannot move across countries. With the help of a suitable general equilibrium model answer the following: (a) Demonstrate the effect of changes in the relative output prices on the relative factor prices, assuming that in both economies f is labour intensive and c is capital intensive. (b) Suppose in economy A, f is labour intensive but c is capital intensive. However, in economy B, f is capital intensive and c is labour intensive. Discuss the effect of changes in factor endowment on the output levels for the two economies. Provide complete formulation for your answer. (4 + 6)
2 Microeconomic Theory Summer Mid-semester Exam 2 There are two questions. Answer both. Marks are given in parentheses.. Consider an economy consisting of two individuals; i =, 2. There are two goods; x and x 2. Utility functions are: u i (x i.x i 2) = x i.x i 2, for i =, 2. Endowments are: e = (2, 8), e 2 = (8, 2), respectively. For this economy: (a) Does allocation x = (x, x 2 ), such that x = (4, 4) and x 2 = (6, 6), belong to the Core? (b) Does the Core have an envy-free allocation? Is it unique? (c) Next, let us expand the above economy by including individuals 3 and 4. So, now the total number of individuals is four. For individuals 3 and 4, utility functions are: u i (x i.x i 2) = x i.x i 2, for i = 3, 4. Endowments are: e 3 = (2, 8), and e 4 = (8, 2). Does allocation x = (x, x 2, x 3, x 4 ) belong to the Core, when x = (4, 4) = x 3 and x 2 = (6, 6) = x 4? Prove your claims. (2+3+3) 2. Consider a pure exchange economy consisting of n individuals, and m goods, ({u i (x i )} n i=, {e i } n i=), where u i (x i ) : R m + R is continuous, strongly increasing and strictly quasi-concave for each i =,.., n. Further, endowment e i R m + are such that n i= ei >> 0. Let z(p) : R m ++ R m denote the excess demand function. Let P be the set of Pareto optimum allocations. Assume that for every profile of endowments (e, e 2,..., e n ), such that n i= ei >> 0, there exists a price vector p R m ++ such that z(p ) = 0. Prove that: (a) The set of Pareto optimum allocations, i.e., P, is non-empty. (b) Every y P can be supported as a Walrasian equilibrium through a suitable transfers of initial endowments. (Note: You are not allowed to use any other information/results, apart from those mentioned here.) (3+4)
3 Microeconomic Theory Summer Mid-semester Exam 2 There are two questions. Answer both. Marks are given in parentheses.. Consider an economy consisting of four individuals; i =,..., 4. There are two goods; x and x 2. Utility functions are: u i (x i.x i 2) = x i.x i 2, for i =,..., 4. Endowments are: e = (, 9), e 2 = (9, ), e 3 = (, 9), and e 4 = (9, ), respectively. (a) Does allocation x = (x, x 2, x 3, x 4 ) belong to the Core, when x = (3, 3) = x 3 and x 2 = (7, 7) = x 4? (b) Does allocation x = (x, x 2, x 3, x 4 ) belong to the Core, when x = (3, 3), x 2 = (7, 7), x 3 = (4, 4), and x 4 = (6, 6)? (c) Suppose ( p, p 2 ) is an equilibrium price vector when the economy consists of only the first two individuals. Is ( p, p 2 ) is also an equilibrium price vector for the above economy consisting of all four individuals? Prove your claims. OR (2+3+3) Consider a pure exchange economy consisting of two individuals, and 2. There are two goods; x and y. Individual strictly prefers bundle (a, b) to bundle (c, d) if, either a > c, or a = c and b > d. Individual 2 s preferences are represented by the utility functions u(x, y) = αx 2 + βy 2, α, β > 0. The endowments are e = (e x, e y) >> (0, 0) and e 2 = (e 2 x, e 2 y) >> (0, 0). Moreover, e x + e 2 x > e y + e 2 y. For this economy: (a) Find out the set of Pareto optimum allocations. (b) Does a competitive equilibrium exist? [Hint: Think in terms of the location of the endowment vector in the Edgeworth box.] Fully explain your answers. (3+5)
4 2. Consider a pure exchange economy consisting of N individuals and M goods, ({u i (x i )} N i=, {e i } N i=), where u i (x i ) : R M + R is continuous, strongly increasing and strictly quasi-concave for each i =,.., N. Further, endowment e i R M + are such that n i= ei >> 0. Let C(e) be the set of Core allocations. For this economy, prove the following. There exists an allocation (x, x 2,..., x N ) C(e) with following properties: For all i, j {,..., N} (a) [u i (.) = u j (.) and e i = e j ] [x i = x j ] (b) [u i (.) = u j (.) and e i e j ] [u i (x i ) > u j (x j )] (c) e i = e j [u i (x i ) u i (x j )], and e i e j [u i (x i ) > u i (x j )] Note: x y holds if every component of vector x is at least as large as the corresponding component of vector y, but one or more components are strictly greater. (3+2+2) 2
5 Micro Economics Summer Mid Semester Exam 2 Answer question 3, and EITHER question OR question 2. Consider a two-person two-goods pure exchange economy. The initial endowment vectors are e = (, 0) and e 2 = (0, ). The two individuals have identical preferences represented by the utility functions: {, when x + y < u (x, y) = u 2 (x, y) = x + y, when x + y, where x is the quantity of the first good and y is the quantity of the second good. For this economy: (a) Find out the set of Walrasian/competitive equilibria, assuming p = p 2 =. (b) Find out the set of Pareto optimum allocations. (c) Will the equal division of the initial endowments be a Pareto efficient allocation? Explain your findings, in view of the results/thoerems regarding Pareto efficiency of Walrasian/competitive equilibria and equal division of initial endowments. (2+3+2) 2. Consider a pure exchange economy; (u i (.), e i ) i I. Let x = (x, x 2,..., x I ) be a feasible allocation. Suppose x is Pareto superior to e. However, there exists a blocking coalition, S {,..., I}, for x = (x, x 2,..., x I ). Which of the following is necessarily true? (a) There exists at least one allocation z = (z, z 2,..., z I ) such that z x, and z is Pareto superior to e. (b) The allocation z = (z, z 2,..., z I ), as in part (a) above belongs to the Core. Explain your answer. (4+3)
6 3. Consider a two person two goods production economy. The goods are; x and y. The utility functions are: u (x, y ) = ln x + ln y u 2 (x 2, y 2 ) = x α 2.y2 α, where x i and y i is the quantity consumed by person i of good x and y, respectively, and α =. The initial endowments are 4 e (.) = e 2 (.) = ( 2, 2 ). The production sector uses x to produce y, subject to a constant returns to scale technology. So, the profits are zero for each firm as well as for the entire production sector. For this economy, (a) Derive the individual demand functions and then the excess demand functions. (b) Find out competitive equilibrium price and allocation vectors when the production function is y = x, assuming that the production sector will meet all the demand as long as profits are non-negative. (c) Find out competitive equilibrium price and allocation vectors when the production function is y = 3x, assuming that the production sector will meet all the demand as long as profits are non-negative. (3+3+2) 2
Market Equilibrium and the Core
Market Equilibrium and the Core Ram Singh Lecture 3-4 September 22/25, 2017 Ram Singh (DSE) Market Equilibrium September 22/25, 2017 1 / 19 Market Exchange: Basics Let us introduce price in our pure exchange
More informationFundamental Theorems of Welfare Economics
Fundamental Theorems of Welfare Economics Ram Singh Lecture 6 September 29, 2015 Ram Singh: (DSE) General Equilibrium Analysis September 29, 2015 1 / 14 First Fundamental Theorem The First Fundamental
More informationMarket Outcomes: Efficient or Fair?
Market Outcomes: Efficient or Fair? Ram Singh Microeconomic Theory Lecture 14 Ram Singh: (DSE) Market Equilibrium Lecture 14 1 / 16 Fair Versus Efficient Question 1 What is a fair allocation? 2 Is a fair
More information4 Lecture Applications
4 Lecture 4 4.1 Applications We now will look at some of the applications of the convex analysis we have learned. First, we shall us a separation theorem to prove the second fundamental theorem of welfare
More informationCore. Ichiro Obara. December 3, 2008 UCLA. Obara (UCLA) Core December 3, / 22
Ichiro Obara UCLA December 3, 2008 Obara (UCLA) Core December 3, 2008 1 / 22 in Edgeworth Box Core in Edgeworth Box Obara (UCLA) Core December 3, 2008 2 / 22 in Edgeworth Box Motivation How should we interpret
More informationThe Ohio State University Department of Economics. Homework Set Questions and Answers
The Ohio State University Department of Economics Econ. 805 Winter 00 Prof. James Peck Homework Set Questions and Answers. Consider the following pure exchange economy with two consumers and two goods.
More information1 General Equilibrium
1 General Equilibrium 1.1 Pure Exchange Economy goods, consumers agent : preferences < or utility : R + R initial endowments, R + consumption bundle, =( 1 ) R + Definition 1 An allocation, =( 1 ) is feasible
More informationWelfare Economics: Lecture 12
Welfare Economics: Lecture 12 Ram Singh Course 001 October 20, 2014 Ram Singh: (DSE) Welfare Economics October 20, 2014 1 / 16 Fair Vs Efficient Question 1 What is a fair allocation? 2 Is a fair allocation
More informationMicroeconomics II. MOSEC, LUISS Guido Carli Problem Set n 3
Microeconomics II MOSEC, LUISS Guido Carli Problem Set n 3 Problem 1 Consider an economy 1 1, with one firm (or technology and one consumer (firm owner, as in the textbook (MWG section 15.C. The set of
More informationDifferentiable Welfare Theorems Existence of a Competitive Equilibrium: Preliminaries
Differentiable Welfare Theorems Existence of a Competitive Equilibrium: Preliminaries Econ 2100 Fall 2017 Lecture 19, November 7 Outline 1 Welfare Theorems in the differentiable case. 2 Aggregate excess
More informationFirst Welfare Theorem
First Welfare Theorem Econ 2100 Fall 2017 Lecture 17, October 31 Outline 1 First Welfare Theorem 2 Preliminaries to Second Welfare Theorem Past Definitions A feasible allocation (ˆx, ŷ) is Pareto optimal
More informationThe Consumer, the Firm, and an Economy
Andrew McLennan October 28, 2014 Economics 7250 Advanced Mathematical Techniques for Economics Second Semester 2014 Lecture 15 The Consumer, the Firm, and an Economy I. Introduction A. The material discussed
More informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program May 2012
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program May 2012 The time limit for this exam is 4 hours. It has four sections. Each section includes two questions. You are
More informationIn the Name of God. Sharif University of Technology. Microeconomics 1. Graduate School of Management and Economics. Dr. S.
In the Name of God Sharif University of Technology Graduate School of Management and Economics Microeconomics 1 44715 (1396-97 1 st term) - Group 1 Dr. S. Farshad Fatemi Chapter 10: Competitive Markets
More informationNotes on General Equilibrium
Notes on General Equilibrium Alejandro Saporiti Alejandro Saporiti (Copyright) General Equilibrium 1 / 42 General equilibrium Reference: Jehle and Reny, Advanced Microeconomic Theory, 3rd ed., Pearson
More informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2016
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2016 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationGeneral Equilibrium. General Equilibrium, Berardino. Cesi, MSc Tor Vergata
General Equilibrium Equilibrium in Consumption GE begins (1/3) 2-Individual/ 2-good Exchange economy (No production, no transaction costs, full information..) Endowment (Nature): e Private property/ NO
More informationGeneral Equilibrium with Production
General Equilibrium with Production Ram Singh Microeconomic Theory Lecture 11 Ram Singh: (DSE) General Equilibrium: Production Lecture 11 1 / 24 Producer Firms I There are N individuals; i = 1,..., N There
More informationEC487 Advanced Microeconomics, Part I: Lecture 5
EC487 Advanced Microeconomics, Part I: Lecture 5 Leonardo Felli 32L.LG.04 27 October, 207 Pareto Efficient Allocation Recall the following result: Result An allocation x is Pareto-efficient if and only
More informationGeneral Equilibrium and Welfare
and Welfare Lectures 2 and 3, ECON 4240 Spring 2017 University of Oslo 24.01.2017 and 31.01.2017 1/37 Outline General equilibrium: look at many markets at the same time. Here all prices determined in the
More informationEconomics 200A part 2 UCSD Fall quarter 2011 Prof. R. Starr Mr. Troy Kravitz1 FINAL EXAMINATION SUGGESTED ANSWERS
Economics 200A part 2 UCSD Fall quarter 2011 Prof. R. Starr Mr. Troy Kravitz1 FINAL EXAMINATION SUGGESTED ANSWERS This exam is take-home, open-book, open-notes. You may consult any published source (cite
More informationExistence, Computation, and Applications of Equilibrium
Existence, Computation, and Applications of Equilibrium 2.1 Art and Bart each sell ice cream cones from carts on the boardwalk in Atlantic City. Each day they independently decide where to position their
More informationMicroeconomic Theory -1- Introduction
Microeconomic Theory -- Introduction. Introduction. Profit maximizing firm with monopoly power 6 3. General results on maximizing with two variables 8 4. Model of a private ownership economy 5. Consumer
More informationA : a b c d a : B C A E B : d b c a b : C A B D E C : d c a c : E D B C D : a d b d : A D E B C E : a b d. A : a b c d a : B C A D E
Microeconomics II( ECO 50) Questions on the comprehensive exam will be chosen from the list below( with possible minor variations) CALCULATORS ARE ALLOWED Matching. Consider the Gale-Shapley marriage problem
More informationEquilibrium in Factors Market: Properties
Equilibrium in Factors Market: Properties Ram Singh Microeconomic Theory Lecture 12 Ram Singh: (DSE) Factor Prices Lecture 12 1 / 17 Questions What is the relationship between output prices and the wage
More informationRegularity of competitive equilibria in a production economy with externalities
Regularity of competitive equilibria in a production economy with externalities Elena del Mercato Vincenzo Platino Paris School of Economics - Université Paris 1 Panthéon Sorbonne QED-Jamboree Copenhagen,
More informationThe Fundamental Welfare Theorems
The Fundamental Welfare Theorems The so-called Fundamental Welfare Theorems of Economics tell us about the relation between market equilibrium and Pareto efficiency. The First Welfare Theorem: Every Walrasian
More informationCompetitive Equilibrium
Competitive Equilibrium Econ 2100 Fall 2017 Lecture 16, October 26 Outline 1 Pareto Effi ciency 2 The Core 3 Planner s Problem(s) 4 Competitive (Walrasian) Equilibrium Decentralized vs. Centralized Economic
More informationThe Walrasian Model and Walrasian Equilibrium
The Walrasian Model and Walrasian Equilibrium 1.1 There are only two goods in the economy and there is no way to produce either good. There are n individuals, indexed by i = 1,..., n. Individual i owns
More informationIntroduction to General Equilibrium
Introduction to General Equilibrium Juan Manuel Puerta November 6, 2009 Introduction So far we discussed markets in isolation. We studied the quantities and welfare that results under different assumptions
More informationIntroduction to General Equilibrium: Framework.
Introduction to General Equilibrium: Framework. Economy: I consumers, i = 1,...I. J firms, j = 1,...J. L goods, l = 1,...L Initial Endowment of good l in the economy: ω l 0, l = 1,...L. Consumer i : preferences
More informationThe Debreu-Scarf Theorem: The Core Converges to the Walrasian Allocations
The Debreu-Scarf Theorem: The Core Converges to the Walrasian Allocations We ve shown that any Walrasian equilibrium allocation (any WEA) is in the core, but it s obvious that the converse is far from
More informationEconomics 501B Final Exam Fall 2017 Solutions
Economics 501B Final Exam Fall 2017 Solutions 1. For each of the following propositions, state whether the proposition is true or false. If true, provide a proof (or at least indicate how a proof could
More informationAdvanced Microeconomic Theory. Chapter 6: Partial and General Equilibrium
Advanced Microeconomic Theory Chapter 6: Partial and General Equilibrium Outline Partial Equilibrium Analysis General Equilibrium Analysis Comparative Statics Welfare Analysis Advanced Microeconomic Theory
More informationPhD Qualifier Examination
PhD Qualifier Examination Department of Agricultural Economics July 26, 2013 Instructions The exam consists of six questions. You must answer all questions. If you need an assumption to complete a question,
More informationDepartment of Economics The Ohio State University Final Exam Questions and Answers Econ 8712
Prof. Peck Fall 20 Department of Economics The Ohio State University Final Exam Questions and Answers Econ 872. (0 points) The following economy has two consumers, two firms, and three goods. Good is leisure/labor.
More informationAdvanced Microeconomics Problem Set 1
dvanced Microeconomics Problem Set László Sándor Central European University Pareto optima With Cobb-Douglas utilities u x ; x 2 ; x 3 = 0:4 log x 2 + 0:6 log x 3 and u x ; x 2 ; x 3 = log x 2 + log x
More informationQuestion 1. (p p) (x(p, w ) x(p, w)) 0. with strict inequality if x(p, w) x(p, w ).
University of California, Davis Date: August 24, 2017 Department of Economics Time: 5 hours Microeconomics Reading Time: 20 minutes PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE Please answer any three
More informationCore equivalence and welfare properties without divisible goods
Core equivalence and welfare properties without divisible goods Michael Florig Jorge Rivera Cayupi First version November 2001, this version May 2005 Abstract We study an economy where all goods entering
More informationEconomics 201B Second Half. Lecture 12-4/22/10. Core is the most commonly used. The core is the set of all allocations such that no coalition (set of
Economics 201B Second Half Lecture 12-4/22/10 Justifying (or Undermining) the Price-Taking Assumption Many formulations: Core, Ostroy s No Surplus Condition, Bargaining Set, Shapley-Shubik Market Games
More informationThe Definition of Market Equilibrium The concept of market equilibrium, like the notion of equilibrium in just about every other context, is supposed to capture the idea of a state of the system in which
More informationSecond Welfare Theorem
Second Welfare Theorem Econ 2100 Fall 2015 Lecture 18, November 2 Outline 1 Second Welfare Theorem From Last Class We want to state a prove a theorem that says that any Pareto optimal allocation is (part
More informationMarket Equilibrium Price: Existence, Properties and Consequences
Market Equilibrium Price: Existence, Properties and Consequences Ram Singh Lecture 5 Ram Singh: (DSE) General Equilibrium Analysis 1 / 14 Questions Today, we will discuss the following issues: How does
More informationAnswers to Spring 2014 Microeconomics Prelim
Answers to Spring 204 Microeconomics Prelim. To model the problem of deciding whether or not to attend college, suppose an individual, Ann, consumes in each of two periods. She is endowed with income w
More informationThe Fundamental Welfare Theorems
The Fundamental Welfare Theorems The so-called Fundamental Welfare Theorems of Economics tell us about the relation between market equilibrium and Pareto efficiency. The First Welfare Theorem: Every Walrasian
More informationLecture Notes October 18, Reading assignment for this lecture: Syllabus, section I.
Lecture Notes October 18, 2012 Reading assignment for this lecture: Syllabus, section I. Economic General Equilibrium Partial and General Economic Equilibrium PARTIAL EQUILIBRIUM S k (p o ) = D k k (po
More informationDuality. for The New Palgrave Dictionary of Economics, 2nd ed. Lawrence E. Blume
Duality for The New Palgrave Dictionary of Economics, 2nd ed. Lawrence E. Blume Headwords: CONVEXITY, DUALITY, LAGRANGE MULTIPLIERS, PARETO EFFICIENCY, QUASI-CONCAVITY 1 Introduction The word duality is
More informationProblem Set Suggested Answers
Problem Set 3 --- Suggested Answers 1. In chapters 15 18 the treatment is generalized to unbounded production technologies, resulting in the observation that when general equilibrium prices are announced,
More informationAdvanced Microeconomics
Advanced Microeconomics Partial and General Equilibrium Giorgio Fagiolo giorgio.fagiolo@sssup.it http://www.lem.sssup.it/fagiolo/welcome.html LEM, Sant Anna School of Advanced Studies, Pisa (Italy) Part
More informationNotes IV General Equilibrium and Welfare Properties
Notes IV General Equilibrium and Welfare Properties In this lecture we consider a general model of a private ownership economy, i.e., a market economy in which a consumer s wealth is derived from endowments
More informationLecture #3. General equilibrium
Lecture #3 General equilibrium Partial equilibrium equality of demand and supply in a single market (assumption: actions in one market do not influence, or have negligible influence on other markets) General
More informationEconomic Core, Fair Allocations, and Social Choice Theory
Chapter 9 Nathan Smooha Economic Core, Fair Allocations, and Social Choice Theory 9.1 Introduction In this chapter, we briefly discuss some topics in the framework of general equilibrium theory, namely
More informationMarket Failure: Externalities
Market Failure: Externalities Ram Singh Lecture 21 November 10, 2015 Ram Singh: (DSE) Externality November 10, 2015 1 / 18 Questions What is externality? What is implication of externality for efficiency
More informationDepartment of Economics The Ohio State University Midterm Answers Econ 805
Department of Economics The Ohio State University Midterm Answers Econ 805 Prof. James Peck Winter 0. (0 points) Consider the following pure-exchange economy with two consumers and two goods. Consumer
More informationEcon 401A: Economic Theory Mid-term. Answers
. Labor suly Econ 40: Economic Theory Mid-term nswers (a) Let be labor suly. Then x 4 The key ste is setting u the budget constraint. x w w(4 x ) Thus the budget constraint can be rewritten as follows:
More informationLecture 1. History of general equilibrium theory
Lecture 1 History of general equilibrium theory Adam Smith: The Wealth of Nations, 1776 many heterogeneous individuals with diverging interests many voluntary but uncoordinated actions (trades) results
More informationPositive Theory of Equilibrium: Existence, Uniqueness, and Stability
Chapter 7 Nathan Smooha Positive Theory of Equilibrium: Existence, Uniqueness, and Stability 7.1 Introduction Brouwer s Fixed Point Theorem. Let X be a non-empty, compact, and convex subset of R m. If
More informationWalrasian Equilibrium in an exchange economy
Microeconomic Teory -1- Walrasian equilibrium Walrasian Equilibrium in an ecange economy 1. Homotetic preferences 2 2. Walrasian equilibrium in an ecange economy 11 3. Te market value of attributes 18
More informationLecture 7: General Equilibrium - Existence, Uniqueness, Stability
Lecture 7: General Equilibrium - Existence, Uniqueness, Stability In this lecture: Preferences are assumed to be rational, continuous, strictly convex, and strongly monotone. 1. Excess demand function
More information5.1 THE ROBINSON CRUSOE ECONOMY
Essential Microeconomics -- 5 THE ROBINSON CRUSOE ECONOMY Ke ideas: Walrasian equilibrium allocation, otimal allocation, invisible hand at work A simle econom with roduction Two commodities, H consumers,
More informationGeneral equilibrium with externalities and tradable licenses
General equilibrium with externalities and tradable licenses Carlos Hervés-Beloso RGEA. Universidad de Vigo. e-mail: cherves@uvigo.es Emma Moreno-García Universidad de Salamanca. e-mail: emmam@usal.es
More information; p. p y p y p y. Production Set: We have 2 constraints on production - demand for each factor of production must be less than its endowment
Exercise 1. Consider an economy with produced goods - x and y;and primary factors (these goods are not consumed) of production A and. There are xedcoe±cient technologies for producing x and y:to produce
More information1 Second Welfare Theorem
Econ 701B Fall 018 University of Pennsylvania Recitation : Second Welfare Theorem Xincheng Qiu (qiux@sas.upenn.edu) 1 Second Welfare Theorem Theorem 1. (Second Welfare Theorem) An economy E satisfies (A1)-(A4).
More informationProblem Set 1 Welfare Economics
Problem Set 1 Welfare Economics Solutions 1. Consider a pure exchange economy with two goods, h = 1,, and two consumers, i =1,, with utility functions u 1 and u respectively, and total endowment, e = (e
More informationAdding Production to the Theory
Adding Production to the Theory We begin by considering the simplest situation that includes production: two goods, both of which have consumption value, but one of which can be transformed into the other.
More information0 Aims of this course
THE UNIVERSITY OF SOUTHAMPTON Paul Klein Office: Murray Building, 35 Email: p.klein@soton.ac.uk URL: http://paulklein.se Economics 31 Topics in Macroeconomics 3 Fall 21 Aims of this course Clear, critical
More informationEntrance Examination for M. A. Economics, Option A (Series 01) Time. 3 hours Maximum marks. 100
Entrance Examination for M. A. Economics, 2014 Option A (Series 01) Time. 3 hours Maximum marks. 100 General Instructions. Please read the following instructions carefully: Check that you have a bubble-sheet
More informationAdvanced Microeconomics
Advanced Microeconomics Leonardo Felli EC441: Room D.106, Z.332, D.109 Lecture 8 bis: 24 November 2004 Monopoly Consider now the pricing behavior of a profit maximizing monopolist: a firm that is the only
More informationMathematical models in economy. Short descriptions
Chapter 1 Mathematical models in economy. Short descriptions 1.1 Arrow-Debreu model of an economy via Walras equilibrium problem. Let us consider first the so-called Arrow-Debreu model. The presentation
More informationMicroeconomics Qualifying Exam
Summer 2013 Microeconomics Qualifying Exam There are 72 points possible on this exam, 36 points each for Prof. Lozada s questions and Prof. Kiefer s questions. However, Prof. Lozada s questions are weighted
More informationPractice Questions for Mid-Term I. Question 1: Consider the Cobb-Douglas production function in intensive form:
Practice Questions for Mid-Term I Question 1: Consider the Cobb-Douglas production function in intensive form: y f(k) = k α ; α (0, 1) (1) where y and k are output per worker and capital per worker respectively.
More informationAnswer Key for M. A. Economics Entrance Examination 2017 (Main version)
Answer Key for M. A. Economics Entrance Examination 2017 (Main version) July 4, 2017 1. Person A lexicographically prefers good x to good y, i.e., when comparing two bundles of x and y, she strictly prefers
More informationEssential Microeconomics : EQUILIBRIUM AND EFFICIENCY WITH PRODUCTION Key ideas: Walrasian equilibrium, first and second welfare theorems
Essential Microeconomics -- 5.2: EQUILIBRIUM AND EFFICIENCY WITH PRODUCTION Key ideas: Walrasian equilibrium, irst and second welare teorems A general model 2 First welare Teorem 7 Second welare teorem
More informationFirms and returns to scale -1- Firms and returns to scale
Firms and returns to scale -1- Firms and returns to scale. Increasing returns to scale and monopoly pricing 2. Constant returns to scale 19 C. The CRS economy 25 D. pplication to trade 47 E. Decreasing
More informationPatryk Pagacz. Equilibrium theory in infinite dimensional Arrow-Debreu s model. Uniwersytet Jagielloński
Patryk Pagacz Uniwersytet Jagielloński Equilibrium theory in infinite dimensional Arrow-Debreu s model Praca semestralna nr 1 (semestr zimowy 2010/11) Opiekun pracy: Marek Kosiek Uniwersytet Jagielloński
More informationEquilibrium and Pareto Efficiency in an exchange economy
Microeconomic Teory -1- Equilibrium and efficiency Equilibrium and Pareto Efficiency in an excange economy 1. Efficient economies 2 2. Gains from excange 6 3. Edgewort-ox analysis 15 4. Properties of a
More information1 Jan 28: Overview and Review of Equilibrium
1 Jan 28: Overview and Review of Equilibrium 1.1 Introduction What is an equilibrium (EQM)? Loosely speaking, an equilibrium is a mapping from environments (preference, technology, information, market
More informationGENERAL EQUILIBRIUM: EXCESS DEMAND AND THE RÔLE OF PRICES
Prerequisites Almost essential General equilibrium: Basics Useful, but optional General Equilibrium: Price Taking GENERAL EQUILIBRIUM: EXCESS DEMAND AND THE RÔLE OF PRICES MICROECONOMICS Principles and
More information3.2 THE FUNDAMENTAL WELFARE THEOREMS
Essential Microeconomics -1-3.2 THE FUNDMENTL WELFRE THEOREMS Walrasian Equilibrium 2 First welfare teorem 3 Second welfare teorem (conve, differentiable economy) 12 Te omotetic preference 2 2 economy
More informationEconomics 604: Microeconomics Deborah Minehart & Rachel Kranton
Economics 604: Microeconomics Deborah Minehart & Rachel Kranton Matthew Chesnes Updated: May 12, 2005 1 Lecture 1: January 27, 2005 1.1 General Equilibrium Model (GE) Primitives: agents (consumers and
More informationContracts under Asymmetric Information
Contracts under Asymmetric Information 1 I Aristotle, economy (oiko and nemo) and the idea of exchange values, subsequently adapted by Ricardo and Marx. Classical economists. An economy consists of a set
More informationAlp Simsek (MIT) Recitation Notes: 1. Gorman s Aggregation Th eorem2. Normative Representative November 9, Household Theorem / 16
14.452 Recitation Notes: 1. Gorman s Aggregation Theorem 2. Normative Representative Household Theorem 3. Representative Firm Theorem (Recitation 2 on November 6, 2009) (Reference: "Introduction to Modern
More information3. THE EXCHANGE ECONOMY
Essential Microeconomics -1-3. THE EXCHNGE ECONOMY Pareto efficient allocations 2 Edgewort box analysis 5 Market clearing prices 13 Walrasian Equilibrium 16 Equilibrium and Efficiency 22 First welfare
More informationLecture Notes for January 8, 2009; part 2
Economics 200B Prof. R. Starr UCSD Winter 2009 Lecture Notes for January 8, 2009; part 2 Integrating Production and Multiple Consumption Decisions: A2 2 2 Model Competitive Equilibrium: Production and
More informationThe Existence of Equilibrium in. Infinite-Dimensional Spaces: Some Examples. John H. Boyd III
The Existence of Equilibrium in Infinite-Dimensional Spaces: Some Examples John H. Boyd III April 1989; Updated June 1995 Abstract. This paper presents some examples that clarify certain topological and
More informationSimon Fraser University, Department of Economics, Econ 201, Prof. Karaivanov FINAL EXAM Answer key
Simon Fraser University, Department of Economics, Econ 01, Prof. Karaivanov 017 FINAL EXAM Answer key I. TRUE or FALSE (5 pts each). [The answers below are just examples of correct answers, other possible
More informationFirms and returns to scale -1- John Riley
Firms and returns to scale -1- John Riley Firms and returns to scale. Increasing returns to scale and monopoly pricing 2. Natural monopoly 1 C. Constant returns to scale 21 D. The CRS economy 26 E. pplication
More informationInformed Principal in Private-Value Environments
Informed Principal in Private-Value Environments Tymofiy Mylovanov Thomas Tröger University of Bonn June 21, 2008 1/28 Motivation 2/28 Motivation In most applications of mechanism design, the proposer
More informationUnlinked Allocations in an Exchange Economy with One Good and One Bad
Unlinked llocations in an Exchange Economy with One Good and One ad Chiaki Hara Faculty of Economics and Politics, University of Cambridge Institute of Economic Research, Hitotsubashi University pril 16,
More informationDepartment of Agricultural Economics. PhD Qualifier Examination. May 2009
Department of Agricultural Economics PhD Qualifier Examination May 009 Instructions: The exam consists of six questions. You must answer all questions. If you need an assumption to complete a question,
More information5. Externalities and Public Goods. Externalities. Public Goods types. Public Goods
5. Externalities and Public Goods 5. Externalities and Public Goods Externalities Welfare properties of Walrasian Equilibria rely on the hidden assumption of private goods: the consumption of the good
More informationShort correct answers are sufficient and get full credit. Including irrelevant (though correct) information in an answer will not increase the score.
Economics 200A Part 2 UCSD Fall 2012 Prof. R. Starr, Mr. Troy Kravitz Final Exam 1 Your Name: Please answer all questions. Each of the six questions marked with a big number counts equally. Designate your
More informationAdvanced Microeconomic Analysis Solutions to Midterm Exam
Advanced Microeconomic Analsis Solutions to Midterm Exam Q1. (0 pts) An individual consumes two goods x 1 x and his utilit function is: u(x 1 x ) = [min(x 1 + x x 1 + x )] (a) Draw some indifference curves
More information(ii) An input requirement set for this technology is clearly not convex as it
LONDON SCHOOL OF ECONOMICS Department of Economics Leonardo Felli 32L.4.02; 7525 Solutions to Assignment 5 EC487 Advanced Microeconomics Part I 1. Sketch of the answers: (i) The map of isoquants for this
More information5. Externalities and Public Goods
5. Externalities and Public Goods Welfare properties of Walrasian Equilibria rely on the hidden assumption of private goods: the consumption of the good by one person has no effect on other people s utility,
More informationECON 255 Introduction to Mathematical Economics
Page 1 of 5 FINAL EXAMINATION Winter 2017 Introduction to Mathematical Economics April 20, 2017 TIME ALLOWED: 3 HOURS NUMBER IN THE LIST: STUDENT NUMBER: NAME: SIGNATURE: INSTRUCTIONS 1. This examination
More informationIMPOSSIBILITY OF A WALRASIAN BARGAINING SOLUTION 1
IMPOSSIBILITY OF A WALRASIAN BARGAINING SOLUTION 1 Murat R. Sertel 2 Turkish Academy of Sciences Muhamet Yıldız 3 MIT Forthcoming in Koray and Sertel (eds.) Advances in Economic Design, Springer, Heidelberg.
More informationCompetitive Market Mechanisms as Social Choice Procedures
Competitive Market Mechanisms as Social Choice Procedures Peter J. Hammond 1 Department of Economics, Stanford University, CA 94305-6072, U.S.A. 1 Introduction and outline 1.1 Markets and social choice
More informationStructural Properties of Utility Functions Walrasian Demand
Structural Properties of Utility Functions Walrasian Demand Econ 2100 Fall 2017 Lecture 4, September 7 Outline 1 Structural Properties of Utility Functions 1 Local Non Satiation 2 Convexity 3 Quasi-linearity
More informationECON FINANCIAL ECONOMICS
ECON 337901 FINANCIAL ECONOMICS Peter Ireland Boston College Spring 2018 These lecture notes by Peter Ireland are licensed under a Creative Commons Attribution-NonCommerical-ShareAlike 4.0 International
More information