ANSWERS TO ODD NUMBERED EXERCISES IN CHAPTER 3
|
|
- Pierce Shelton
- 6 years ago
- Views:
Transcription
1 John Riley 5 Setember 0 NSWERS T DD NUMERED EXERCISES IN CHPTER 3 SECTIN 3: Equilibrium and Efficiency Exercise 3-: Prices with Quasi-linear references (a) Since references are convex, an allocation is a Walrasian Equilibrium if and only if it is Pareto Efficient We begin by characterizing the Pareto Efficient allocations and then solve for the no-trade equilibrium rices given that an endowment is Pareto Efficient gent h has a MRS( x, x ) ( x ) h h h / = Fig D3-: Efficient allocations For an efficient allocation in the interior of the Edgeworth ox, the two agents must have the same MRS hence the equilibrium rice ratio / = 0 (a) long the line segment, x = x = 00 long the line the MRS is 0 Thus MRS( x, x ) = (00 + α) > (00 α) = MRS( x, x ) / / Thus agent s indifference curve is steeer than that of agent and so all the allocations on are Pareto Efficient long the line segment agent s indifference curve is steeer so these allocations are also Pareto Efficient nswers Ch 3 age
2 John Riley 5 Setember 0 Consider the line segment Since these oints are in the interior of agent s consumtion set, the equilibrium rice line must be tangential That is, / = MRS( x, x ) = (00 + α) / Thus the rice ratio rises along from 0 to 0 rguing symmetrically, the rice ratio again rises from 0 to 0 along Exercise 3-3: Walrasian Equilibrium (a) Each igg has symmetric Cobb-Douglas references with endowment (4,8) Thus a igg sends half his income 4 + 8on each commodity His demand for commodity is therefore x = r+ 4, where r = / Define ˆ x = x + a, where a= (4,6) and ˆ ω = ω + a = (4,6) Then each ittle s otimization roblem can be rewritten as follows Max{ln xˆ + ln xˆ xˆ = ( x + a) ˆ ω} xˆ ˆ ˆ This is again the symmetric Cobb-Douglas case so x = ω Hence xˆ = r + 8 and so x = r+ Summing, the market demand for commodity by each igg-ittle air is x = 4r + 6 Suly is 8 Equating suly and demand, the equilibrium rice is / (b) t an interior PE allocation the marginal rates of substitution must be equal Thus MRS 6 + x x = = = MRS 4 + x x 6+ x x 6+ x 6+ ω 4 lying the Ratio Rule, MRS = = = = = = 4+ x x 4+ x 4+ ω 48 (c) Note that the MRS is constant for all interior PE allocations so that a change in the distribution of the total endowment has no effect on the equilibrium rice unless the new equilibrium is no longer in the interior of the Edgeworth ox nswers Ch 3 age
3 John Riley 5 Setember 0 C Fig D3-: Equilibrium Price Ratios (d) This is the endowment oint C Since it is Pareto Efficient there is no trade and the equilibrium rice ratio is ½ (e) For any endowment in the unshaded region the Walrasian equilibrium rice is ½ For any endowment in the shaded region the equilibrium allocation is on the boundary of the Edgeworth ox Since (4,8) is a Pareto Efficient allocation in the interior of iggs consumtion set, MRS x 8 3 ( x, x) = x = = = 4 7 Thus the new Walrasian equilibrium rice is 3/7 Exercise 3-5: More on the iggs and ittles Since the ittles get no satisfaction from commodity an efficient allocation gives all of this commodity to the iggs Similarly, all of commodity must be allocated to the ittles Thus the only PE allocation is the oint in the South East corner of the Edgeworth ox nswers Ch 3 age 3
4 John Riley 5 Setember 0 (4,8) 0 Fig D3-3: Unique Equilibrium llocation The sloe of the line segment connecting the endowment oint and the PE allocation is 8/0 = /5 Thus the Walrasian equilibrium rice is /5 iggs sells his 8 units of commodity and urchases 0 units of commodity Exercise 3-5: Market Excess Demand (a) While not necessary, it roves useful to define excess of (,), that is y = x j j y to be lex s consumtion in Then lex s budget constraint, x + x (7 + α) + ( α), can be rewritten as follows y + y (5 + α) ( α) lex then solves the following standard Cobb-Douglas otimization roblem Max{ U = y y y + y (5 + α) ( + α)} y 4 + The consumtion set is the set of all y Thus to be able to urchase a vector in the consumtion set it is necessary and sufficient that (5 + α) ( α) 0 Hence nswers Ch 3 age 4
5 John Riley 5 Setember 0 α 5 + α rguing symmetrically, ev s otimization roblem can be written as follows Max{ U = y y y + y ( + α) + (5 + α)} y 5 Thus for ev to be able to make a urchase in her consumtion set, 5 + α α (b) We have reduced the otimization roblems to standard Cobb-Douglas otimization roblems Solving, Hence y = ( (5 + α) ( + α)) and y = ( ( + α) + (5 + α)) x 5 6 (5 α) ( α) = and x = ( + α) + (5 + α) 6 6 (c) dding these two exression and then subtracting aggregate suly, market excess demand is α e( ) = x + x 8= ( ) 3 (d) Excess demand for commodity thus increases with if and only if α > 0 Note that lex has a very large fraction of the aggregate endowment if α > 0 He is a net seller of commodity thus the income effect on his demand for commodity is large and ositive ev has a small endowment of commodity so her income effect is negative but small The market income effect is therefore ositive This ositive effect more than offsets the negative substitution effects for both consumers (e) For all rice rations satisfying the inequalities in (a), excess demand is zero Thus all these rice rations are WE rice ratios Thus we have shown by examle that there can be a continuum of equilibrium rice ratios! nswers Ch 3 age 5
6 John Riley 5 Setember 0 Exercise 3-7: Suorting and searating hyerlanes (a) Suose there exist y inty such that y = y 0 For δ > 0 sufficiently small ŷ y δ Y = + Then ŷ = y + δ = y 0 + δ > y 0 which contradicts (i) (b) If s or t is in the interior then y = s t int Y since there exists a neighborhood around y that is in Y, the same neighborhood around s or t that is in S or T Then y < 0, that is, s < t SECTIN 3: The Fundamental Welfare Theorems Exercise 3-: Second welfare theorem with identical homothetic references Consider the economy with a single reresentative agent et xˆ = arg Max{ U( x) x y+ ω, y Y } where Y is the aggregate roduction set, that xy, F f f f is, Y = { y y = y, y Y } The aggregate roduction set Y is convex since it is f = the sum of convex sets Since U is strictly increasing, xˆ = yˆ+ ω lies on the boundary of the aggregate roduction set Thus by the searating hyerlane theorem there exists a non-zero vector such that (i) y y y U( x) > U( x) x> x * Y and (ii) ˆ ˆ It is readily shown that, if (i) is true, then f f f f y Y y yˆ From (ii), nswers Ch 3 age 6
7 John Riley 5 Setember 0 xˆ = arg Max{ U( x) x xˆ = ( yˆ+ ω)} xy, h Finally MRS( θ xˆ) = MRS( xˆ) Thus for any { θ h } H, h h= θ =, { h ˆ } H θ x h= is Pareto efficient H h= nswers Ch 3 age 7
Econ 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 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 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 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 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 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 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 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 informationANSWERS TO ODD NUMBERED EXERCISES IN CHAPTER 5. The constraint is binding at the maximum therefore we can substitute for y
John Rile Aril 0 ANSWERS TO ODD NUMBERED EXERCISES IN CHAPTER 5 Section 5: The Robinson Crusoe Econom Eercise 5-: Equilibrium (a) = ( + ω) = ( + 47, ) Then = 47 Substituting or in the / roduction unction,
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 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 informationEconomics 101. Lecture 7 - Monopoly and Oligopoly
Economics 0 Lecture 7 - Monooly and Oligooly Production Equilibrium After having exlored Walrasian equilibria with roduction in the Robinson Crusoe economy, we will now ste in to a more general setting.
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 information, αβ, > 0 is strictly quasi-concave on
John Riley 8 Setember 9 Econ Diagnostic Test Time allowed: 9 minutes. Attemt all three questions. Note that the last two arts of questions and 3 are marked with an asterisk (). These do not carry many
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 informationEconomics 201b Spring 2010 Solutions to Problem Set 1 John Zhu
Economics 201b Spring 2010 Solutions to Problem Set 1 John Zhu 1a The following is a Edgeworth box characterization of the Pareto optimal, and the individually rational Pareto optimal, along with some
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 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 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 informationTheory of Externalities Partial Equilibrium Analysis
Theory of Externalities Partial Equilibrium Analysis Definition: An externality is resent whenever the well being of a consumer or the roduction ossibilities of a firm are directly affected by the actions
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 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 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 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 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 informationMarket 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 informationε and ε > 0 we can find a δ > 0 such that
John Riley June 5, 3 ANSWERS TO EXERCISES IN APPENDIX A SECTION A: MAPPINGS OF A SINGLE VARIABLE Eercise A-: Rules of limits (a) Limit of the sum = the sum of the limits We wish to estalish that for any
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 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 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 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 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 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 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 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 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 informationExercise 2: Equivalence of the first two definitions for a differentiable function. is a convex combination of
March 07 Mathematical Foundations John Riley Module Marginal analysis and single variable calculus 6 Eercises Eercise : Alternative definitions of a concave function (a) For and that 0, and conve combination
More informationECON 500 Fall Exam #2 Answer Key.
ECO 500 Fall 004. Eam # Answer Key. ) While standing in line at your favourite movie theatre, you hear someone behind you say: I like ocorn, but I m not buying any because it isn t worth the high rice.
More information2.2 BUDGET-CONSTRAINED CHOICE WITH TWO COMMODITIES
Essential Miroeonomis -- 22 BUDGET-CONSTRAINED CHOICE WITH TWO COMMODITIES Continuity of demand 2 Inome effets 6 Quasi-linear, Cobb-Douglas and CES referenes 9 Eenditure funtion 4 Substitution effets and
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 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 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 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 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 informationEcon 101A Midterm 2 Th 8 April 2009.
Econ A Midterm Th 8 Aril 9. You have aroximately hour and minutes to answer the questions in the midterm. I will collect the exams at. shar. Show your work, and good luck! Problem. Production (38 oints).
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 informationMicroeconomics Fall 2017 Problem set 1: Possible answers
Microeconomics Fall 07 Problem set Possible answers Each answer resents only one way of solving the roblem. Other right answers are ossible and welcome. Exercise For each of the following roerties, draw
More informationInternational Trade with a Public Intermediate Good and the Gains from Trade
International Trade with a Public Intermediate Good and the Gains from Trade Nobuhito Suga Graduate School of Economics, Nagoya University Makoto Tawada Graduate School of Economics, Nagoya University
More informationCOMMUNICATION BETWEEN SHAREHOLDERS 1
COMMUNICATION BTWN SHARHOLDRS 1 A B. O A : A D Lemma B.1. U to µ Z r 2 σ2 Z + σ2 X 2r ω 2 an additive constant that does not deend on a or θ, the agents ayoffs can be written as: 2r rθa ω2 + θ µ Y rcov
More informationMicroeconomics, Block I Part 2
Microeconomics, Block I Part 2 Piero Gottardi EUI Sept. 20, 2015 Piero Gottardi (EUI) Microeconomics, Block I Part 2 Sept. 20, 2015 1 / 48 Pure Exchange Economy H consumers with: preferences described
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 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 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 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 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 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 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 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 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 informationIntroductory Microeconomics
Prof. Wolfram Elsner Faculty of Business Studies and Economics iino Institute of Institutional and Innovation Economics Introductory Microeconomics The Ideal Neoclassical Market and General Equilibrium
More informationThe B.E. Journal of Theoretical Economics
The B.E. Journal of Theoretical Economics Topics Volume 9, Issue 1 2009 Article 43 Simple Economies with Multiple Equilibria Theodore C. Bergstrom Ken-Ichi Shimomura Takehiko Yamato University of California,
More informationStationary Monetary Equilibria with Strictly Increasing Value Functions and Non-Discrete Money Holdings Distributions: An Indeterminacy Result
CIRJE-F-615 Stationary Monetary Equilibria with Strictly Increasing Value Functions and Non-Discrete Money Holdings Distributions: An Indeterminacy Result Kazuya Kamiya University of Toyo Taashi Shimizu
More informationFinal Examination with Answers: Economics 210A
Final Examination with Answers: Economics 210A December, 2016, Ted Bergstrom, UCSB I asked students to try to answer any 7 of the 8 questions. I intended the exam to have some relatively easy parts and
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 informationEconomics 101 Lecture 5 - Firms and Production
Economics 101 Lecture 5 - Firms and Production 1 The Second Welfare Theorem Last week we proved the First Basic Welfare Theorem, which states that under fairly weak assumptions, a Walrasian equilibrium
More informationAdvanced Microeconomic Analysis, Lecture 6
Advanced Microeconomic Analysis, Lecture 6 Prof. Ronaldo CARPIO April 10, 017 Administrative Stuff Homework # is due at the end of class. I will post the solutions on the website later today. The midterm
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 informationECONOMICS 001 Microeconomic Theory Summer Mid-semester Exam 2. There are two questions. Answer both. Marks are given in parentheses.
Microeconomic Theory Summer 206-7 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
More informationEcon 401A Version 3 John Riley. Homework 3 Due Tuesday, Nov 28. Answers. (a) Double both sides of the second equation and subtract the second equation
Econ 40 Version John Riley Homeork Due uesdy, Nov 8 nsers nser to question () Double both sides of the second eqution nd subtrct the second eqution 60q 0q 0 60q 0q 0 b b 00q 0 hen q 0 (b) he vlue of the
More informationEconS 501 Final Exam - December 10th, 2018
EconS 501 Final Exam - December 10th, 018 Show all your work clearly and make sure you justify all your answers. NAME 1. Consider the market for smart pencil in which only one firm (Superapiz) enjoys a
More informationRecitation #2 (August 31st, 2018)
Recitation #2 (August 1st, 2018) 1. [Checking properties of the Cobb-Douglas utility function.] Consider the utility function u(x) = n i=1 xα i i, where x denotes a vector of n different goods x R n +,
More informationPROFIT MAXIMIZATION. π = p y Σ n i=1 w i x i (2)
PROFIT MAXIMIZATION DEFINITION OF A NEOCLASSICAL FIRM A neoclassical firm is an organization that controls the transformation of inuts (resources it owns or urchases into oututs or roducts (valued roducts
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 informationMicroeconomic Theory-I Washington State University Midterm Exam #1 - Answer key. Fall 2016
Microeconomic Theory-I Washington State University Midterm Exam # - Answer key Fall 06. [Checking properties of preference relations]. Consider the following preference relation de ned in the positive
More informationBeyond CES: Three Alternative Classes of Flexible Homothetic Demand Systems
Beyond CES: Three Alternative Classes of Flexible Homothetic Demand Systems Kiminori Matsuyama 1 Philip Ushchev 2 October 2017 1 Department of Economics, Northwestern University, Evanston, USA. Email:
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 informationMicro I. Lesson 5 : Consumer Equilibrium
Microecono mics I. Antonio Zabalza. Universit of Valencia 1 Micro I. Lesson 5 : Consumer Equilibrium 5.1 Otimal Choice If references are well behaved (smooth, conve, continuous and negativel sloed), then
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 informationBeyond CES: Three Alternative Classes of Flexible Homothetic Demand Systems
Beyond CES: Three Alternative Classes of Flexible Homothetic Demand Systems Kiminori Matsuyama 1 Philip Ushchev 2 December 19, 2017, Keio University December 20. 2017, University of Tokyo 1 Department
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 informationNote on social choice allocation in exchange economies with Cobb-Douglas preferences
Note on social choice allocation in exchange economies with Cobb-Douglas preferences Takeshi Momi Department of Economics, Doshisha University April, 2011 Abstract In this note we show that in a pure exchange
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 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 informationEconomics 101. Lecture 2 - The Walrasian Model and Consumer Choice
Economics 101 Lecture 2 - The Walrasian Model and Consumer Choice 1 Uncle Léon The canonical model of exchange in economics is sometimes referred to as the Walrasian Model, after the early economist Léon
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 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 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 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 information2x2x2 Heckscher-Ohlin-Samuelson (H-O-S) model with factor substitution
2x2x2 Heckscher-Ohlin-amuelson (H-O- model with factor substitution The HAT ALGEBRA of the Heckscher-Ohlin model with factor substitution o far we were dealing with the easiest ossible version of the H-O-
More informationKIER DISCUSSION PAPER SERIES
KIER DISCUSSION PAPER SERIES KYOTO INSTITUTE OF ECONOMIC RESEARCH Discussion Paper No.992 Intertemporal efficiency does not imply a common price forecast: a leading example Shurojit Chatterji, Atsushi
More informationCHAPTER 3: OPTIMIZATION
John Riley 8 February 7 CHAPTER 3: OPTIMIZATION 3. TWO VARIABLES 8 Second Order Conditions Implicit Function Theorem 3. UNCONSTRAINED OPTIMIZATION 4 Necessary and Sufficient Conditions 3.3 CONSTRAINED
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 informationOverview. Producer Theory. Consumer Theory. Exchange
Overview Consumer Producer Exchange Edgeworth Box All Possible Exchange Points Contract Curve Overview Consumer Producer Exchange (Multiplicity) Walrasian Equilibrium Walrasian Equilibrium Requirements:
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 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, Block I Part 1
Microeconomics, Block I Part 1 Piero Gottardi EUI Sept. 26, 2016 Piero Gottardi (EUI) Microeconomics, Block I Part 1 Sept. 26, 2016 1 / 53 Choice Theory Set of alternatives: X, with generic elements x,
More informationEcon 101A Problem Set 6 Solutions Due on Monday Dec. 9. No late Problem Sets accepted, sorry!
Econ 0A Problem Set 6 Solutions Due on Monday Dec. 9. No late Problem Sets accepted, sry! This Problem set tests the knowledge that you accumulated mainly in lectures 2 to 26. The problem set is focused
More informationPure exchange competitive equilibrium under uncertainty
J Ambient Intell Human Comut 7) 8:759 768 DOI.7/s65-7-5-x ORIGINAL RESEARCH Pure exchange cometitive equilibrium under uncertainty Qiqiong Chen Yuanguo Zhu Received: 7 February 7 / Acceted: 4 Aril 7 /
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 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 information