Economics 101A Spring A Revised Version of the Slutsky Equation Using the Expenditure Function or, the expenditure function is our friend!
|
|
- Geraldine Mills
- 6 years ago
- Views:
Transcription
1 Brief review... Economics 11A Spring 25 A Revised Version of the Slutsky Equation Using the Expenditure Function or, the expenditure function is our friend! e(p 1, u ) = min p 1 + p 2 x 2 s.t. U(, x 2 ) = u = p 1 x 1 (p 1, u ) + p 2 x 2 (p 1, u ) where x 1 and x 2 are the compensated demands : the choices you would make to get utility level u as cheaply as possible at prices (p 1 ). Remember that the Lagrangean for the exp-min problem is: L(, x 2, :) = p 1 + p 2 x 2! : ( U(, x 2 )! u ) The foc are: a) p 1! : U 1 (, x 2 ) = b) p 2! : U 2 (, x 2 ) = c) U(, x 2 ) = u What are the derivatives of the expenditure function w.r.t. (p 1 )? From the definition e(p 1, u ) = p 1 x 1 (p 1, u ) + p 2 x 2 (p 1, u ), and so: ( ) Me(p 1, u ) / Mp 1 = x 1 (p 1, u ) + p 1 Mx 1 (p 1, u ) / Mp 1 + p 2 Mx 2 (p 1, u ) / Mp 1. n tutorial we discussed the envelope theorem which says that the 2 nd and 3 rd terms cancel out. A quick way to prove that: Use the constraint: U( x 1 (p 1, u ), x 2 (p 1, u ) = u, and differentiate w.r.t. p 1 to get U 1 Mx 1 (p 1, u ) / Mp 1 + U 2 Mx 2 (p 1, u ) / Mp 1 = But U 1 (, x 2 ) = p 1 /: and U 2 (, x 2 ) = p 2 /: from the f.o.c. Substituting we get p 1 /: Mx 1 (p 1, u ) / Mp 1 + p 2 /: Mx 2 (p 1, u ) / Mp 1 = which means that p 1 Mx 1 (p 1, u ) / Mp 1 + p 2 Mx 2 (p 1, u ) / Mp 1 =. Thus we have:
2 Me(p 1, u ) / Mp 1 = x 1 (p 1, u ). There is a story we tell to go along with this. f you are initially minimizing expenditure, and the price of good 1 goes up, what do you do? Your first order adjustment is to simply continue buying the old bundle that will increase your spending by x 1 )p 1. That is the first term in ( ). But then you would like to re-adjust your choices of goods 1 and 2 to reflect the new prices. Those adjustments are the second and third terms in ( ). But because your initial choice was optimal (satisfying the f.o.c) when you try and re-adjust and x 2 you don t save any more. Now we are ready to analyze what happens to the uncompensated or regular demand when prices rise. Suppose we start at an intial situation with prices (p 1 ) and income. The initial choices are = (p 1, ), x 2 = x 2 (p 1, ) where the ( ) and x 2 ( ) functions without superscripts are the regular demand functions We decompose the effect of a change in price )p 1 = p 1 N! p 1 as follows: a) starting from, x 2, think of the adjustment you would make if you could keep utility constant (remain on the old indifference curve). This gets you to a new position, x 2. Since prices have risen this position costs more than you were initially spending. This move is called the substitution effect of the price increase. b) then from, x 2 think of the adjustment you make to get back to spending only the amount of income that you actually have. This is a movement inward along an income expansion path (EP). You end up at N, x 2 N. This move is called the income effect of the price increase. Note that the total change in is ) = N!
3 = ( N! ) + (! ) = ) + ) S. How big are these two parts? To begin, notice that (, x 2 ) and (, x 2 ) are on the u indifference curve. = (p 1, ) But it is also true that = (p 1, u ). Also, = (p 1 N, u ) So ) S =! = (p 1 N, u )! (p 1, u ). Mx 1 (p 1, u ) / Mp 1 )p 1 The substitution effect depends on the rate at which compensated demands change: this is purely a function of the curvature of the indifference curve. How about the income effect? ) = N! First note that N = (p 1 N, ) : its just your regular demand choice at (p 1 N, ). But what is? t is the choice when you have enough income to get to the old indifference curve at the new prices. How much money do you need to get there? That s just e(p 1 N, u )! So Thus = (p 1 N, e(p 1 N, u ) ) Make sure this makes sense to you! ) = (p 1 N, )! (p 1 N, e(p 1 N, u ) ). M (p 1, ) / M (! e(p 1 N, u ) ) So the income effect depends on the income derivative of demand times the size of the income change ) =! e(p 1 N, u ). Note that ) <, since you need more than to get to the u indifference curve when prices are (p 1 N ).
4 But how big is )? We have to use one last trick. We know that = e(p 1, p 2, u ). So we can write ) =! e(p 1 N, p 2, u ). = e(p 1, p 2, u )! e(p 1 N, p 2, u ). Me(p 1, p 2, u ) / Mp 1 ( p 1 - p 1 N) = Me(p 1, p 2, u ) / Mp 1 (!)p 1 ) =! Me(p 1, u ) / Mp 1 )p 1 Note that this is negative for a rise in the price of good 1. Finally (almost done) we have Me(p 1, u ) / Mp 1 = x 1 (p 1, u ) from the first page of this lecture note = because is also the compensated demand choice All this together means that ).! )p 1. Note that the size of the income effect depends on how much you were buying. Pulling it all together, ) = M (p 1, ) / M ) =! M (p 1, ) / M )p 1 Thus ) = ) + ) S =! M (p 1, )/M )p 1 + Mx 1 (p 1, u ) / Mp 1 )p 1 or ) / )p 1 =! M (p 1, )/M + Mx 1 (p 1, u ) / Mp 1. Now take the limit as )p 1 gets small and the ratio ) / )p 1 tells us the derivative of the regular demand function. We have established: M (p 1, ) / Mp 1 =! M (p 1, )/M + Mx 1 (p 1, u ) / Mp 1
5 This is called Slutsky s equation, after the Russian economist who first proved it about 1 years ago. Slutsky s equation says that the derivative of the regular demand with respect to p 1 is a combination of the income and substitution effects. The income effect depends on the derivative of demand w.r.t income, times the amount of you initially consume. The substitution effect depends on the derivative of the compensated demand for good 1. A neat thing about the Slutsky equation is that it gives us a way to recover information about indifference curves from the derivatives of demand w.r.t. prices and incomes. n principle, we can observe M (p 1, ) / Mp 1 and M (p 1, )/M. So we can infer: Mx 1 (p 1, u ) / Mp 1 = M (p 1, ) / Mp 1 + M (p 1, )/M Suppose we get an estimate of Mx 1 (p 1, u ) / Mp 1 that is close to. That means indifference curves must be almost like right angles.
Lecture Demand Functions
Lecture 6.1 - Demand Functions 14.03 Spring 2003 1 The effect of price changes on Marshallian demand A simple change in the consumer s budget (i.e., an increase or decrease or I) involves a parallel shift
More informationMarshall and Hicks Understanding the Ordinary and Compensated Demand
Marshall and Hicks Understanding the Ordinary and Compensated Demand K.J. Wainwright March 3, 213 UTILITY MAXIMIZATION AND THE DEMAND FUNCTIONS Consider a consumer with the utility function =, who faces
More informationEcon 101A Midterm 1 Th 28 February 2008.
Econ 0A Midterm Th 28 February 2008. You have approximately hour and 20 minutes to answer the questions in the midterm. Dan and Mariana will collect the exams at.00 sharp. Show your work, and good luck!
More informationp 1 _ x 1 (p 1 _, p 2, I ) x 1 X 1 X 2
Today we will cover some basic concepts that we touched on last week in a more quantitative manner. will start with the basic concepts then give specific mathematical examples of the concepts. f time permits
More informationEconomics 2450A: Public Economics Section 1-2: Uncompensated and Compensated Elasticities; Static and Dynamic Labor Supply
Economics 2450A: Public Economics Section -2: Uncompensated and Compensated Elasticities; Static and Dynamic Labor Supply Matteo Paradisi September 3, 206 In today s section, we will briefly review the
More informationBudget Constrained Choice with Two Commodities
1 Budget Constrained Choice with Two Commodities Joseph Tao-yi Wang 2013/9/25 (Lecture 5, Micro Theory I) The Consumer Problem 2 We have some powerful tools: Constrained Maximization (Shadow Prices) Envelope
More informationTheory of Consumer Behavior First, we need to define the agents' goals and limitations (if any) in their ability to achieve those goals.
Theory of Consumer Behavior First, we need to define the agents' goals and limitations (if any) in their ability to achieve those goals. We will deal with a particular set of assumptions, but we can modify
More informationPlease do not leave the exam room within the final 15 minutes of the exam, except in an emergency.
Economics 21: Microeconomics (Spring 2000) Midterm Exam 1 - Answers Professor Andreas Bentz instructions You can obtain a total of 100 points on this exam. Read each question carefully before answering
More informationTaxation and Efficiency : (a) : The Expenditure Function
Taxation and Efficiency : (a) : The Expenditure Function The expenditure function is a mathematical tool used to analyze the cost of living of a consumer. This function indicates how much it costs in dollars
More informationEconS Constrained Consumer Choice
EconS 305 - Constrained Consumer Choice Eric Dunaway Washington State University eric.dunaway@wsu.edu September 21, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 12 September 21, 2015 1 / 49 Introduction
More information1 Two Period Exchange Economy
University of British Columbia Department of Economics, Macroeconomics (Econ 502) Prof. Amartya Lahiri Handout # 2 1 Two Period Exchange Economy We shall start our exploration of dynamic economies with
More informationChapter 19: Compensating and Equivalent Variations
Chapter 19: Compensating and Equivalent Variations 19.1: Introduction This chapter is interesting and important. It also helps to answer a question you may well have been asking ever since we studied quasi-linear
More informationEconomics 101. Lecture 3 - Consumer Demand
Economics 101 Lecture 3 - Consumer Demand 1 Intro First, a note on wealth and endowment. Varian generally uses wealth (m) instead of endowment. Ultimately, these two are equivalent. Given prices p, if
More informationLecture 7. The consumer s problem(s) Randall Romero Aguilar, PhD I Semestre 2018 Last updated: April 28, 2018
Lecture 7 The consumer s problem(s) Randall Romero Aguilar, PhD I Semestre 2018 Last updated: April 28, 2018 Universidad de Costa Rica EC3201 - Teoría Macroeconómica 2 Table of contents 1. Introducing
More informationEcon 1101 Summer 2013 Lecture 7. Section 005 6/26/2013
Econ 1101 Summer 2013 Lecture 7 Section 005 6/26/2013 Announcements Homework 6 is due tonight at 11:45pm, CDT Midterm tomorrow! Will start at 5:40pm, there is a recitation beforehand. Make sure to work
More informationDo Not Write Below Question Maximum Possible Points Score Total Points = 100
University of Toronto Department of Economics ECO 204 Summer 2012 Ajaz Hussain TEST 2 SOLUTIONS TIME: 1 HOUR AND 50 MINUTES YOU CANNOT LEAVE THE EXAM ROOM DURING THE LAST 10 MINUTES OF THE TEST. PLEASE
More informationX ln( +1 ) +1 [0 ] Γ( )
Problem Set #1 Due: 11 September 2014 Instructor: David Laibson Economics 2010c Problem 1 (Growth Model): Recall the growth model that we discussed in class. We expressed the sequence problem as ( 0 )=
More informationLecture 5. Varian, Ch. 8; MWG, Chs. 3.E, 3.G, and 3.H. 1 Summary of Lectures 1, 2, and 3: Production theory and duality
Lecture 5 Varian, Ch. 8; MWG, Chs. 3.E, 3.G, and 3.H Summary of Lectures, 2, and 3: Production theory and duality 2 Summary of Lecture 4: Consumption theory 2. Preference orders 2.2 The utility function
More informationPractice Problems: First-Year M. Phil Microeconomics, Consumer and Producer Theory Vincent P. Crawford, University of Oxford Michaelmas Term 2010
Practice Problems: First-Year M. Phil Microeconomics, Consumer and Producer Theory Vincent P. Crawford, University of Oxford Michaelmas Term 2010 Problems from Mas-Colell, Whinston, and Green, Microeconomic
More informationLecture Note 7 Linking Compensated and Uncompensated Demand: Theory and Evidence. David Autor, MIT Department of Economics
Lecture Note 7 Linking Compensated and Uncompensated Demand: Theory and Evidence David Autor, MIT Department of Economics 1 1 Normal, Inferior and Giffen Goods The fact that the substitution effect is
More informationEconS Firm Optimization
EconS 305 - Firm Optimization Eric Dunaway Washington State University eric.dunaway@wsu.edu October 9, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 18 October 9, 2015 1 / 40 Introduction Over the past two
More informationCHAPTER 4 APPENDIX DEMAND THEORY A MATHEMATICAL TREATMENT
CHAPTER 4 APPENDI DEMAND THEOR A MATHEMATICAL TREATMENT EERCISES. Which of the following utility functions are consistent with convex indifference curves, and which are not? a. U(, ) = + b. U(, ) = ()
More informationECON 459 Game Theory. Lecture Notes Auctions. Luca Anderlini Spring 2017
ECON 459 Game Theory Lecture Notes Auctions Luca Anderlini Spring 2017 These notes have been used and commented on before. If you can still spot any errors or have any suggestions for improvement, please
More informationARE 202: Welfare: Tools and Applications Spring Lecture notes 03 Applications of Revealed Preferences
ARE 202: Welfare: Tools and Applications Spring 2018 Thibault FALLY Lecture notes 03 Applications of Revealed Preferences ARE202 - Lec 03 - Revealed Preferences 1 / 40 ARE202 - Lec 03 - Revealed Preferences
More information9 D/S of/for Labor. 9.1 Demand for Labor. Microeconomics I - Lecture #9, April 14, 2009
Microeconomics I - Lecture #9, April 14, 2009 9 D/S of/for Labor 9.1 Demand for Labor Demand for labor depends on the price of labor, price of output and production function. In optimum a firm employs
More informationChapter 8. Slutsky Equation
Chapter 8 Slutsky Equation Effects of a Price Change When a commodity s price decreases: Substitution Effect: Consumers substitute this cheaper good for now relatively more expensive other commodities.
More informationBudget Constrained Choice with Two Commodities
Budget Constrained Choice with Two Commodities Joseph Tao-yi Wang 2009/10/2 (Lecture 4, Micro Theory I) 1 The Consumer Problem We have some powerful tools: Constrained Maximization (Shadow Prices) Envelope
More informationChapter 6: Supply and Demand with Income in the Form of Endowments
Chapter 6: Supply and Demand with Income in the Form of Endowments 6.1: Introduction This chapter and the next contain almost identical analyses concerning the supply and demand implied by different kinds
More informationMacroeconomics. Lecture 5: Consumption. Hernán D. Seoane. Spring, 2016 MEDEG, UC3M UC3M
Macroeconomics MEDEG, UC3M Lecture 5: Consumption Hernán D. Seoane UC3M Spring, 2016 Introduction A key component in NIPA accounts and the households budget constraint is the consumption It represents
More informationUniversity of Toronto Department of Economics ECO 204 Summer 2013 Ajaz Hussain TEST 1 SOLUTIONS GOOD LUCK!
University of Toronto Department of Economics ECO 204 Summer 2013 Ajaz Hussain TEST 1 SOLUTIONS TIME: 1 HOUR AND 50 MINUTES DO NOT HAVE A CELL PHONE ON YOUR DESK OR ON YOUR PERSON. ONLY AID ALLOWED: A
More information(Note: Please label your diagram clearly.) Answer: Denote by Q p and Q m the quantity of pizzas and movies respectively.
1. Suppose the consumer has a utility function U(Q x, Q y ) = Q x Q y, where Q x and Q y are the quantity of good x and quantity of good y respectively. Assume his income is I and the prices of the two
More informationLecture 4 - Utility Maximization
Lecture 4 - Utility Maximization David Autor, MIT and NBER 1 1 Roadmap: Theory of consumer choice This figure shows you each of the building blocks of consumer theory that we ll explore in the next few
More informationEffects of a Price Change. Chapter Eight. Effects of a Price Change. Effects of a Price Change. Effects of a Price Change. Effects of a Price Change
Chapter Eight Slutsky Equation What happens when a commodity s price decreases? Substitution effect: the commodity is relatively cheaper, so consumers substitute it for now relatively more expensive other
More informationJournal of College Teaching & Learning February 2007 Volume 4, Number 2 ABSTRACT
How To Teach Hicksian Compensation And Duality Using A Spreadsheet Optimizer Satyajit Ghosh, (Email: ghoshs1@scranton.edu), University of Scranton Sarah Ghosh, University of Scranton ABSTRACT Principle
More informationMathematical Economics dr Wioletta Nowak. Lecture 2
Mathematical Economics dr Wioletta Nowak Lecture 2 The Utility Function, Examples of Utility Functions: Normal Good, Perfect Substitutes, Perfect Complements, The Quasilinear and Homothetic Utility Functions,
More informationEconS Substitution E ects
EconS 305 - Substitution E ects Eric Dunaway Washington State University eric.dunaway@wsu.edu September 25, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 14 September 25, 2015 1 / 40 Introduction Last time,
More informationChapter Eight. Slutsky Equation
Chapter Eight Slutsky Equation Effects of a Price Change What happens when a commodity s price decreases? Substitution effect: the commodity is relatively cheaper, so consumers substitute it for now relatively
More informationChapter 4 Topics. Behavior of the representative consumer Behavior of the representative firm Pearson Education, Inc.
Chapter 4 Topics Behavior of the representative consumer Behavior of the representative firm 1-1 Representative Consumer Consumer s preferences over consumption and leisure as represented by indifference
More informationAAEC 6524: Environmental Economic Theory and Policy Analysis. Outline. Introduction to Non-Market Valuation Part A. Klaus Moeltner Spring 2017
AAEC 6524: Environmental Economic Theory and Policy Analysis to Non-Market Valuation Part A Klaus Moeltner Spring 207 March 4, 207 / 38 Outline 2 / 38 Methods to estimate damage and cost functions needed
More informationChoice. A. Optimal choice 1. move along the budget line until preferred set doesn t cross the budget set. Figure 5.1.
Choice 34 Choice A. Optimal choice 1. move along the budget line until preferred set doesn t cross the budget set. Figure 5.1. Optimal choice x* 2 x* x 1 1 Figure 5.1 2. note that tangency occurs at optimal
More informationCOMM 220 Practice Problems 1
COMM 220 RCTIC ROLMS 1. (a) Statistics Canada calculates the Consumer rice Index (CI) using a similar basket of goods for all cities in Canada. The CI is 143.2 in Vancouver, 135.8 in Toronto, and 126.5
More informationLecture 19 Monday, Oct. 26. Lecture. 1 Indifference Curves: Perfect Substitutes. 1. Problem Set 2 due tomorrow night.
Lecture 19 Monday, Oct. 1. Problem Set due tomorrow night.. At the course web site, I have posted some practice questions about consumer theory. I recommend taking a look at this. This material will be
More informationEconomics II - Exercise Session # 3, October 8, Suggested Solution
Economics II - Exercise Session # 3, October 8, 2008 - Suggested Solution Problem 1: Assume a person has a utility function U = XY, and money income of $10,000, facing an initial price of X of $10 and
More informationChapter Four. Utility Functions. Utility Functions. Utility Functions. Utility
Functions Chapter Four A preference relation that is complete, reflexive, transitive and continuous can be represented by a continuous utility function. Continuity means that small changes to a consumption
More informationProblem Set 4 - Answers. Specific Factors Models
Page 1 of 5 1. In the Extreme Specific Factors Model, a. What does a country s excess demand curve look like? The PPF in the Extreme Specific Factors Model is just a point in goods space (X,Y space). Excess
More informationIntroductory Mathematics for Economics MSc s: Course Outline. Huw David Dixon. Cardiff Business School. September 2008.
Introductory Maths: course outline Huw Dixon. Introductory Mathematics for Economics MSc s: Course Outline. Huw David Dixon Cardiff Business School. September 008. The course will consist of five hour
More informationBUEC 280 LECTURE 6. Individual Labour Supply Continued
BUEC 280 ECTURE 6 Individual abour Supply Continued ast day Defined budget constraint Defined optimal allocation of leisure and consumption Changes in non-labour income generate a pure income effect Change
More informationLecture 10: Two-Period Model
Lecture 10: Two-Period Model Consumer s consumption/savings decision responses of consumer to changes in income and interest rates. Government budget deficits and the Ricardian Equivalence Theorem. Budget
More informationBuying and Selling. Chapter Nine. Endowments. Buying and Selling. Buying and Selling
Buying and Selling Chapter Nine Buying and Selling Trade involves exchange -- when something is bought something else must be sold. What will be bought? What will be sold? Who will be a buyer? Who will
More informationTutorial 4 - Pigouvian Taxes and Pollution Permits II. Corrections
Johannes Emmerling Natural resources and environmental economics, TSE Tutorial 4 - Pigouvian Taxes and Pollution Permits II Corrections Q 1: Write the environmental agency problem as a constrained minimization
More informationDepartment of Agricultural Economics PhD Qualifier Examination January 2005
Department of Agricultural Economics PhD Qualifier Examination January 2005 Instructions: The exam consists of six questions. You must answer all questions. If you need an assumption to complete a question,
More informationThis appendix discusses two extensions of the cost concepts developed in Chapter 10.
CHAPTER 10 APPENDIX MATHEMATICAL EXTENSIONS OF THE THEORY OF COSTS This appendix discusses two extensions of the cost concepts developed in Chapter 10. The Relationship Between Long-Run and Short-Run Cost
More information14.03 Fall 2004 Problem Set 2 Solutions
14.0 Fall 004 Problem Set Solutions October, 004 1 Indirect utility function and expenditure function Let U = x 1 y be the utility function where x and y are two goods. Denote p x and p y as respectively
More informationPROBLEM SET 3 SOLUTIONS. 1. Question 1
PROBLEM SET 3 SOLUTIONS RICH LANGFORD 1.1. Recall that 1. Question 1 CV = E(P x,, U) E(,, U) = By the envelope theorem, we know that E p dp. E(p,, U) p = (h x, h y, p,, U) p = p (ph x + h y + λ(u u(h x,
More informationLecture 2 Consumer theory (continued)
Lecture 2 Consumer theory (continued) Topics 1.4 : Indirect Utility function and Expenditure function. Relation between these two functions. mf620 1/2007 1 1.4.1 Indirect Utility Function The level of
More informationEconomics 11: Solutions to Practice Final
Economics 11: s to Practice Final September 20, 2009 Note: In order to give you extra practice on production and equilibrium, this practice final is skewed towards topics covered after the midterm. The
More informationEliminating Substitution Bias. One eliminate substitution bias by continuously updating the market basket of goods purchased.
Eliminating Substitution Bias One eliminate substitution bias by continuously updating the market basket of goods purchased. 1 Two-Good Model Consider a two-good model. For good i, the price is p i, and
More informationFall Midterm Examination Solutions Monday 10 November 2014
EC 03. & 03.3 Fall 04 Deniz Selman Bo¼gaziçi University Midterm Examination Solutions Monday 0 November 04. (5 pts) Defne is now in her senior year of high school and is preparing for her university entrance
More informationHomework 2 ECN205 Spring 2011 Wake Forest University Instructor: McFall
Homework 2 ECN205 Spring 2011 Wake Forest University Instructor: McFall Instructions: Answer the following problems and questions carefully. Just like with the first homework, I ll call names randomly
More informationFinal Examination December 14, Economics 5010 AF3.0 : Applied Microeconomics. time=2.5 hours
YORK UNIVERSITY Faculty of Graduate Studies Final Examination December 14, 2010 Economics 5010 AF3.0 : Applied Microeconomics S. Bucovetsky time=2.5 hours Do any 6 of the following 10 questions. All count
More informationCharacterization of the Optimum
ECO 317 Economics of Uncertainty Fall Term 2009 Notes for lectures 5. Portfolio Allocation with One Riskless, One Risky Asset Characterization of the Optimum Consider a risk-averse, expected-utility-maximizing
More informationMIDTERM EXAM ANSWERS
MIDTERM EXAM ANSWERS ECON 20 PROFESSOR GUSE Instructions. You have 3 hours to complete the exam. There are a total of 85 points on the exam. The exam is designed to take about minute per point. You are
More informationEcon 1101 Spring 2013 Week 10. Section 038 3/27/2013
Econ 1101 Spring 2013 Week 10 Section 038 3/27/2013 nnouncements Homework due on plia this Friday! In recitation this week: Consumer theory worksheet that is very helpful for understanding consumer theory.
More informationMICROECONOMICS II Gisela Rua 2,5 hours
MICROECONOMICS II st Test Fernando Branco 07-04 005 Gisela Rua,5 hours I (6,5 points) James has an income of 0, which he spends in the consumption of goods and whose prices are and 5, respectively Detective
More informationDemand and income. Income and Substitution Effects. How demand rises with income. How demand rises with income. The Shape of the Engel Curve
Demand and income Engel Curves and the Slutsky Equation If your income is initially 1, you buy 1 apples When your income rises to 2, you buy 2 apples. To make the obvious point, demand is a function of
More informationIntroductory Microeconomics (ES10001)
Topic 2: Household ehaviour Introductory Microeconomics (ES11) Topic 2: Consumer Theory Exercise 4: Suggested Solutions 1. Which of the following statements is not valid? utility maximising consumer chooses
More informationUnderstand general-equilibrium relationships, such as the relationship between barriers to trade, and the domestic distribution of income.
Review of Production Theory: Chapter 2 1 Why? Understand the determinants of what goods and services a country produces efficiently and which inefficiently. Understand how the processes of a market economy
More informationEcon 121b: Intermediate Microeconomics
Econ 121b: Intermediate Microeconomics Dirk Bergemann, Spring 2012 1 Introduction 1.1 What s Economics? This is an exciting time to study economics, even though may not be so exciting to be part of this
More informationPractice Questions Chapters 9 to 11
Practice Questions Chapters 9 to 11 Producer Theory ECON 203 Kevin Hasker These questions are to help you prepare for the exams only. Do not turn them in. Note that not all questions can be completely
More informationMath: Deriving supply and demand curves
Chapter 0 Math: Deriving supply and demand curves At a basic level, individual supply and demand curves come from individual optimization: if at price p an individual or firm is willing to buy or sell
More informationThe Rational Consumer. The Objective of Consumers. Maximizing Utility. The Budget Set for Consumers. Slope =
The Rational Consumer The Objective of Consumers 2 Chapter 8 and the appendix Announcements We have studied demand curves. We now need to develop a model of consumer behavior to understand where demand
More information14.05: SECTION HANDOUT #4 CONSUMPTION (AND SAVINGS) Fall 2005
14.05: SECION HANDOU #4 CONSUMPION (AND SAVINGS) A: JOSE ESSADA Fall 2005 1. Motivation In our study of economic growth we assumed that consumers saved a fixed (and exogenous) fraction of their income.
More informationIntro to Economic analysis
Intro to Economic analysis Alberto Bisin - NYU 1 The Consumer Problem Consider an agent choosing her consumption of goods 1 and 2 for a given budget. This is the workhorse of microeconomic theory. (Notice
More informationWe want to solve for the optimal bundle (a combination of goods) that a rational consumer will purchase.
Chapter 3 page1 Chapter 3 page2 The budget constraint and the Feasible set What causes changes in the Budget constraint? Consumer Preferences The utility function Lagrange Multipliers Indifference Curves
More informationOptimal Portfolio Selection
Optimal Portfolio Selection We have geometrically described characteristics of the optimal portfolio. Now we turn our attention to a methodology for exactly identifying the optimal portfolio given a set
More informationMicroeconomics (Week 3) Consumer choice and demand decisions (part 1): Budget lines Indifference curves Consumer choice
Microeconomics (Week 3) onsumer choice and demand decisions (part 1): Budget lines Indifference curves onsumer choice The budget constraint The budget constraint describes the different bundles that the
More information3/1/2016. Intermediate Microeconomics W3211. Lecture 4: Solving the Consumer s Problem. The Story So Far. Today s Aims. Solving the Consumer s Problem
1 Intermediate Microeconomics W3211 Lecture 4: Introduction Columbia University, Spring 2016 Mark Dean: mark.dean@columbia.edu 2 The Story So Far. 3 Today s Aims 4 We have now (exhaustively) described
More informationIntermediate Micro HW 2
Intermediate Micro HW June 3, 06 Leontief & Substitution An individual has Leontief preferences over goods x and x He starts ith income y and the to goods have respective prices p and p The price of good
More informationChapter 4. Consumer and Firm Behavior: The Work- Leisure Decision and Profit Maximization. Copyright 2014 Pearson Education, Inc.
Chapter 4 Consumer and Firm Behavior: The Work- Leisure Decision and Profit Maximization Copyright Chapter 4 Topics Behavior of the representative consumer Behavior of the representative firm 1-2 Representative
More informationMathematical Economics dr Wioletta Nowak. Lecture 1
Mathematical Economics dr Wioletta Nowak Lecture 1 Syllabus Mathematical Theory of Demand Utility Maximization Problem Expenditure Minimization Problem Mathematical Theory of Production Profit Maximization
More informationEconomics 101 Fall 2013 Homework 5 Due Thursday, November 21, 2013
Economics 101 Fall 2013 Homework 5 Due Thursday, November 21, 2013 Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the
More informationTrade on Markets. Both consumers' initial endowments are represented bythesamepointintheedgeworthbox,since
Trade on Markets A market economy entails ownership of resources. The initial endowment of consumer 1 is denoted by (x 1 ;y 1 ), and the initial endowment of consumer 2 is denoted by (x 2 ;y 2 ). Both
More informationMICROECONOMICS Principles and Analysis Frank Cowell
Prerequisites Almost essential Consumer: Optimisation Useful, but optional Firm: Optimisation HOUSEHOLD DEMAND AND SUPPLY MICROECONOMICS Principles and Analysis Frank Cowell Note: the detail in slides
More informationFundamental Theorems of Welfare Economics
Fundamental Theorems of Welfare Economics Ram Singh October 4, 015 This Write-up is available at photocopy shop. Not for circulation. In this write-up we provide intuition behind the two fundamental theorems
More information1. Suppose a production process is described by a Cobb-Douglas production function f(v 1, v 2 ) = v 1 1/2 v 2 3/2.
1. Suppose a production process is described by a Cobb-Douglas production function f(v 1, v 2 ) = v 1 1/2 v 2 3/2. a. Write an expression for the marginal product of v 1. Does the marginal product of v
More informationTOBB-ETU, Economics Department Macroeconomics II (ECON 532) Practice Problems I (Solutions)
TOBB-ETU, Economics Department Macroeconomics II (ECON 532) Practice Problems I (Solutions) Q: The Solow-Swan Model: Constant returns Prove that, if the production function exhibits constant returns, all
More informationGPP 501 Microeconomic Analysis for Public Policy Fall 2017
GPP 501 Microeconomic Analysis for Public Policy Fall 2017 Given by Kevin Milligan Vancouver School of Economics University of British Columbia Lecture Sept 12th: Demand GPP501: Lecture Sept 12 1 of 24
More informationINTERMEDIATE MICROECONOMICS LECTURE 9 THE COSTS OF PRODUCTION
9-1 INTERMEDIATE MICROECONOMICS LECTURE 9 THE COSTS OF PRODUCTION The opportunity cost of an asset (or, more generally, of a choice) is the highest valued opportunity that must be passed up to allow current
More informationChapter 3. A Consumer s Constrained Choice
Chapter 3 A Consumer s Constrained Choice If this is coffee, please bring me some tea; but if this is tea, please bring me some coffee. Abraham Lincoln Chapter 3 Outline 3.1 Preferences 3.2 Utility 3.3
More informationEconomics 101 Section 5
Economics 101 Section 5 Lecture #10 February 17, 2004 The Budget Constraint Marginal Utility Consumer Choice Indifference Curves Overview of Chapter 5 Consumer Choice Consumer utility and marginal utility
More informationECON Micro Foundations
ECON 302 - Micro Foundations Michael Bar September 13, 2016 Contents 1 Consumer s Choice 2 1.1 Preferences.................................... 2 1.2 Budget Constraint................................ 3
More informationChoice. A. Optimal choice 1. move along the budget line until preferred set doesn t cross the budget set. Figure 5.1.
Choice 2 Choice A. choice. move along the budget line until preferred set doesn t cross the budget set. Figure 5.. choice * 2 * Figure 5. 2. note that tangency occurs at optimal point necessary condition
More informationChapter 4 UTILITY MAXIMIZATION AND CHOICE
Chapter 4 UTILITY MAXIMIZATION AND CHOICE 1 Our Consumption Choices Suppose that each month we have a stipend of $1250. What can we buy with this money? 2 What can we buy with this money? Pay the rent,
More informationPart I. The consumer problems
Part I The consumer problems Individual decision-making under certainty Course outline We will divide decision-making under certainty into three units: 1 Producer theory Feasible set defined by technology
More informationLecture 1: A Robinson Crusoe Economy
Lecture 1: A Robinson Crusoe Economy Di Gong SBF UIBE & European Banking Center c Macro teaching group: Zhenjie Qian & Di Gong March 3, 2016 Di Gong (UIBE & EBC) Intermediate Macro March 3, 2016 1 / 27
More informationCosts. Lecture 5. August Reading: Perlo Chapter 7 1 / 63
Costs Lecture 5 Reading: Perlo Chapter 7 August 2015 1 / 63 Introduction Last lecture, we discussed how rms turn inputs into outputs. But exactly how much will a rm wish to produce? 2 / 63 Introduction
More informationGraphs Details Math Examples Using data Tax example. Decision. Intermediate Micro. Lecture 5. Chapter 5 of Varian
Decision Intermediate Micro Lecture 5 Chapter 5 of Varian Decision-making Now have tools to model decision-making Set of options At-least-as-good sets Mathematical tools to calculate exact answer Problem
More informationChapter 3: Model of Consumer Behavior
CHAPTER 3 CONSUMER THEORY Chapter 3: Model of Consumer Behavior Premises of the model: 1.Individual tastes or preferences determine the amount of pleasure people derive from the goods and services they
More informationMicroeconomics Review in a Two Good World
Economics 131 ection Notes GI: David Albouy Microeconomics Review in a Two Good World Note: These notes are not meant to be a substitute for attending section. It may in fact be difficult to understand
More informationEconS Income E ects
EconS 305 - Income E ects Eric Dunaway Washington State University eric.dunaway@wsu.edu September 23, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 13 September 23, 2015 1 / 41 Introduction Over the net
More information