Utility. M. Utku Ünver Micro Theory. M. Utku Ünver Micro Theory Utility 1 / 15


 Regina Jones
 7 years ago
 Views:
Transcription
1 Utility M. Utku Ünver Micro Theory M. Utku Ünver Micro Theory Utility 1 / 15
2 Utility Function The preferences are the fundamental description useful for analyzing choice and utility is simply a way of describing preferences. A utility function is a way of assigning a number to every possible consumption bundle such that morepreferred bundles get assigned bigger numbers than lesspreferred bundles. That is; (x 1, x 2 ) (y 1, y 2 ) u(x 1, x 2 ) > u(y 1, y 2 ) The only property of a utility assignment that is important is how it orders the bundles of goods. The magnitude is important only to an extent it effects the ranking of different bundles, the size of the utility difference does not matter. M. Utku Ünver Micro Theory Utility 2 / 15
3 Example: Suppose (w 1, w 2 ) (x 1, x 2 ) (y 1, y 2 ) (z 1, z 2 ) Utility function representing these preferences u(w 1, w 2 ) = 20 > u(x 1, x 2 ) = 10 > u(y 1, y 2 ) = 4 > u(z 1, z 2 ) = Since only the ranking of the bundles matters, there can be no unique way to assign utilities to bundles of goods. Example continued: We can also use the following utility function representing the above preferences v(w 1, w 2 ) = 12 > v(x 1, x 2 ) = 11 > v(y 1, y 2 ) = 10 > v(z 1, z 2 ) = 0 A monotonic transformation is a way of transforming one set of numbers into another set of numbers in a way that preserves the order of the numbers. Example continued There is a monotonic transformation f that transforms u to v, that is v = f (u) : 0 = f (0.001), 10 = f (4), 11 = f (10), 12 = f (20) As u goes up f goes up. So f is monotonic. M. Utku Ünver Micro Theory Utility 3 / 15
4 Examples of monotonic transformations: v = 2u v = u 2 (if u 0) v = ln u (if u > 0) v = 1 u v = u + 5 M. Utku Ünver Micro Theory Utility 4 / 15
5 A monotonic transformation M. Utku Ünver Micro Theory Utility 5 / 15
6 We typically represent a monotonic transformation by a function f (u) that transforms each u into another f (u) in a way that preserves the order of the numbers; u 1 > u 2 f (u 1 ) > f (u 2 ). Here f (u(x 1, x 2 )) is also a utility function that represents those same preferences. The reason is the following; 1 u(x 1, x 2 ) represents some preferences means; u(x 1, x 2 ) > u(y 1, y 2 ) (x 1, x 2 ) (y 1, y 2 ) 2 But f (u) is a monotonic transformation, therefore 3 1 and 2 imply; u(x 1, x 2 ) > u(y 1, y 2 ) f (u(x 1, x 2 )) > f (u(y 1, y 2 )) f (u(x 1, x 2 )) > f (u(y 1, y 2 )) (x 1, x 2 ) (y 1, y 2 ) 4 But that means f (u(x 1, x 2 )) represents these preferences as well. Geometrically, a utility function is a way to label indifference curves. A monotonic transformation is a relabeling of the indifference curves. M. Utku Ünver Micro Theory Utility 6 / 15
7 Indifference curves from Utility functions Given a utility function u(x 1, x 2 ), we should plot all the points (x 1, x 2 ) such that u(x 1, x 2 ) equals a constant. Different constants will correspond to different utility levels (i. e. different indifference curves). M. Utku Ünver Micro Theory Utility 7 / 15
8 Example: u(x 1, x 2 ) = x 1 x 2 u(x 1, x 2 ) = k x 2 = k x 1 Remark: If we use any monotonic transformation it will give us the same curves. M. Utku Ünver Micro Theory Utility 8 / 15
9 Perfect Substitutes: u(x 1, x 2 ) = ax 1 + bx 2 M. Utku Ünver Micro Theory Utility 9 / 15
10 Perfect Complements: Suppose a consumer always uses 2 teaspoons of sugar with each cup of tea. If x 1 is the cups of tea and x 2 is the teaspoons of sugar available, then the number of correctly sweetened cups of tea will be min{x 1, 1 2 x 2}. In general u(x 1, x 2 ) = min{ax 1, bx 2 } M. Utku Ünver Micro Theory Utility 10 / 15
11 Quasilinear Preferences: u(x 1, x 2 ) = v(x 1 ) + x 2 Ex: u = ln x 1 + x 2, u = x 1 + x 2 Each indifference curve is a vertical shifted version of a single indifference curve. M. Utku Ünver Micro Theory Utility 11 / 15
12 Other preferences with kinks: Example: u = min{x 1 + 2x 2, 2x 1 + x 2 } M. Utku Ünver Micro Theory Utility 12 / 15
13 CobbDouglas Preferences: u(x 1, x 2 ) = x c 1 x d 2 These are nice convex and monotonic preferences. If we take the natural logarithm then; v(x 1, x 2 ) = ln(u(x 1 x 2 )) = c ln x 1 + d ln x 2. Since ln is a monotonic transformation this represents the same utility function. If we raise the utility function to 1 c+d power, then c+d v(x 1 x 2 ) = x c c+d 1 x d 2 and if we name a = c c+d then v(x 1, x 2 ) = x a 1 x 1 a 2 That means we can always take a monotonic transformation of the CobbDouglas utility function that make the exponents sum to 1. This will turn out to have a useful interpretation later on. M. Utku Ünver Micro Theory Utility 13 / 15
14 Marginal Utility Consider a consumer who is consuming some bundle of goods (x 1, x 2 ). How does his utility change as we give him a little more of good 1? This rate of change is called marginal utility with respect to good 1. Formally it is: MU 1 = u x 1 = u(x 1 + x 1, x 2 ) u(x 1, x 2 ) x 1 As x 1 0, MU 1 = u(x 1,x 2 ) x 1. Marginal Utility depends on the particular utility function. Note that U = MU 1 x 1 measures the change in utility, when consumption of good 1 changes by x 1. M. Utku Ünver Micro Theory Utility 14 / 15
15 Marginal Utility and MRS A utility function u(x 1, x 2 ) can be used to measure the MRS defined in Ch3. Recall that the MRS measures the slope of the indifference curve at the given bundle of goods; it can be interpreted as the rate at which a consumer is just willing to substitute a small amount of good 2 for good 1. Consider a change in the consumption of each good ( x 1, x 2 ) that keeps utility constant. In other words this change in consumption moves us along the indifference curve. Then Therefore; MU 1 x 1 + MU 2 x 2 = U = 0 MRS = x 2 x 1 = MU 1 MU 2 = u(x 1,x 2 ) x 1 u(x 1,x 2 ) x 2 While the marginal utilities depend on the particular utility function, their ratio (i. e. the MRS) does not. M. Utku Ünver Micro Theory Utility 15 / 15
Preferences. M. Utku Ünver Micro Theory. Boston College. M. Utku Ünver Micro Theory (BC) Preferences 1 / 20
Preferences M. Utku Ünver Micro Theory Boston College M. Utku Ünver Micro Theory (BC) Preferences 1 / 20 Preference Relations Given any two consumption bundles x = (x 1, x 2 ) and y = (y 1, y 2 ), the
More informationc 2008 Je rey A. Miron We have described the constraints that a consumer faces, i.e., discussed the budget constraint.
Lecture 2b: Utility c 2008 Je rey A. Miron Outline: 1. Introduction 2. Utility: A De nition 3. Monotonic Transformations 4. Cardinal Utility 5. Constructing a Utility Function 6. Examples of Utility Functions
More information4.1 Ordinal versus cardinal utility
Microeconomics I. Antonio Zabalza. Universit of Valencia 1 Micro I. Lesson 4. Utilit In the previous lesson we have developed a method to rank consistentl all bundles in the (,) space and we have introduced
More informationChapter 4 Online Appendix: The Mathematics of Utility Functions
Chapter 4 Online Appendix: The Mathematics of Utility Functions We saw in the text that utility functions and indifference curves are different ways to represent a consumer s preferences. Calculus can
More informationEconomics 121b: Intermediate Microeconomics Problem Set 2 1/20/10
Dirk Bergemann Department of Economics Yale University s by Olga Timoshenko Economics 121b: Intermediate Microeconomics Problem Set 2 1/20/10 This problem set is due on Wednesday, 1/27/10. Preliminary
More informationANSWER KEY 3 UTILITY FUNCTIONS, THE CONSUMER S PROBLEM, DEMAND CURVES
ANSWER KEY 3 UTILITY FUNCTIONS, THE CONSUMER S PROBLEM, DEMAND CURVES ECON 210 (1) Perfect Substitutes. Suppose that Jack s utility is entirely based on number of hours spent camping (c) and skiing (s).
More informationChapter 4 NAME. Utility
Chapter 4 Utility NAME Introduction. In the previous chapter, you learned about preferences and indifference curves. Here we study another way of describing preferences, the utility function. A utility
More informationEconomic Principles Solutions to Problem Set 1
Economic Principles Solutions to Problem Set 1 Question 1. Let < be represented b u : R n +! R. Prove that u (x) is strictl quasiconcave if and onl if < is strictl convex. If part: ( strict convexit of
More informationEcon 100A: Intermediate Microeconomics Notes on Consumer Theory
Econ 100A: Interediate Microeconoics Notes on Consuer Theory Linh Bun Winter 2012 (UCSC 1. Consuer Theory Utility Functions 1.1. Types of Utility Functions The following are soe of the type of the utility
More informationPrice Elasticity of Supply; Consumer Preferences
1 Price Elasticity of Supply 1 14.01 Principles of Microeconomics, Fall 2007 ChiaHui Chen September 12, 2007 Lecture 4 Price Elasticity of Supply; Consumer Preferences Outline 1. Chap 2: Elasticity 
More informationSlutsky Equation. M. Utku Ünver Micro Theory. Boston College. M. Utku Ünver Micro Theory (BC) Slutsky Equation 1 / 15
Slutsky Equation M. Utku Ünver Micro Theory Boston College M. Utku Ünver Micro Theory (BC) Slutsky Equation 1 / 15 Effects of a Price Change: What happens when the price of a commodity decreases? 1 The
More informationProblem Set #5Key. Economics 305Intermediate Microeconomic Theory
Problem Set #5Key Sonoma State University Economics 305Intermediate Microeconomic Theory Dr Cuellar (1) Suppose that you are paying your for your own education and that your college tuition is $200 per
More informationMicroeconomic Theory: Basic Math Concepts
Microeconomic Theory: Basic Math Concepts Matt Van Essen University of Alabama Van Essen (U of A) Basic Math Concepts 1 / 66 Basic Math Concepts In this lecture we will review some basic mathematical concepts
More informationDeriving Demand Functions  Examples 1
Deriving Demand Functions  Examples 1 What follows are some examples of different preference relations and their respective demand functions. In all the following examples, assume we have two goods x
More informationConstrained Optimisation
CHAPTER 9 Constrained Optimisation Rational economic agents are assumed to make choices that maximise their utility or profit But their choices are usually constrained for example the consumer s choice
More informationCHAPTER 3 CONSUMER BEHAVIOR
CHAPTER 3 CONSUMER BEHAVIOR EXERCISES 2. Draw the indifference curves for the following individuals preferences for two goods: hamburgers and beer. a. Al likes beer but hates hamburgers. He always prefers
More informationREVIEW OF MICROECONOMICS
ECO 352 Spring 2010 Precepts Weeks 1, 2 Feb. 1, 8 REVIEW OF MICROECONOMICS Concepts to be reviewed Budget constraint: graphical and algebraic representation Preferences, indifference curves. Utility function
More informationConsumer Theory. The consumer s problem
Consumer Theory The consumer s problem 1 The Marginal Rate of Substitution (MRS) We define the MRS(x,y) as the absolute value of the slope of the line tangent to the indifference curve at point point (x,y).
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 informationUC Berkeley Haas School of Business Economic Analysis for Business Decisions (EWMBA 201A)
UC Berkeley Haas School of Business Economic Analysis for Business Decisions (EWMBA 201A) The economic agent (PR 3.13.4) Standard economics vs. behavioral economics Lectures 12 Aug. 15, 2009 Prologue
More informationProblem Set 2: Solutions ECON 301: Intermediate Microeconomics Prof. Marek Weretka. Problem 1 (Marginal Rate of Substitution)
Proble Set 2: Solutions ECON 30: Interediate Microeconoics Prof. Marek Weretka Proble (Marginal Rate of Substitution) (a) For the third colun, recall that by definition MRS(x, x 2 ) = ( ) U x ( U ). x
More informationAK 4 SLUTSKY COMPENSATION
AK 4 SLUTSKY COMPENSATION ECON 210 A. JOSEPH GUSE (1) (a) First calculate the demand at the original price p b = 2 b(p b,m) = 1000 20 5p b b 0 = b(2) = 40 In general m c = m+(p 1 b p0 b )b 0. If the price
More informationThe fundamental question in economics is 2. Consumer Preferences
A Theory of Consumer Behavior Preliminaries 1. Introduction The fundamental question in economics is 2. Consumer Preferences Given limited resources, how are goods and service allocated? 1 3. Indifference
More informationCHAPTER 4 Consumer Choice
CHAPTER 4 Consumer Choice CHAPTER OUTLINE 4.1 Preferences Properties of Consumer Preferences Preference Maps 4.2 Utility Utility Function Ordinal Preference Utility and Indifference Curves Utility and
More informationDemand. Lecture 3. August 2015. Reading: Perlo Chapter 4 1 / 58
Demand Lecture 3 Reading: Perlo Chapter 4 August 2015 1 / 58 Introduction We saw the demand curve in chapter 2. We learned about consumer decision making in chapter 3. Now we bridge the gap between the
More informationAdvanced Microeconomics
Advanced Microeconomics Ordinal preference theory Harald Wiese University of Leipzig Harald Wiese (University of Leipzig) Advanced Microeconomics 1 / 68 Part A. Basic decision and preference theory 1 Decisions
More informationMERSİN UNIVERSITY FACULTY OF ECONOMICS AND ADMINISTRATIVE SCİENCES DEPARTMENT OF ECONOMICS MICROECONOMICS MIDTERM EXAM DATE 18.11.
MERSİN UNIVERSITY FACULTY OF ECONOMICS AND ADMINISTRATIVE SCİENCES DEPARTMENT OF ECONOMICS MICROECONOMICS MIDTERM EXAM DATE 18.11.2011 TİIE 12:30 STUDENT NAME AND NUMBER MULTIPLE CHOICE. Choose the one
More informationFollow links for Class Use and other Permissions. For more information send email to: permissions@pupress.princeton.edu
COPYRIGHT NOTICE: Ariel Rubinstein: Lecture Notes in Microeconomic Theory is published by Princeton University Press and copyrighted, c 2006, by Princeton University Press. All rights reserved. No part
More informationEconomics 2020a / HBS 4010 / HKS API111 FALL 2010 Solutions to Practice Problems for Lectures 1 to 4
Economics 00a / HBS 4010 / HKS API111 FALL 010 Solutions to Practice Problems for Lectures 1 to 4 1.1. Quantity Discounts and the Budget Constraint (a) The only distinction between the budget line with
More informationFollow links for Class Use and other Permissions. For more information send email to: permissions@pupress.princeton.edu
COPYRIGHT NOTICE: Ariel Rubinstein: Lecture Notes in Microeconomic Theory is published by Princeton University Press and copyrighted, c 2006, by Princeton University Press. All rights reserved. No part
More informationDifferent Types of Tastes
Chapter 5 Different Types of Tastes In Chapter 4 we demonstrated how tastes can be represented by maps of indifference curves and how 5 basic assumptions about tastes result in particular features of these
More informationManagerial Economics Prof. Trupti Mishra S.J.M. School of Management Indian Institute of Technology, Bombay. Lecture  13 Consumer Behaviour (Contd )
(Refer Slide Time: 00:28) Managerial Economics Prof. Trupti Mishra S.J.M. School of Management Indian Institute of Technology, Bombay Lecture  13 Consumer Behaviour (Contd ) We will continue our discussion
More informationChapter 3 Consumer Behavior
Chapter 3 Consumer Behavior Read Pindyck and Rubinfeld (2013), Chapter 3 Microeconomics, 8 h Edition by R.S. Pindyck and D.L. Rubinfeld Adapted by Chairat Aemkulwat for Econ I: 2900111 1/29/2015 CHAPTER
More informationEconomics 2020a / HBS 4010 / HKS API111 Fall 2011 Practice Problems for Lectures 1 to 11
Economics 2020a / HBS 4010 / HKS API111 Fall 2011 Practice Problems for Lectures 1 to 11 LECTURE 1: BUDGETS AND REVEALED PREFERENCE 1.1. Quantity Discounts and the Budget Constraint Suppose that a consumer
More informationIndifference Curves: An Example (pp. 6579) 2005 Pearson Education, Inc.
Indifference Curves: An Example (pp. 6579) Market Basket A B D E G H Units of Food 20 10 40 30 10 10 Units of Clothing 30 50 20 40 20 40 Chapter 3 1 Indifference Curves: An Example (pp. 6579) Graph the
More informationLecture Notes on Elasticity of Substitution
Lecture Notes on Elasticity of Substitution Ted Bergstrom, UCSB Economics 210A March 3, 2011 Today s featured guest is the elasticity of substitution. Elasticity of a function of a single variable Before
More informationEconomics 100A. Final Exam
Name form number 1 Economics 100A Final Exam Fill in the bubbles on your scantron with your id number (starting from the left side of the box), your name, and the form type. Students who do this successfully
More informationName. Final Exam, Economics 210A, December 2011 Here are some remarks to help you with answering the questions.
Name Final Exam, Economics 210A, December 2011 Here are some remarks to help you with answering the questions. Question 1. A firm has a production function F (x 1, x 2 ) = ( x 1 + x 2 ) 2. It is a price
More informationLesson 2. Preferences and Utility 1. Lesson 2 Preferences and Utility. c 2010, 2011 Roberto Serrano and Allan M. Feldman All rights reserved Version C
Lesson 2. Preferences and Utility 1 Lesson 2 Preferences and Utility c 2010, 2011 Roberto Serrano and Allan M. Feldman All rights reserved Version C 1. Introduction Life is like a shopping center. The
More informationTable of Contents MICRO ECONOMICS
economicsentrance.weebly.com Basic Exercises Micro Economics AKG 09 Table of Contents MICRO ECONOMICS Budget Constraint... 4 Practice problems... 4 Answers... 4 Supply and Demand... 7 Practice Problems...
More informationSample Midterm Solutions
Sample Midterm Solutions Instructions: Please answer both questions. You should show your working and calculations for each applicable problem. Correct answers without working will get you relatively few
More informationLIST OF MEMBERS WHO PREPARED QUESTION BANK FOR ECONOMICS FOR CLASS XII TEAM MEMBERS. Sl. No. Name Designation
LIST OF MEMBERS WHO PREPARED QUESTION BANK FOR ECONOMICS FOR CLASS XII TEAM MEMBERS Sl. No. Name Designation 1. Mrs. Neelam Vinayak V. Principal (Team Leader) G.G.S.S. Deputy Ganj, Sadar Bazar Delhi110006
More informationChapter 21: The Discounted Utility Model
Chapter 21: The Discounted Utility Model 21.1: Introduction This is an important chapter in that it introduces, and explores the implications of, an empirically relevant utility function representing intertemporal
More informationChoices. Preferences. Indifference Curves. Preference Relations. ECON 370: Microeconomic Theory Summer 2004 Rice University Stanley Gilbert
Choices Preferences ECON 370: Microeconomic Theor Summer 2004 Rice Universit Stanle Gilbert The theor of consumer preferences is based fundamentall on choices The steak dinner or the salad bar Major in
More informationThe CobbDouglas Production Function
171 10 The CobbDouglas Production Function This chapter describes in detail the most famous of all production functions used to represent production processes both in and out of agriculture. First used
More informationTastes and Indifference Curves
C H A P T E R 4 Tastes and Indifference Curves This chapter begins a chapter treatment of tastes or what we also call preferences. In the first of these chapters, we simply investigate the basic logic
More information1. Briefly explain what an indifference curve is and how it can be graphically derived.
Chapter 2: Consumer Choice Short Answer Questions 1. Briefly explain what an indifference curve is and how it can be graphically derived. Answer: An indifference curve shows the set of consumption bundles
More informationCONSUMER PREFERENCES THE THEORY OF THE CONSUMER
CONSUMER PREFERENCES The underlying foundation of demand, therefore, is a model of how consumers behave. The individual consumer has a set of preferences and values whose determination are outside the
More informationReview of Fundamental Mathematics
Review of Fundamental Mathematics As explained in the Preface and in Chapter 1 of your textbook, managerial economics applies microeconomic theory to business decision making. The decisionmaking tools
More informationChoice under Uncertainty
Choice under Uncertainty Part 1: Expected Utility Function, Attitudes towards Risk, Demand for Insurance Slide 1 Choice under Uncertainty We ll analyze the underlying assumptions of expected utility theory
More informationPART A: For each worker, determine that worker's marginal product of labor.
ECON 3310 Homework #4  Solutions 1: Suppose the following indicates how many units of output y you can produce per hour with different levels of labor input (given your current factory capacity): PART
More informationOn Lexicographic (Dictionary) Preference
MICROECONOMICS LECTURE SUPPLEMENTS Hajime Miyazaki File Name: lexico95.usc/lexico99.dok DEPARTMENT OF ECONOMICS OHIO STATE UNIVERSITY Fall 993/994/995 Miyazaki.@osu.edu On Lexicographic (Dictionary) Preference
More informationIntermediate Microeconomics. by Jinwoo Kim
Intermediate Microeconomics by Jinwoo Kim 1 Contents 1 The Market 4 2 Budget Constraint 8 3 Preferences 10 4 Utility 14 5 Choice 18 6 Demand 24 7 Revealed Preference 27 8 Slutsky Equation 30 9 Buying and
More information17. If a good is normal, then the Engel curve A. Slopes upward B. Slopes downward C. Is vertical D. Is horizontal
Sample Exam 1 1. Suppose that when the price of hot dogs is $2 per package, there is a demand for 10,000 bags of hot dog buns. When the price of hot dogs is $3 per package, the demand for hot dog buns
More informationProductioin OVERVIEW. WSG5 7/7/03 4:35 PM Page 63. Copyright 2003 by Academic Press. All rights of reproduction in any form reserved.
WSG5 7/7/03 4:35 PM Page 63 5 Productioin OVERVIEW This chapter reviews the general problem of transforming productive resources in goods and services for sale in the market. A production function is the
More informationRisk and Uncertainty. Vani K Borooah University of Ulster
Risk and Uncertainty Vani K Borooah University of Ulster Basic Concepts Gamble: An action with more than one possible outcome, such that with each outcome there is an associated probability of that outcome
More informationIntermediate Micro. Expected Utility
Intermediate Micro Expected Utility Workhorse model of intermediate micro Utility maximization problem Consumers Max U(x,y) subject to the budget constraint, I=P x x + P y y Health Economics Spring 2015
More informationDeriving MRS from Utility Function, Budget Constraints, and Interior Solution of Optimization
Utilit Function, Deriving MRS. Principles of Microeconomics, Fall ChiaHui Chen September, Lecture Deriving MRS from Utilit Function, Budget Constraints, and Interior Solution of Optimization Outline.
More informationAn increase in the number of students attending college. shifts to the left. An increase in the wage rate of refinery workers.
1. Which of the following would shift the demand curve for new textbooks to the right? a. A fall in the price of paper used in publishing texts. b. A fall in the price of equivalent used text books. c.
More informationA Utility Maximization Example
A Utilit Maximization Example Charlie Gibbons Universit of California, Berkele September 17, 2007 Since we couldn t finish the utilit maximization problem in section, here it is solved from the beginning.
More informationName: ID: Discussion Section:
Math 28 Midterm 3 Spring 2009 Name: ID: Discussion Section: This exam consists of 6 questions: 4 multiple choice questions worth 5 points each 2 handgraded questions worth a total of 30 points. INSTRUCTIONS:
More informationChapter 4 The Theory of Individual Behavior
Managerial Economics & Business Strategy Chapter 4 The Theory of Individual Behavior McGrawHill/Irwin Copyright 2010 by the McGrawHill Companies, Inc. All rights reserved. Overview I. Consumer Behavior
More information8. Average product reaches a maximum when labor equals A) 100 B) 200 C) 300 D) 400
Ch. 6 1. The production function represents A) the quantity of inputs necessary to produce a given level of output. B) the various recipes for producing a given level of output. C) the minimum amounts
More information1 Sufficient statistics
1 Sufficient statistics A statistic is a function T = rx 1, X 2,, X n of the random sample X 1, X 2,, X n. Examples are X n = 1 n s 2 = = X i, 1 n 1 the sample mean X i X n 2, the sample variance T 1 =
More informationECON 305 Tutorial 7 (Week 9)
H. K. Chen (SFU) ECON 305 Tutorial 7 (Week 9) July 2,3, 2014 1 / 24 ECON 305 Tutorial 7 (Week 9) Questions for today: Ch.9 Problems 15, 7, 11, 12 MC113 Tutorial slides will be posted Thursday after 10:30am,
More informationTOPIC 4: DERIVATIVES
TOPIC 4: DERIVATIVES 1. The derivative of a function. Differentiation rules 1.1. The slope of a curve. The slope of a curve at a point P is a measure of the steepness of the curve. If Q is a point on the
More informationThis means there are two equilibrium solutions 0 and K. dx = rx(1 x). x(1 x) dt = r
Verhulst Model For Population Growth The first model (t) = r is not that realistic as it either led to a population eplosion or to etinction. This simple model was improved on by building into this differential
More informationThe Market ... ... ... ... ... ... ... 2. for large numbers of people, this is essentially a smooth curve as in Figure 1.2. The Market 1. Figure 1.
The Market 1 The Market A. Example of an economic model the market for apartments 1. models are simplifications of reality 2. for example, assume all apartments are identical 3. some are close to the university,
More informationU = x 1 2. 1 x 1 4. 2 x 1 4. What are the equilibrium relative prices of the three goods? traders has members who are best off?
Chapter 7 General Equilibrium Exercise 7. Suppose there are 00 traders in a market all of whom behave as price takers. Suppose there are three goods and the traders own initially the following quantities:
More informationSimple Model Economy. Business Economics Theory of Consumer Behavior Thomas & Maurice, Chapter 5. Circular Flow Model. Modeling Household Decisions
Business Economics Theory of Consumer Behavior Thomas & Maurice, Chapter 5 Herbert Stocker herbert.stocker@uibk.ac.at Institute of International Studies University of Ramkhamhaeng & Department of Economics
More informationPPF's of Germany and France
Economics 165 Winter 2 Problem Set #1 Problem 1: Let Germany and France have respective labor forces of 8 and 6. Suppose both countries produce wine and cares according to the following unit labor requirements:
More informationPrinciples of Economics: Micro: Exam #2: Chapters 110 Page 1 of 9
Principles of Economics: Micro: Exam #2: Chapters 110 Page 1 of 9 print name on the line above as your signature INSTRUCTIONS: 1. This Exam #2 must be completed within the allocated time (i.e., between
More informationNotes on indifference curve analysis of the choice between leisure and labor, and the deadweight loss of taxation. Jon Bakija
Notes on indifference curve analysis of the choice between leisure and labor, and the deadweight loss of taxation Jon Bakija This example shows how to use a budget constraint and indifference curve diagram
More informationMicroeconomics Sept. 16, 2010 NOTES ON CALCULUS AND UTILITY FUNCTIONS
DUSP 11.203 Frank Levy Microeconomics Sept. 16, 2010 NOTES ON CALCULUS AND UTILITY FUNCTIONS These notes have three purposes: 1) To explain why some simple calculus formulae are useful in understanding
More information15 Kuhn Tucker conditions
5 Kuhn Tucker conditions Consider a version of the consumer problem in which quasilinear utility x 2 + 4 x 2 is maximised subject to x +x 2 =. Mechanically applying the Lagrange multiplier/common slopes
More informationTheoretical Tools of Public Economics. Part2
Theoretical Tools of Public Economics Part2 Previous Lecture Definitions and Properties Utility functions Marginal utility: positive (negative) if x is a good ( bad ) Diminishing marginal utility Indifferences
More informationCorrelation key concepts:
CORRELATION Correlation key concepts: Types of correlation Methods of studying correlation a) Scatter diagram b) Karl pearson s coefficient of correlation c) Spearman s Rank correlation coefficient d)
More informationWeek 3: Demand Theory and Welfare Analysis
Week 3: Demand Theory and Welfare Analysis 1. Suppose the price of good increases so that the optimal chosen bundle changes from B 1 to B 2. If we think of good y as a numeraire good so that p y =1, then
More information3. George W. Bush is the current U.S. President. This is an example of a: A. Normative statement B. Positive statement
Econ 3144 Fall 2006 Test 1 Dr. Rupp Name Sign Pledge I have neither given nor received aid on this exam Multiple Choice Questions (3 points each) 1. What you give up to obtain an item is called your A.
More informationECN 221 Chapter 5 practice problems This is not due for a grade
ECN 221 Chapter 5 practice problems This is not due for a grade 1. Assume the price of pizza is $2.00 and the price of Beer is $1.00 and that at your current levels of consumption, the Marginal Utility
More informationChapter 27: Taxation. 27.1: Introduction. 27.2: The Two Prices with a Tax. 27.2: The PreTax Position
Chapter 27: Taxation 27.1: Introduction We consider the effect of taxation on some good on the market for that good. We ask the questions: who pays the tax? what effect does it have on the equilibrium
More informationProblem Set #3 Answer Key
Problem Set #3 Answer Key Economics 305: Macroeconomic Theory Spring 2007 1 Chapter 4, Problem #2 a) To specify an indifference curve, we hold utility constant at ū. Next, rearrange in the form: C = ū
More informationLecture 11 Uncertainty
Lecture 11 Uncertainty 1. Contingent Claims and the StatePreference Model 1) Contingent Commodities and Contingent Claims Using the simple twogood model we have developed throughout this course, think
More informationSlopeIntercept Form of a Linear Equation Examples
SlopeIntercept Form of a Linear Equation Examples. In the figure at the right, AB passes through points A(0, b) and B(x, y). Notice that b is the yintercept of AB. Suppose you want to find an equation
More informationInsurance. Michael Peters. December 27, 2013
Insurance Michael Peters December 27, 2013 1 Introduction In this chapter, we study a very simple model of insurance using the ideas and concepts developed in the chapter on risk aversion. You may recall
More informationCURVE FITTING LEAST SQUARES APPROXIMATION
CURVE FITTING LEAST SQUARES APPROXIMATION Data analysis and curve fitting: Imagine that we are studying a physical system involving two quantities: x and y Also suppose that we expect a linear relationship
More informationWhere are we? To do today: finish the derivation of the demand curve using indifference curves. Go on then to chapter Production and Cost
Where are we? To do today: finish the derivation of the demand curve using indifference curves Go on then to chapter Production and Cost Utility and indifference curves The point is to find where on the
More informationA Detailed Price Discrimination Example
A Detailed Price Discrimination Example Suppose that there are two different types of customers for a monopolist s product. Customers of type 1 have demand curves as follows. These demand curves include
More informationCHAPTER FIVE. Solutions for Section 5.1. Skill Refresher. Exercises
CHAPTER FIVE 5.1 SOLUTIONS 265 Solutions for Section 5.1 Skill Refresher S1. Since 1,000,000 = 10 6, we have x = 6. S2. Since 0.01 = 10 2, we have t = 2. S3. Since e 3 = ( e 3) 1/2 = e 3/2, we have z =
More informationCameron ECON 100: FIRST MIDTERM (A) Winter 01
Cameron ECON 100: FIRST MIDTERM (A) Winter 01 Answer all questions in the space provided on the exam. Total of 40 points (and worth 22.5% of final grade). Read each question carefully, so that you answer
More informationExpected Utility Analysis
Expected Utility Analysis L A T E X file: expectedutility Daniel A. Graham, September 8, 2 Preferences for Probabilities We now turn to characterizing preferences for lotteries with the goal of identifying
More informationIntroductory Notes on Demand Theory
Introductory Notes on Demand Theory (The Theory of Consumer Behavior, or Consumer Choice) This brief introduction to demand theory is a preview of the first part of Econ 501A, but it also serves as a prototype
More information19 : Theory of Production
19 : Theory of Production 1 Recap from last session Long Run Production Analysis Return to Scale Isoquants, Isocost Choice of input combination Expansion path Economic Region of Production Session Outline
More informationLecture 10  Risk and Insurance
Lecture 10  Risk and Insurance 14.03 Spring 2003 1 Risk Aversion and Insurance: Introduction To have a passably usable model of choice, we need to be able to say something about how risk affects choice
More informationD) Marginal revenue is the rate at which total revenue changes with respect to changes in output.
Ch. 9 1. Which of the following is not an assumption of a perfectly competitive market? A) Fragmented industry B) Differentiated product C) Perfect information D) Equal access to resources 2. Which of
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationLecture 2. Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization
Lecture 2. Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization 2.1. Introduction Suppose that an economic relationship can be described by a realvalued
More informationExamples on Monopoly and Third Degree Price Discrimination
1 Examples on Monopoly and Third Degree Price Discrimination This hand out contains two different parts. In the first, there are examples concerning the profit maximizing strategy for a firm with market
More informationLecture notes for Choice Under Uncertainty
Lecture notes for Choice Under Uncertainty 1. Introduction In this lecture we examine the theory of decisionmaking under uncertainty and its application to the demand for insurance. The undergraduate
More informationNonlinear Regression Functions. SW Ch 8 1/54/
Nonlinear Regression Functions SW Ch 8 1/54/ The TestScore STR relation looks linear (maybe) SW Ch 8 2/54/ But the TestScore Income relation looks nonlinear... SW Ch 8 3/54/ Nonlinear Regression General
More information