Econ 100A: Intermediate Microeconomics Notes on Consumer Theory
|
|
- Russell Gibbs
- 7 years ago
- Views:
Transcription
1 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 functions that are iportant: Perfect Copleents Perfect Substitutes Cobb-Douglas Quasilinear 1.2. Perfect Copleents The Utility function: U(x, y Min {x, y} The Budget Constraint: x + y where is incoe, and and is the price of good x and y respectively. The graph of the indifference curves for Perfect Copletents is as follows: Y U U X Perfect copleents: L-shaped indifference curves This notes is prepared with soe help fro Aadil Nakhoda 1
2 Exaple: Right shoe and Left shoe: If we purchase one right shoe, we need to purchase one left shoe also. The cosuer axiization proble for Perfect Copleents: subject to Max U (x, y x + y The optial allocation, the consuption bundle that gives the highest utility (x, y, is when x y Replacing y with x into the budget constraint since x y, we have the following: x + x x ( + x y Perfect Substitutes Y Budget line U1 U2 X Consider the above graph: The slope of the budget line is Steeper than the slope of the indifference curves., The slope of the budge line in absolute value is px where px and is the price of good x and y respectively. The slope of the indifference curves in absolute value is MRS, where MRS is the Marginal Rate of Substitutions [ ] [ ] [ U(x,y ] Marginal Utility of Good x MUx Marginal Utility of Good y MU U(x,y y The slope of the budget line is Steeper than the slope of the indifference curves. This is equivalent to having the following: > MRS The Optial Allocation (x, y is (0, py. Equivalently, the quantity of good x and y deanded is (0, py. Exaple: Suppose we have two goods, Pepsi (x and Coke (y. Which good would you prefer to purchase? Spending all incoe on Coke (y, i.e. purchasing only Coke (y, will put you on the highest indifference curve given the budget constraint. The budget line is tangent to a higher indifference curve at the y Axis, than it is at the x Axis. 2
3 Y Budget line U1 U2 X Consider the above graph: The slope of the budget line is Flatter than the slope of the indifference curves., The slope of the budge line in absolute value is px where px and is the price of good x and y respectively. The slope of the indifference curves in absolute value is MRS, where MRS is the Marginal Rate of Substitutions MRS Marginal Utility of Good x Marginal Utility of Good y MU x MU y U(x,y U(x,y The slope of the budget line is Flatter than the slope of the indifference curves. This is equivalent to having the following: < MRS ( The Optial Allocation (x, y is, 0. Equivalently, the quantity of good x and y deanded is (, 0. Exaple: Suppose we have two goods, Pepsi (x and Coke (y. Which good would you purchase? Spending all incoe on Pepsi (x, i.e. purchasing only Pepsi (x, will put you on the highest indifference curve given the budget constraint. The budget line is tangent to a higher indifference curve at the x axis, than it is at the y axis. Perfect Substitutes: Rules to follow: If the slope of the budget constraint is Steeper than the slope of the indifference curve, we consue the good on the y axis. In particular, > MRS Where and is the price of good x and y respectively. If the slope of the budget constraint is Flatter than the slope of the indifference curve, we consue the good on the x axis. In particular, < MRS Where and is the price of good x and y respectively. If we were to consue the good on the x axis, we represent it as: 3
4 Exaple: Suppose we have the utility function: U (x, y x + 5y and the budget constraint is as follows: 2x + 3y 10 The Marginal Rate of Substitution is as follows: 5 The MRS in absolute value is: MRS 5 5 The slope of the budget line is as follows: Slope (BC 2 3 The slope of the budget line in absolute value Slope (BC MRS > Slope (BC As a result, agents consue only goods x. The quantity of good x and y deanded, i.e. the Optial Allocation, is (x, y ( 10 2, 0 Note that when y 0 we have 2x 10 fro the budget constraint. x 5, y 0 The highest level of utility is 1.. Cobb-Douglas Utility Function The Cobb-Douglas utility function: U (5, 0 ( (5 + (5 (0 20 U(x, y x a y b, where a > 0 and b > 0 Alternatively, using onotonic transforation, Cobb-Douglas utility function could also be represented as follows: U (x, y a log (x + b log (y, where a > 0 and b > 0. This indifference curve will have a negative slope, which will incorporate the individual s willingness to ake tradeoffs between good x and y. How to solve for an Optial Bundle or Optial Allocation given a Cobb-Douglas function: ( px x a 1 y b bx a y b 1 ( y b x
5 ( y b x To solve for y, we can rewrite the above as: b y x Fro the budget constraint, we have the following: b y + y b + 1 y ( y b ( ( b y And, now to solve for x Substitute y above into the budget constraint: [( ( ] b x + Cancelling in above equation, we have the following: ( b x + The Optial Bundle is: ( b x x (x, y ( ( 1 b ( b x x ( ( b, This should be siilar to the case presented in the textbook. ( 5
6 1.5. Quasilinear Utility Functions A Quasilinear utility function is as follows: U(x, y ln (x + y where ln (x is the natural logarith. The function U(x, y is linear in y. Let us solve for the above function: At the Optial Bundle (x, y, we have the following equations ( px i.e. the slope of the indifference curve at the Optial Bundle is equal to the slope of the budget line. The Marginal Rate of Substitutions MRS is as follows: [ ] [ ] [ U(x,y ] Marginal Utility of Good x MUx Marginal Utility of Good y MU U(x,y y U (x, y [ln (x + y] ln (x 1 x Recalling the rule for differentiating a natural logarith function ln (x : d [ln (x] dx 1 x U (x, y [ln (x + y] 1 ( 1 x ( px ( 1 x 1 1 x x Substitute the above into the following budget constraint: x + y ( + y So our optial bundle is: y 1 (x, y (, 1 6
7 2. Practice Probles: 2.1. Copleents: Utility function is U (x 1, x 2 Min(x 1, 2x 2 Suppose an accountant needs 1 eraser for every 2 pencils he/she uses. Any ore pencils will not be useful as the accountant will not be able to erase the caluclations. Any ore erasers will also not serve his purpose also. Therefore, x 1 is pencil and x 2 is eraser. To solve for axiization proble: where The budget constraint: Max U (x 1, x 2 U (x 1, x 2 Min(x 1, 2x 2 p 1 x 2 + p 2 x 2 where p 1 and p 2 is the price of good x 1 and x 2 respectively. With x 1 2x 2 2p 1 x 2 + p 2 x 1 x 2 2p 1 + p 2 And for x 1 : p 1 x p 2x 1 x 1 p p Substitutes: U 3 (Coke + 6 (P epsi The price of Pepsi is $2, and the price of Coke is $0.8. What is the Optial Consuption Bundle for the individual? First assue, Coke to be on y axis ( ( slope of budget line ( 2 5 ( We know that the slope of the budget line is greater than the MRS, the slope of the indifference curve. So what good will the individual consue and why? 2.3. Cobb-Douglas: Find the Optial Consuption Bundles of x and y for the following utility functions: U (x, y x 2 3 y 5 U (x, y x 2 + y Where the price of good x is $2 and the price of good y is $1, and incoe is $10. 7
Problem 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 informationUtility. M. Utku Ünver Micro Theory. M. Utku Ünver Micro Theory Utility 1 / 15
Utility M. Utku Ünver Micro Theory M. Utku Ünver Micro Theory Utility 1 / 15 Utility Function The preferences are the fundamental description useful for analyzing choice and utility is simply a way of
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 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 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 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 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 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 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 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 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 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 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 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 (ES30025)
Advanced Microeconoics (ES3005) Advanced Microeconoics (ES3005) Matheatics Review : The Lagrange Multiplier Outline: I. Introduction II. Duality Theory: Co Douglas Exaple III. Final Coents I. Introduction
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 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 informationEconomics 2020a / HBS 4010 / HKS API-111 FALL 2010 Solutions to Practice Problems for Lectures 1 to 4
Economics 00a / HBS 4010 / HKS API-111 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 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 decision-making tools
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 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 The Theory of Individual Behavior
Managerial Economics & Business Strategy Chapter 4 The Theory of Individual Behavior McGraw-Hill/Irwin Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved. Overview I. Consumer Behavior
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 informationPreferences. 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 informationOnline Appendix I: A Model of Household Bargaining with Violence. In this appendix I develop a simple model of household bargaining that
Online Appendix I: A Model of Household Bargaining ith Violence In this appendix I develop a siple odel of household bargaining that incorporates violence and shos under hat assuptions an increase in oen
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 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 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 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 informationCalculus AB 2014 Scoring Guidelines
P Calculus B 014 Scoring Guidelines 014 The College Board. College Board, dvanced Placement Program, P, P Central, and the acorn logo are registered trademarks of the College Board. P Central is the official
More informationTheory of Demand. ECON 212 Lecture 7. Tianyi Wang. Winter 2013. Queen s Univerisity. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter 2013 1 / 46
Theory of Demand ECON 212 Lecture 7 Tianyi Wang Queen s Univerisity Winter 2013 Tianyi Wang (Queen s Univerisity) Lecture 7 Winter 2013 1 / 46 Intro Note: Quiz 1 can be picked up at Distribution Center.
More information1 Calculus of Several Variables
1 Calculus of Several Variables Reading: [Simon], Chapter 14, p. 300-31. 1.1 Partial Derivatives Let f : R n R. Then for each x i at each point x 0 = (x 0 1,..., x 0 n) the ith partial derivative is defined
More informationProblem Set #5-Key. Economics 305-Intermediate Microeconomic Theory
Problem Set #5-Key Sonoma State University Economics 305-Intermediate Microeconomic Theory Dr Cuellar (1) Suppose that you are paying your for your own education and that your college tuition is $200 per
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 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 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 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 informationUnderstanding the Slutsky Decomposition: Substitution & Income Effect
Understanding the Slutsky Decomposition: Substitution & Income Effect age 1 lacement of the Final Bundle when p : Substitute or Complement Goods? egion A egion B egion C BC 2 S When p, BC rotates inwards
More information5.1 Derivatives and Graphs
5.1 Derivatives and Graphs What does f say about f? If f (x) > 0 on an interval, then f is INCREASING on that interval. If f (x) < 0 on an interval, then f is DECREASING on that interval. A function has
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 real-valued
More informationFelix Munoz-Garcia 1. School of Economic Sciences. Washington State University
ECONS 301 - INTERMEDIATE MICROECONOMICS LECTURE NOTES Felix Munoz-Garcia 1 School of Economic Sciences Washington State University This document contains a set of partial lecture notes that are intended
More informationDeriving MRS from Utility Function, Budget Constraints, and Interior Solution of Optimization
Utilit Function, Deriving MRS. Principles of Microeconomics, Fall Chia-Hui Chen September, Lecture Deriving MRS from Utilit Function, Budget Constraints, and Interior Solution of Optimization Outline.
More informationPrice Elasticity of Supply; Consumer Preferences
1 Price Elasticity of Supply 1 14.01 Principles of Microeconomics, Fall 2007 Chia-Hui Chen September 12, 2007 Lecture 4 Price Elasticity of Supply; Consumer Preferences Outline 1. Chap 2: Elasticity -
More informationThe Cobb-Douglas Production Function
171 10 The Cobb-Douglas 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 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 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 informationChapter 6 Competitive Markets
Chapter 6 Competitive Markets After reading Chapter 6, COMPETITIVE MARKETS, you should be able to: List and explain the characteristics of Perfect Competition and Monopolistic Competition Explain why a
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 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 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 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 informationPPA 723, Fall 2006 Professor John McPeak
Quiz One PPA 723, Fall 2006 Professor John McPeak Name: The total quiz is worth 20 points. Each question is worth 2 points, and each sub question is worth an equal share of the two points. 1) The demand
More informationPrinciples of Economics: Micro: Exam #2: Chapters 1-10 Page 1 of 9
Principles of Economics: Micro: Exam #2: Chapters 1-10 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 informationConstrained optimization.
ams/econ 11b supplementary notes ucsc Constrained optimization. c 2010, Yonatan Katznelson 1. Constraints In many of the optimization problems that arise in economics, there are restrictions on the values
More informationAverage rate of change of y = f(x) with respect to x as x changes from a to a + h:
L15-1 Lecture 15: Section 3.4 Definition of the Derivative Recall the following from Lecture 14: For function y = f(x), the average rate of change of y with respect to x as x changes from a to b (on [a,
More informationWalrasian Demand. u(x) where B(p, w) = {x R n + : p x w}.
Walrasian Demand Econ 2100 Fall 2015 Lecture 5, September 16 Outline 1 Walrasian Demand 2 Properties of Walrasian Demand 3 An Optimization Recipe 4 First and Second Order Conditions Definition Walrasian
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 10. Consumer Choice and Behavioral Economics
Chapter 10. Consumer Choice and Behavioral Economics Instructor: JINKOOK LEE Department of Economics / Texas A&M University ECON 202 504 Principles of Microeconomics Utility Utility: the satisfaction people
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More informationEconomics 2020a / HBS 4010 / HKS API-111 Fall 2011 Practice Problems for Lectures 1 to 11
Economics 2020a / HBS 4010 / HKS API-111 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 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 informationSlope-Intercept Form of a Linear Equation Examples
Slope-Intercept 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 y-intercept of AB. Suppose you want to find an equation
More informationWork, Energy, Conservation of Energy
This test covers Work, echanical energy, kinetic energy, potential energy (gravitational and elastic), Hooke s Law, Conservation of Energy, heat energy, conservative and non-conservative forces, with soe
More informationMICROECONOMICS AND POLICY ANALYSIS - U8213 Professor Rajeev H. Dehejia Class Notes - Spring 2001
MICROECONOMICS AND POLICY ANALYSIS - U8213 Professor Rajeev H. Dehejia Class Notes - Spring 2001 General Equilibrium and welfare with production Wednesday, January 24 th and Monday, January 29 th Reading:
More informationECO364 - International Trade
ECO364 - International Trade Chapter 2 - Ricardo Christian Dippel University of Toronto Summer 2009 Christian Dippel (University of Toronto) ECO364 - International Trade Summer 2009 1 / 73 : The Ricardian
More informationChapter 6. Elasticity: The Responsiveness of Demand and Supply
Chapter 6. Elasticity: The Responsiveness of Demand and Supply Instructor: JINKOOK LEE Department of Economics / Texas A&M University ECON 202 504 Principles of Microeconomics Elasticity Demand curve:
More informationProfit and Revenue Maximization
WSG7 7/7/03 4:36 PM Page 95 7 Profit and Revenue Maximization OVERVIEW The purpose of this chapter is to develop a general framework for finding optimal solutions to managerial decision-making problems.
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 informationTheoretical Tools of Public Economics. Part-2
Theoretical Tools of Public Economics Part-2 Previous Lecture Definitions and Properties Utility functions Marginal utility: positive (negative) if x is a good ( bad ) Diminishing marginal utility Indifferences
More information( ) = ( ) = {,,, } β ( ), < 1 ( ) + ( ) = ( ) + ( )
{ } ( ) = ( ) = {,,, } ( ) β ( ), < 1 ( ) + ( ) = ( ) + ( ) max, ( ) [ ( )] + ( ) [ ( )], [ ( )] [ ( )] = =, ( ) = ( ) = 0 ( ) = ( ) ( ) ( ) =, ( ), ( ) =, ( ), ( ). ln ( ) = ln ( ). + 1 ( ) = ( ) Ω[ (
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 3.1-3.4) Standard economics vs. behavioral economics Lectures 1-2 Aug. 15, 2009 Prologue
More informationPRACTICE FINAL. Problem 1. Find the dimensions of the isosceles triangle with largest area that can be inscribed in a circle of radius 10cm.
PRACTICE FINAL Problem 1. Find the dimensions of the isosceles triangle with largest area that can be inscribed in a circle of radius 1cm. Solution. Let x be the distance between the center of the circle
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 informationAbsolute Value Equations and Inequalities
Key Concepts: Compound Inequalities Absolute Value Equations and Inequalities Intersections and unions Suppose that A and B are two sets of numbers. The intersection of A and B is the set of all numbers
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 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 informationHomework #5: Answers. b. How can land rents as well as total wages be shown in such a diagram?
Homework #5: Answers Text questions, hapter 6, problems 1-4. Note that in all of these questions, the convention in the text, whereby production of food uses land and labor, and clothing uses capital and
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 informationLecture 2: Consumer Theory
Lecture 2: Consumer Theory Preferences and Utility Utility Maximization (the primal problem) Expenditure Minimization (the dual) First we explore how consumers preferences give rise to a utility fct which
More informationLong-Run Average Cost. Econ 410: Micro Theory. Long-Run Average Cost. Long-Run Average Cost. Economies of Scale & Scope Minimizing Cost Mathematically
Slide 1 Slide 3 Econ 410: Micro Theory & Scope Minimizing Cost Mathematically Friday, November 9 th, 2007 Cost But, at some point, average costs for a firm will tend to increase. Why? Factory space and
More informationor, put slightly differently, the profit maximizing condition is for marginal revenue to equal marginal cost:
Chapter 9 Lecture Notes 1 Economics 35: Intermediate Microeconomics Notes and Sample Questions Chapter 9: Profit Maximization Profit Maximization The basic assumption here is that firms are profit maximizing.
More informationThe Point-Slope Form
7. The Point-Slope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope
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 hand-graded questions worth a total of 30 points. INSTRUCTIONS:
More informationMath 120 Final Exam Practice Problems, Form: A
Math 120 Final Exam Practice Problems, Form: A Name: While every attempt was made to be complete in the types of problems given below, we make no guarantees about the completeness of the problems. Specifically,
More information3 The Utility Maximization Problem
3 The Utility Mxiiztion Proble We hve now discussed how to describe preferences in ters of utility functions nd how to forulte siple budget sets. The rtionl choice ssuption, tht consuers pick the best
More informationElasticity. I. What is Elasticity?
Elasticity I. What is Elasticity? The purpose of this section is to develop some general rules about elasticity, which may them be applied to the four different specific types of elasticity discussed in
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 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 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 informationConsumer Theory: The Mathematical Core
Consumer Theory: The Mathematical Core Dan McFadden, C13 Suppose an individual has a utility function U(x) which is a function of non-negative commodity vectors x = (x 1,x,...,x N ), and seeks to maximize
More informationMarginal cost. Average cost. Marginal revenue 10 20 40
Economics 101 Fall 2011 Homework #6 Due: 12/13/2010 in lecture 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 homework
More informationChapter 8. Competitive Firms and Markets
Chapter 8. Competitive Firms and Markets We have learned the production function and cost function, the question now is: how much to produce such that firm can maximize his profit? To solve this question,
More information100. In general, we can define this as if b x = a then x = log b
Exponents and Logarithms Review 1. Solving exponential equations: Solve : a)8 x = 4! x! 3 b)3 x+1 + 9 x = 18 c)3x 3 = 1 3. Recall: Terminology of Logarithms If 10 x = 100 then of course, x =. However,
More informationIndifference Curves: An Example (pp. 65-79) 2005 Pearson Education, Inc.
Indifference Curves: An Example (pp. 65-79) 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. 65-79) Graph the
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 informationProduction Function in the Long-Run. Business Economics Theory of the Firm II Production and Cost in the Long Run. Description of Technology
Business Economics Theory of the Firm II Production and Cost in the ong Run Two or more variable input factors Thomas & Maurice, Chapter 9 Herbert Stocker herbert.stocker@uibk.ac.at Institute of International
More informationChoice Under Uncertainty Insurance Diversification & Risk Sharing AIG. Uncertainty
Uncertainty Table of Contents 1 Choice Under Uncertainty Budget Constraint Preferences 2 Insurance Choice Framework Expected Utility Theory 3 Diversification & Risk Sharing 4 AIG States of Nature and Contingent
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 Delhi-110006
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 informationSOLVING EQUATIONS WITH EXCEL
SOLVING EQUATIONS WITH EXCEL Excel and Lotus software are equipped with functions that allow the user to identify the root of an equation. By root, we mean the values of x such that a given equation cancels
More information