market opportunity line fair odds line Example 6.6, p. 120.
|
|
- Sophia Charlotte Blake
- 5 years ago
- Views:
Transcription
1 September 5 The market opportunity line depicts in the plane the different combinations of outcomes and that are available to the individual at the prevailing market prices, depending on how much of an asset he chooses to purchase. A market opportunity line is a fair odds line if it can be written in the form +( ) = for some constant, where denotes the actual probability of occurrence of and is the probability of occurrence of. Campbell is defining this term as a prelude to graphically depicting optimal investments and insurance. Let s go back to Problem above. An individual has a utility-of-wealth function () =ln( +)and a current wealth of $0. How much of this wealth will the person use to purchase an asset that yields zero with probability and with probability returns $4 for every dollar invested? Again, we ll use for the amount that the individual chooses to invest. If the asset yields zero, the individual receives =0 and if the asset succeeds, he receives =0 +4 =0+3 Solve each euation for : 0 = = = 0 80 = 3 + We can check that this is correct by considering =0(which produces = =0)and =0(which produces =0and =80). The market opportunity line thus depicts the range of risky positions that the individual can take on given the asset available for purchase. This is not a fair odds line because it cannot be rewritten in the form + = for some constant. Example 6.6, p. 0. An individual with current wealth of $00 will have 70% of it stolen with a probability of 0.3. He can purchase insurance for 40 cents per dollar of coverage. Determine the market opportunity line. Let 70 be the amount of coverage that he buys. If he is not robbed, his wealth is = If he is robbed, then his wealth is =30 (04) + =30+(06) Solving for in both euations produces = =
2 Figure : Cross-multiplying produces 06(00 ) = 04( 30) 60 + = (04) +(06) 7 = (04) +(06) Let s check our answer by considering a few points on the line. With =0,we have =30and = 00. This satisfies the euation. With =70we have = = 00 (04)70 = 7, which also satisfies the euation. Notice that this is not a fair odds line because doesn t occur with probability 070. Notice that the probability of the low outcome occurring plays no role in the definition of the market opportunity line. The market opportunity line purely reflects the opportunities for purchases available in the market (e.g., from an insurance company or a stock broker). Of course, the market prices may reflect the probability of loss, but the market opportunity line is purely defined by the market prices themselves Section 7 Insurance There are two aspects of the market for insurance that we will address later in the course:. moral hazard: Individuals may take preventative action to diminish the likelihood of losses, and having insurance that covers losses may make one less diligent in taking such actions.. adverse selection: Different individuals may face different probabilities of losses, and 48
3 posting prices for insurance attracts those who are most likely to benefit from coverage (i.e., those with the greatest likelihood of losses). This is an adverse selection for an insurance company from the entire pool of individuals who may benefit from coverage. We re going to ignore both of these issues in this chapter for simplicity and to establish the following benchmark result. Theorem (Complete Insurance Theorem) A risk averse individual faced with fair odds will maximize his expected utility at the point on the fair odds line at which =. Proof. A risk aversion person, faced with the option to buy insurance at prices that reflect the true probabilities of the outcome, will choose to insure himself against losses completely by opting for a point = (i.e., the individual bears no risk because his wealth is the same regardless of the outcome). Let 0 denote the probability of a loss (i.e., the bad or low outcome) and the probability of no loss (the good or high outcome). The assumption is that the market opportunity line is a fair odds line, i.e., it can be rewritten in the form +( ) = where is a constant. The value of is determined by the individual s wealth, the market prices, etc.. We don t need to do this derivation here; we ll just take it as a constant. The individual s problem is to maximize ( ) =()+( ) () subject to the constraint +( ) = and 0. We can use the fair odds line to substitute for in terms of and reduce this to a problem in the single variable : µ () =()+( ) I ve added the notation () to simplify the discussion below. We have the first order condition µ µ 0= 0 () = 0 ()+( ) 0 µ = 0 () 0 = 0 () 0 () Risk aversion implies 00 0, i.e., 0 is strictly decreasing. The last euation therefore reuires that = in order to satisfy the first order condition. Finally, 00 () = 00 () 00 () 0 and so the second derivative test therefore implies that this point is indeed the maximizer of expected utility. 49
4 It is also possible to prove this result by forming the Lagrangian ( ) =()+( ) () [ +( ) ] Campbell uses the techniue of substituting for with to keep the math as elementary as possible. Example 7., p. 7. Insurance without fair odds. An individual s utility function is () = and she faces the following situation: state probability wealth no accident accident She can buy a dollar s worth of coverage for $040. How much insurance does she buy? We figured out the market opportunity line above: (04) +(06) =7 The number 04, 06 sum to but do not reflect the true probabilities of 03 and 07. This market opportunity line is not a fair odds line. We therefore cannot conclude that the individual purchases coverage of =70, i.e., = =7. What is the optimal coverage for this person? Her expected utility is () = (03) +(07) = (03) p 30 + (06) +(07) p 00 (04) Taking the derivative and setting it eual to zero produces 0=(03) (06) p +(07) (04) p 30 + (06) 00 (04) = p p 30 + (06) 00 (04) 08 p 00 (04) =08 p 30 + (06) µ 08 (00 (04)) =30+(06) 08 µ 9 (00 (04)) =30+(06) 4 µ 8 96 (00 (04)) =30+(06) = = = Going back above, we can see that the second derivative of expected utility is (03) µ (06) (30 + (06)) 3 (06)+ (07) µ ( 04) (00 (04)) 3 ( 04) 0 50
5 and so =48 is indeed the maximal value. We can then demonstrate that 6= by calculating =30+(06) (48) = 3888 and = 00 (04)(48) = 9408 There is another way to solve this problem using the market opportunity line. The individual wishes to maximize (03) +(07) subject to the constraint that and are on the market opportunity line (04) +(06) =7 We substitute for in the objective s (03) 7 (04) +(07) (06) Set the derivative with respect to eual to 0: 0=(03) Cancel the and simplify: 0=(03) (07) (07) 7 (04) (06) (04) (06) 7 (04) (06) 3 7 (04) (06) = 9 4 Suaring each side produces (06) 7 (04) = = = = This is the same value of that we obtained above. From the market opportunity line we can calculate (04) (06) =7 =9408 The premium paid is 04 = =48 5
Section 9, Chapter 2 Moral Hazard and Insurance
September 24 additional problems due Tuesday, Sept. 29: p. 194: 1, 2, 3 0.0.12 Section 9, Chapter 2 Moral Hazard and Insurance Section 9.1 is a lengthy and fact-filled discussion of issues of information
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 informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More information1 Rational Expectations Equilibrium
1 Rational Expectations Euilibrium S - the (finite) set of states of the world - also use S to denote the number m - number of consumers K- number of physical commodities each trader has an endowment vector
More information1 Consumption and saving under uncertainty
1 Consumption and saving under uncertainty 1.1 Modelling uncertainty As in the deterministic case, we keep assuming that agents live for two periods. The novelty here is that their earnings in the second
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 informationDepartment of Economics The Ohio State University Final Exam Answers Econ 8712
Department of Economics The Ohio State University Final Exam Answers Econ 8712 Prof. Peck Fall 2015 1. (5 points) The following economy has two consumers, two firms, and two goods. Good 2 is leisure/labor.
More informationand, we have z=1.5x. Substituting in the constraint leads to, x=7.38 and z=11.07.
EconS 526 Problem Set 2. Constrained Optimization Problem 1. Solve the optimal values for the following problems. For (1a) check that you derived a minimum. For (1b) and (1c), check that you derived a
More informationJEFF MACKIE-MASON. x is a random variable with prior distrib known to both principal and agent, and the distribution depends on agent effort e
BASE (SYMMETRIC INFORMATION) MODEL FOR CONTRACT THEORY JEFF MACKIE-MASON 1. Preliminaries Principal and agent enter a relationship. Assume: They have access to the same information (including agent effort)
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 informationFinancial Economics Field Exam January 2008
Financial Economics Field Exam January 2008 There are two questions on the exam, representing Asset Pricing (236D = 234A) and Corporate Finance (234C). Please answer both questions to the best of your
More informationConsumer Budgets, Indifference Curves, and Utility Maximization 1 Instructional Primer 2
Consumer Budgets, Indifference Curves, and Utility Maximization 1 Instructional Primer 2 As rational, self-interested and utility maximizing economic agents, consumers seek to have the greatest level of
More informationECON 6022B Problem Set 2 Suggested Solutions Fall 2011
ECON 60B Problem Set Suggested Solutions Fall 0 September 7, 0 Optimal Consumption with A Linear Utility Function (Optional) Similar to the example in Lecture 3, the household lives for two periods and
More informationOctober An Equilibrium of the First Price Sealed Bid Auction for an Arbitrary Distribution.
October 13..18.4 An Equilibrium of the First Price Sealed Bid Auction for an Arbitrary Distribution. We now assume that the reservation values of the bidders are independently and identically distributed
More informationEconomics 202 (Section 05) Macroeconomic Theory Problem Set 1 Professor Sanjay Chugh Fall 2013 Due: Thursday, October 3, 2013
Department of Economics Boston College Economics 202 (Section 05) Macroeconomic Theory Problem Set 1 Professor Sanjay Chugh Fall 2013 Due: Thursday, October 3, 2013 Instrtions: Written (typed is strongly
More informationCHOICE THEORY, UTILITY FUNCTIONS AND RISK AVERSION
CHOICE THEORY, UTILITY FUNCTIONS AND RISK AVERSION Szabolcs Sebestyén szabolcs.sebestyen@iscte.pt Master in Finance INVESTMENTS Sebestyén (ISCTE-IUL) Choice Theory Investments 1 / 65 Outline 1 An Introduction
More informationδ j 1 (S j S j 1 ) (2.3) j=1
Chapter The Binomial Model Let S be some tradable asset with prices and let S k = St k ), k = 0, 1,,....1) H = HS 0, S 1,..., S N 1, S N ).) be some option payoff with start date t 0 and end date or maturity
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 informationLecture 18 - Information, Adverse Selection, and Insurance Markets
Lecture 18 - Information, Adverse Selection, and Insurance Markets 14.03 Spring 2003 1 Lecture 18 - Information, Adverse Selection, and Insurance Markets 1.1 Introduction Risk is costly to bear (in utility
More informationECO 317 Economics of Uncertainty Fall Term 2009 Notes for lectures 9. Demand for Insurance
The Basic Two-State Model ECO 317 Economics of Uncertainty Fall Term 2009 Notes for lectures 9. Demand for Insurance Insurance is a method for reducing (or in ideal circumstances even eliminating) individual
More informationSIMON FRASER UNIVERSITY Department of Economics. Intermediate Macroeconomic Theory Spring PROBLEM SET 1 (Solutions) Y = C + I + G + NX
SIMON FRASER UNIVERSITY Department of Economics Econ 305 Prof. Kasa Intermediate Macroeconomic Theory Spring 2012 PROBLEM SET 1 (Solutions) 1. (10 points). Using your knowledge of National Income Accounting,
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 informationMicroeconomics Qualifying Exam
Summer 2018 Microeconomics Qualifying Exam There are 100 points possible on this exam, 50 points each for Prof. Lozada s questions and Prof. Dugar s questions. Each professor asks you to do two long questions
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 informationUniversity of California, Davis Department of Economics Giacomo Bonanno. Economics 103: Economics of uncertainty and information PRACTICE PROBLEMS
University of California, Davis Department of Economics Giacomo Bonanno Economics 03: Economics of uncertainty and information PRACTICE PROBLEMS oooooooooooooooo Problem :.. Expected value Problem :..
More informationMacro (8701) & Micro (8703) option
WRITTEN PRELIMINARY Ph.D EXAMINATION Department of Applied Economics Jan./Feb. - 2010 Trade, Development and Growth For students electing Macro (8701) & Micro (8703) option Instructions Identify yourself
More informationThe Lagrangian method is one way to solve constrained maximization problems.
LECTURE 4: CONSTRAINED OPTIMIZATION QUESTIONS AND PROBLEMS True/False Questions The Lagrangian method is one way to solve constrained maximization problems. The substitution method is a way to avoid using
More informationDepartment of Economics The Ohio State University Final Exam Answers Econ 8712
Department of Economics The Ohio State University Final Exam Answers Econ 872 Prof. Peck Fall 207. (35 points) The following economy has three consumers, one firm, and four goods. Good is the labor/leisure
More informationExercises - Moral hazard
Exercises - Moral hazard 1. (from Rasmusen) If a salesman exerts high e ort, he will sell a supercomputer this year with probability 0:9. If he exerts low e ort, he will succeed with probability 0:5. The
More informationDepartment of Economics The Ohio State University Final Exam Questions and Answers Econ 8712
Prof. Peck Fall 016 Department of Economics The Ohio State University Final Exam Questions and Answers Econ 871 1. (35 points) The following economy has one consumer, two firms, and four goods. Goods 1
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 informationTechniques for Calculating the Efficient Frontier
Techniques for Calculating the Efficient Frontier Weerachart Kilenthong RIPED, UTCC c Kilenthong 2017 Tee (Riped) Introduction 1 / 43 Two Fund Theorem The Two-Fund Theorem states that we can reach any
More informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program August 2017
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program August 2017 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
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 informationChapter 1 Microeconomics of Consumer Theory
Chapter Microeconomics of Consumer Theory The two broad categories of decision-makers in an economy are consumers and firms. Each individual in each of these groups makes its decisions in order to achieve
More informationA Baseline Model: Diamond and Dybvig (1983)
BANKING AND FINANCIAL FRAGILITY A Baseline Model: Diamond and Dybvig (1983) Professor Todd Keister Rutgers University May 2017 Objective Want to develop a model to help us understand: why banks and other
More informationModels and Decision with Financial Applications UNIT 1: Elements of Decision under Uncertainty
Models and Decision with Financial Applications UNIT 1: Elements of Decision under Uncertainty We always need to make a decision (or select from among actions, options or moves) even when there exists
More informationIntroductory to Microeconomic Theory [08/29/12] Karen Tsai
Introductory to Microeconomic Theory [08/29/12] Karen Tsai What is microeconomics? Study of: Choice behavior of individual agents Key assumption: agents have well-defined objectives and limited resources
More informationLecture 7 - Locational equilibrium continued
Lecture 7 - Locational euilibrium continued Lars Nesheim 3 January 28 Review. Constant returns to scale (CRS) production function 2. Pro ts are y = f (K; L) () = K L (p tx) K L K r (x) L Businesses hire
More informationProblem 1 / 25 Problem 2 / 25 Problem 3 / 25 Problem 4 / 25
Department of Economics Boston College Economics 202 (Section 05) Macroeconomic Theory Midterm Exam Suggested Solutions Professor Sanjay Chugh Fall 203 NAME: The Exam has a total of four (4) problems and
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 informationPortfolio Investment
Portfolio Investment Robert A. Miller Tepper School of Business CMU 45-871 Lecture 5 Miller (Tepper School of Business CMU) Portfolio Investment 45-871 Lecture 5 1 / 22 Simplifying the framework for analysis
More informationRadner Equilibrium: Definition and Equivalence with Arrow-Debreu Equilibrium
Radner Equilibrium: Definition and Equivalence with Arrow-Debreu Equilibrium Econ 2100 Fall 2017 Lecture 24, November 28 Outline 1 Sequential Trade and Arrow Securities 2 Radner Equilibrium 3 Equivalence
More informationEC202. Microeconomic Principles II. Summer 2009 examination. 2008/2009 syllabus
Summer 2009 examination EC202 Microeconomic Principles II 2008/2009 syllabus Instructions to candidates Time allowed: 3 hours. This paper contains nine questions in three sections. Answer question one
More informationLimits to Arbitrage. George Pennacchi. Finance 591 Asset Pricing Theory
Limits to Arbitrage George Pennacchi Finance 591 Asset Pricing Theory I.Example: CARA Utility and Normal Asset Returns I Several single-period portfolio choice models assume constant absolute risk-aversion
More informationMoral Hazard. Two Performance Outcomes Output is denoted by q {0, 1}. Costly effort by the agent makes high output more likely.
Moral Hazard Two Performance Outcomes Output is denoted by q {0, 1}. Costly effort by the agent makes high output more likely. Pr(q = 1 a) = p(a) with p > 0 and p < 0. Principal s utility is V (q w) and
More informationEconS Micro Theory I Recitation #8b - Uncertainty II
EconS 50 - Micro Theory I Recitation #8b - Uncertainty II. Exercise 6.E.: The purpose of this exercise is to show that preferences may not be transitive in the presence of regret. Let there be S states
More information1. Introduction of another instrument of savings, namely, capital
Chapter 7 Capital Main Aims: 1. Introduction of another instrument of savings, namely, capital 2. Study conditions for the co-existence of money and capital as instruments of savings 3. Studies the effects
More informationComparing Allocations under Asymmetric Information: Coase Theorem Revisited
Comparing Allocations under Asymmetric Information: Coase Theorem Revisited Shingo Ishiguro Graduate School of Economics, Osaka University 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan August 2002
More informationRevision Lecture Microeconomics of Banking MSc Finance: Theory of Finance I MSc Economics: Financial Economics I
Revision Lecture Microeconomics of Banking MSc Finance: Theory of Finance I MSc Economics: Financial Economics I April 2005 PREPARING FOR THE EXAM What models do you need to study? All the models we studied
More informationThe Neoclassical Growth Model
The Neoclassical Growth Model 1 Setup Three goods: Final output Capital Labour One household, with preferences β t u (c t ) (Later we will introduce preferences with respect to labour/leisure) Endowment
More informationPhD Qualifier Examination
PhD Qualifier Examination Department of Agricultural Economics May 29, 2015 Instructions This exam consists of six questions. You must answer all questions. If you need an assumption to complete a question,
More informationEconomics 101. Lecture 8 - Intertemporal Choice and Uncertainty
Economics 101 Lecture 8 - Intertemporal Choice and Uncertainty 1 Intertemporal Setting Consider a consumer who lives for two periods, say old and young. When he is young, he has income m 1, while when
More informationSolutions to Midterm Exam. ECON Financial Economics Boston College, Department of Economics Spring Tuesday, March 19, 10:30-11:45am
Solutions to Midterm Exam ECON 33790 - Financial Economics Peter Ireland Boston College, Department of Economics Spring 209 Tuesday, March 9, 0:30 - :5am. Profit Maximization With the production function
More informationLecture Notes 1
4.45 Lecture Notes Guido Lorenzoni Fall 2009 A portfolio problem To set the stage, consider a simple nite horizon problem. A risk averse agent can invest in two assets: riskless asset (bond) pays gross
More informationEcon 277A: Economic Development I. Final Exam (06 May 2012)
Econ 277A: Economic Development I Semester II, 2011-12 Tridip Ray ISI, Delhi Final Exam (06 May 2012) There are 2 questions; you have to answer both of them. You have 3 hours to write this exam. 1. [30
More informationProblem Set # Public Economics
Problem Set #3 14.41 Public Economics DUE: October 29, 2010 1 Social Security DIscuss the validity of the following claims about Social Security. Determine whether each claim is True or False and present
More informationEconomics Homework 5 Fall 2006 Dickert-Conlin / Conlin
Economics 31 - Homework 5 Fall 26 Dickert-Conlin / Conlin Answer Key 1. Suppose Cush Bring-it-Home Cash has a utility function of U = M 2, where M is her income. Suppose Cush s income is $8 and she is
More informationAppendix for: Price Setting in Forward-Looking Customer Markets
Appendix for: Price Setting in Forward-Looking Customer Markets Emi Nakamura and Jón Steinsson Columbia University Appendix A. Second Order Approximations Appendix A.. A Derivation of a nd Order Approximation
More informationA. Introduction to choice under uncertainty 2. B. Risk aversion 11. C. Favorable gambles 15. D. Measures of risk aversion 20. E.
Microeconomic Theory -1- Uncertainty Choice under uncertainty A Introduction to choice under uncertainty B Risk aversion 11 C Favorable gambles 15 D Measures of risk aversion 0 E Insurance 6 F Small favorable
More informationBasic Informational Economics Assignment #4 for Managerial Economics, ECO 351M, Fall 2016 Due, Monday October 31 (Halloween).
Basic Informational Economics Assignment #4 for Managerial Economics, ECO 351M, Fall 2016 Due, Monday October 31 (Halloween). The Basic Model One must pick an action, a in a set of possible actions A,
More informationUNCERTAINTY AND INFORMATION
UNCERTAINTY AND INFORMATION M. En C. Eduardo Bustos Farías 1 Objectives After studying this chapter, you will be able to: Explain how people make decisions when they are uncertain about the consequences
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 informationBasic Informational Economics Assignment #4 for Managerial Economics, ECO 351M, Fall 2016 Due, Monday October 31 (Halloween).
Basic Informational Economics Assignment #4 for Managerial Economics, ECO 351M, Fall 2016 Due, Monday October 31 (Halloween). The Basic Model One must pick an action, a in a set of possible actions A,
More informationEconomics 101A (Lecture 25) Stefano DellaVigna
Economics 101A (Lecture 25) Stefano DellaVigna April 29, 2014 Outline 1. Hidden Action (Moral Hazard) II 2. The Takeover Game 3. Hidden Type (Adverse Selection) 4. Evidence of Hidden Type and Hidden Action
More informationAnswer: Let y 2 denote rm 2 s output of food and L 2 denote rm 2 s labor input (so
The Ohio State University Department of Economics Econ 805 Extra Problems on Production and Uncertainty: Questions and Answers Winter 003 Prof. Peck () In the following economy, there are two consumers,
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 informationName. Final Exam, Economics 210A, December 2014 Answer any 7 of these 8 questions Good luck!
Name Final Exam, Economics 210A, December 2014 Answer any 7 of these 8 questions Good luck! 1) For each of the following statements, state whether it is true or false. If it is true, prove that it is true.
More information1 Asset Pricing: Bonds vs Stocks
Asset Pricing: Bonds vs Stocks The historical data on financial asset returns show that one dollar invested in the Dow- Jones yields 6 times more than one dollar invested in U.S. Treasury bonds. The return
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 informationCHAPTER17 DIVIDENDS AND DIVIDEND POLICY
CHAPTER17 DIVIDENDS AND DIVIDEND POLICY Learning Objectives LO1 Dividend types and how dividends are paid. LO2 The issues surrounding dividend policy decisions. LO3 The difference between cash and stock
More informationMean-Variance Analysis
Mean-Variance Analysis Mean-variance analysis 1/ 51 Introduction How does one optimally choose among multiple risky assets? Due to diversi cation, which depends on assets return covariances, the attractiveness
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 informationTwo Equivalent Conditions
Two Equivalent Conditions The traditional theory of present value puts forward two equivalent conditions for asset-market equilibrium: Rate of Return The expected rate of return on an asset equals the
More informationMoral Hazard. Economics Microeconomic Theory II: Strategic Behavior. Instructor: Songzi Du
Moral Hazard Economics 302 - Microeconomic Theory II: Strategic Behavior Instructor: Songzi Du compiled by Shih En Lu (Chapter 25 in Watson (2013)) Simon Fraser University July 9, 2018 ECON 302 (SFU) Lecture
More informationLockbox Separation. William F. Sharpe June, 2007
Lockbox Separation William F. Sharpe June, 2007 Introduction This note develops the concept of lockbox separation for retirement financial strategies in a complete market. I show that in such a setting
More informationChoice Under Uncertainty (Chapter 12)
Choice Under Uncertainty (Chapter 12) January 6, 2011 Teaching Assistants Updated: Name Email OH Greg Leo gleo[at]umail TR 2-3, PHELP 1420 Dan Saunders saunders[at]econ R 9-11, HSSB 1237 Rish Singhania
More informationMicroeconomic Theory May 2013 Applied Economics. Ph.D. PRELIMINARY EXAMINATION MICROECONOMIC THEORY. Applied Economics Graduate Program.
Ph.D. PRELIMINARY EXAMINATION MICROECONOMIC THEORY Applied Economics Graduate Program May 2013 *********************************************** COVER SHEET ***********************************************
More informationAdverse Selection and Moral Hazard with Multidimensional Types
6631 2017 August 2017 Adverse Selection and Moral Hazard with Multidimensional Types Suehyun Kwon Impressum: CESifo Working Papers ISSN 2364 1428 (electronic version) Publisher and distributor: Munich
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 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 informationEU i (x i ) = p(s)u i (x i (s)),
Abstract. Agents increase their expected utility by using statecontingent transfers to share risk; many institutions seem to play an important role in permitting such transfers. If agents are suitably
More informationMoral Hazard. Economics Microeconomic Theory II: Strategic Behavior. Shih En Lu. Simon Fraser University (with thanks to Anke Kessler)
Moral Hazard Economics 302 - Microeconomic Theory II: Strategic Behavior Shih En Lu Simon Fraser University (with thanks to Anke Kessler) ECON 302 (SFU) Moral Hazard 1 / 18 Most Important Things to Learn
More informationThe monopolist solves. maxp(q,a)q C(q) yielding FONCs and SOSCs. p(q (a),a)+p q (q (a),a)q (a) C (q (a)) = 0
Problem Set : The implicit function and envelope theorems. (i) A monopolist faces inverse demand curve p(, a), where a is advertising expenditure, and has costs C(). Solve for the monopolist s optimal
More informationOptimizing Portfolios
Optimizing Portfolios An Undergraduate Introduction to Financial Mathematics J. Robert Buchanan 2010 Introduction Investors may wish to adjust the allocation of financial resources including a mixture
More informationMarch 30, Why do economists (and increasingly, engineers and computer scientists) study auctions?
March 3, 215 Steven A. Matthews, A Technical Primer on Auction Theory I: Independent Private Values, Northwestern University CMSEMS Discussion Paper No. 196, May, 1995. This paper is posted on the course
More informationDepartment of Agricultural Economics. PhD Qualifier Examination. August 2010
Department of Agricultural Economics PhD Qualifier Examination August 200 Instructions: The exam consists of six questions. You must answer all questions. If you need an assumption to complete a question,
More informationExponential Modeling. Growth and Decay
Exponential Modeling Growth and Decay Identify each as growth or Decay What you should Know y Exponential functions 0
More informationThese notes essentially correspond to chapter 7 of the text.
These notes essentially correspond to chapter 7 of the text. 1 Costs When discussing rms our ultimate goal is to determine how much pro t the rm makes. In the chapter 6 notes we discussed production functions,
More informationd. Find a competitive equilibrium for this economy. Is the allocation Pareto efficient? Are there any other competitive equilibrium allocations?
Answers to Microeconomics Prelim of August 7, 0. Consider an individual faced with two job choices: she can either accept a position with a fixed annual salary of x > 0 which requires L x units of labor
More informationDepartment of Economics ECO 204 Microeconomic Theory for Commerce Ajaz Hussain Test 2 Solutions
Department of Economics ECO 204 Microeconomic Theory for Commerce 2012 2013 Ajaz Hussain Test 2 Solutions IMPORTANT NOTES: Proceed with this exam only after the go-ahead from the Instructor or the proctor
More informationSTA Module 3B Discrete Random Variables
STA 2023 Module 3B Discrete Random Variables Learning Objectives Upon completing this module, you should be able to 1. Determine the probability distribution of a discrete random variable. 2. Construct
More informationChapter 4 Inflation and Interest Rates in the Consumption-Savings Model
Chapter 4 Inflation and Interest Rates in the Consumption-Savings Model The lifetime budget constraint (LBC) from the two-period consumption-savings model is a useful vehicle for introducing and analyzing
More informationCOS 511: Theoretical Machine Learning. Lecturer: Rob Schapire Lecture #24 Scribe: Jordan Ash May 1, 2014
COS 5: heoretical Machine Learning Lecturer: Rob Schapire Lecture #24 Scribe: Jordan Ash May, 204 Review of Game heory: Let M be a matrix with all elements in [0, ]. Mindy (called the row player) chooses
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 informationArrow-Debreu Equilibrium
Arrow-Debreu Equilibrium Econ 2100 Fall 2017 Lecture 23, November 21 Outline 1 Arrow-Debreu Equilibrium Recap 2 Arrow-Debreu Equilibrium With Only One Good 1 Pareto Effi ciency and Equilibrium 2 Properties
More informationSCREENING BY THE COMPANY YOU KEEP: JOINT LIABILITY LENDING AND THE PEER SELECTION EFFECT
SCREENING BY THE COMPANY YOU KEEP: JOINT LIABILITY LENDING AND THE PEER SELECTION EFFECT Author: Maitreesh Ghatak Presented by: Kosha Modi February 16, 2017 Introduction In an economic environment where
More information1 Two Period Production Economy
University of British Columbia Department of Economics, Macroeconomics (Econ 502) Prof. Amartya Lahiri Handout # 3 1 Two Period Production Economy We shall now extend our two-period exchange economy model
More informationLecture - Adverse Selection, Risk Aversion and Insurance Markets
Lecture - Adverse Selection, Risk Aversion and Insurance Markets David Autor 14.03 Fall 2004 1 Adverse Selection, Risk Aversion and Insurance Markets Risk is costly to bear (in utility terms). If we can
More informationMean Variance Portfolio Theory
Chapter 1 Mean Variance Portfolio Theory This book is about portfolio construction and risk analysis in the real-world context where optimization is done with constraints and penalties specified by the
More information