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### eco331-02-PenaltySchemesHandout

Course: ECONOMICS 331, Spring 2009
School: Northwestern
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of Review Interpretations Probabilty Probability and Forecasts Eco331: Subjective Probability as a Rational Forecast Marciano Siniscalchi September 27, 2009 Review Interpretations of Probabilty Probability and Forecasts Probability, Random Variables, Expectation Denition A probability over a nite set S of states is a function P : P (S ) R such that: 1 2 3 P (E ) 0; P () = 0; P (S ) = 1. If E F = , then...

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Northwestern - ECONOMICS - 331
Northwestern University Fall 2009Marciano Siniscalchi Econ 331-0BAYESIAN INFERENCE AND THE FREQUENTIST VIEW1. Introduction This lecture has two main objectives. First, it will briey introduce you to Bayes Rule, which plays an important role in the subj
Northwestern - ECONOMICS - 331
Northwestern University Fall 2009 THE EXPECTED UTILITY CRITERIONMarciano Siniscalchi Econ 331-01. Introduction We nally turn to the main subject matter of this course: choice under risk and uncertainty, and in particular expected-utility theory. I will
Northwestern - ECONOMICS - 331
OverviewPreferencesChoice under Risk and UncertaintyExpected UtilityCertainty EquivalentApplicationsEco331: Preferences and Expected UtilityMarciano SiniscalchiOctober 5, 2009OverviewPreferencesChoice under Risk and UncertaintyExpected Utility
Northwestern - ECONOMICS - 331
Some practice EU calculationsX = R+2 X = 100, 1 ; 1, 3 . 3Preferences: u (x ) = log10 x Expected Value: E[X ] =1 3 100 +1 32 3 1 = 34.Expected Utility: E[u (X )] =log10 100 + 2 log10 1 = 2 . 3 3Some practice EU calculationsX = R+2 X = 100, 1
Northwestern - ECONOMICS - 331
Northwestern University Fall 2009 RISK AND RISK AVERSIONMarciano Siniscalchi Econ 331-01. Introduction The main reason why expected-utility theory is interesting is the phenomenon of risk aversion. The key idea is that people are typically unwilling to
Northwestern - ECONOMICS - 331
OverviewRisk AversionComparing Risk AttitudesTerminal WealthEco331: Risk AversionMarciano SiniscalchiOctober 12, 2009OverviewRisk AversionComparing Risk AttitudesTerminal WealthOverviewReview of denitions Risk Aversion: Behavioral Denition Ris
Northwestern - ECONOMICS - 331
Northwestern University Fall 2009 RISK AVERSION AND PORTFOLIO CHOICEMarciano Siniscalchi Econ 331-01. Introduction We continue our analysis of choice under risk. The main focus of this lecture is on comparing risk attitudes of dierent individuals: when
Northwestern - ECONOMICS - 331
OverviewPortfolio ChoiceThe Equity-Premium PuzzleEco331: Comparative Risk Aversion and Portfolio ChoiceMarciano SiniscalchiOctober 19, 2009OverviewPortfolio ChoiceThe Equity-Premium PuzzleOverviewReview of key denitions The Portfolio-Choice Prob
Northwestern - ECONOMICS - 331
Northwestern University Fall 2009Marciano Siniscalchi Econ 331-0MORE ON THE ARROW-PRATT MEASURE(S) OF RISK AVERSION1. Introduction Recall that, when comparing risk attitudes, the Arrow-Pratt measure of (absolute) risk aversion, A( w ) = u (w ) u (w)pl
Northwestern - ECONOMICS - 331
OverviewRisk PremiumEco331: The Arrow-Pratt Measure(s) of Risk AversionMarciano SiniscalchiOctober 21, 2009OverviewRisk PremiumOverviewRisk Premium Characterizing Risk Aversion via Risk Premia The Arrow-Pratt measure and Risk PremiaOverviewRisk
Northwestern - ECONOMICS - 331
Northwestern University Fall 2009 STOCHASTIC DOMINANCEMarciano Siniscalchi Econ 331-01. Introduction Our analysis so far builds upon expected-utility theory. An unpleasant implication of this approach is that, without knowledge of an individuals utility
Northwestern - ECONOMICS - 331
OverviewFirst-Order Stochastic DominanceSecond-Order Stochastic DominanceEco331: Stochastic DominanceMarciano SiniscalchiNovember 1, 2009OverviewFirst-Order Stochastic DominanceSecond-Order Stochastic DominanceOverviewCan we make predictions wit
Northwestern - ECONOMICS - 331
Northwestern University Fall 2009 MEAN-VARIANCE ANALYSIS AND PORTFOLIO CHOICE WITH MANY ASSETSMarciano Siniscalchi Econ 331-01. Mean is Good, Variance is Bad (or is it?) Portfolio choice with a single risky asset reduces to a simple trade-o: stocks (gen
Northwestern - ECONOMICS - 331
OverviewMean-Variance PreferencesPortfolio ChoiceEco331: Mean-Variance AnalysisMarciano SiniscalchiNovember 2OverviewMean-Variance PreferencesPortfolio ChoiceOverviewWhen Mean and Variance are All That Matters The portfolio problem in the Mean-V
Northwestern - ECONOMICS - 331
Northwestern University Fall 2009 THE VALUE OF INFORMATIONMarciano Siniscalchi Econ 331-01. Introduction This lecture marks the beginning of our study of dynamic choice. This week we focus on a simple, but extremely important type of problems: prior to
Northwestern - ECONOMICS - 331
OverviewA Monopoly ProblemSignalsEco331: Value of InformationMarciano SiniscalchiNovember 9, 2009OverviewA Monopoly ProblemSignalsOverviewDynamic choice: take actions at multiple points in time Value of Information: two choices:Time 1 : Acquire
Northwestern - ECONOMICS - 331
OverviewFormal SetupFoundationsA Diversion: AmbiguityEco331: Value of Information FoundationsMarciano SiniscalchiNovember 11OverviewFormal SetupFoundationsA Diversion: AmbiguityOverviewValue of Information: Formal Denition Emphasize general ca
Northwestern - ECONOMICS - 331
Northwestern University Fall 2009 HOMEWORK 2 DUE MONDAY, OCTOBER 19, IN CLASS.Marciano Siniscalchi Econ 331-01. Forecasting and Random Variables Consider a nite state space S , a probability P on S , and a random variable X : S R. Suppose that the follo
Northwestern - ECONOMICS - 331
HOMEWORK 2 SOLUTIONSNorthwestern University Fall 2008Marciano Siniscalchi Econ 331-01. Forecasting and Random Variables The individual minimizes s P (cfw_s)[X (s) ]2 with respect to . Dierentiating with respect to this variable yields s P (cfw_s)2[X (s
Northwestern - ECONOMICS - 331
Northwestern University Fall 2009 HOMEWORK 3 DUE MONDAY, OCTOBER 26, IN CLASS PLUS PRACTICE PROBLEMSMarciano Siniscalchi Econ 331-0Note These questions are from the midterms I gave in 2007 and 2008, so you can get a sense for the kind of questions I ask
Northwestern - ECONOMICS - 331
Northwestern University Fall 2009 HOMEWORK 3 DUE MONDAY, OCTOBER 26, IN CLASS.Marciano Siniscalchi Econ 331-0Note These questions are from the midterms I gave in 2007 and 2008, so you can get a sense for the kind of questions I ask in an exam. For your
Northwestern - ECONOMICS - 331
Northwestern University Fall 2009Marciano Siniscalchi Econ 331-0HOMEWORK 4 DUE MONDAY, NOVEMBER 16, 2009, IN CLASS. PLUS ONE PRACTICE PROBLEM1 Consider an economy with one risk-free asset, with return rf = 1.01, and two risky returns r1 , r2 . The latt
Northwestern - ECONOMICS - 331
HOMEWORK 1 SOLUTION Northwestern University Fall 2009 Marciano Siniscalchi Econ 331-01. The Peter Lynch Problem This was pretty straightforward. For the rst part, we rst compute the probability of k successes 1 in n = 13 trials, for k = 11, 12, 13, where
Northwestern - ECONOMICS - Econ339
Econ 339 Fall Quarter 2009 Problem Set 1 - SolutionsSolve the following Problems. Show your work.1. Book Problems (p. 66): 2-1 2-1. How many hours will a person allocate to leisure activities if her indifference curves between consumption and goods are
Northwestern - ECONOMICS - Econ339
Econ 339 Fall Quarter 2009 Problem Set 1 Due Date: 10/8/2009Solve the following Problems. Show your work. 1. Book Problems (p. 66): 2-1 2. Read chapter one in the book and answer the following questions: a. Why do we need theoretical models? b. Why is it
Northwestern - ECONOMICS - Econ339
Econ 339 Fall Quarter 2009 Problem Set 2 - Solutions Solve the following Problems. Show your work. Book Problems (p. 66): 2-2 ,2-3 ,2-10, 2-11, 2-122-2. What is the effect of an increase in the price of market goods on a workers reservation wage, probabi
Northwestern - ECONOMICS - Econ339
Econ 339 Fall Quarter 2009 Problem Set 2 - Due Date: 10/14/2009Solve the following Problems. Show your work. 1. Book Problems (p. 66): 2-2 ,2-3 ,2-10, 2-11, 2-12 2. Illustrate the effect of a wage decrease that leads to an increase in hours worked by an
Northwestern - ECONOMICS - Econ339
Econ 339 Fall Quarter 2009 Problem Set 3 - Due Date: 10/19/2009 Solve the following Problems. Show your work. 1. Problems: 3-1, 3-4, 3-7, 2. Problems: 4-63. (a) What happens to the long-run demand curve for labor if the demand for the firmsoutput increa
Northwestern - ECONOMICS - Econ339
Econ 339 Fall Quarter 2009 Problem Set 4 Due Date: 11/4/09Solve the following Problems. Show your work. 1. Chapter 5 Problems: 5-2, 5-3, 5-4, 5-5, 5-6, 5-7 2. Chapter 6 Problems: 6-1, 6-3, 6-4, 6-7 3. Suppose wages and health insurance are the only two j
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Econ 339 Fall Quarter 2009 Problem Set 5 Due Date: 11/4/2009Solve the following Problems. Show your work. 1. Chapter 7 Problems: 7-3, 7-11 2. Chapter 8 Problems: 8-1 3. Nick and Jane are married. They currently reside in Minnesota. Nicks present value of
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Key Points on Midterm 1 1. Juhn/Potter article about the future of labor force participation Ans: the article concludes that the rise of the labor force participation rate that we have seen since WWII has most likely come to an end. They dont expect femal
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Changes in Labor Force ParticipationJuhn/Potter JEP 06Measuring the Labor Force Labor Force (LF) = Employed + Unemployed Labor Force Participation Rate = LF/Pop In 2005 Civilian Non-Institutionalized Population (16 and older) = 226 Mil. 1% change in L
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Labor SupplyEcon 339 Labor EconomicsLabor Supply: DefinitionIndividual Labor Supply = relationship between the real wage and supply of labor of an individual Aggregate Labor Supply = relationship between the real wage and the economy-wide supply of lab
Northwestern - ECONOMICS - Econ339
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Compensating Wage DifferentialsChapter 6Chapter 6: Compensating Wage Differentials So far we assumed all workers are equal In reality workers AND jobs are different (heterogenous) Jobs differ in wage AND amenities workers differ in skills AND preferen
Northwestern - ECONOMICS - Econ339
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Northwestern - ECONOMICS - Econ339
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MATH 2930: Quiz 1. SolutionsOctober 29, 2009 Problem 1For each of the following statements, indicate whether its True or False and explain your reasoning. (a) The functions f (x) = ex , g (x) = cos x, h(x) = sin x are linearly independent on the real li
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