MicroEconomics 5e by besanko braeutigam chapter 15

Copyright (c)2014 John Wiley & Sons, Inc Chapter 15 Risk and Information Chapter Fifteen Overview 1 Introduction: Introduction:Amazon.com Amazon.com 2 Describing DescribingRisky RiskyOutcome Outcome––Basic BasicTools Tools •• •• •• Lotteries and Probabilities Lotteries and Probabilities Expected Values Expected Values Variance Variance 3 Evaluating EvaluatingRisky RiskyOutcomes Outcomes Risk Preferences and the Utility Function Risk Preferences and the Utility Function Copyright (c)2014 John Wiley & Sons, Inc •• 4 Avoiding Avoidingand andBearing BearingRisk Risk •• •• •• The Demand for Insurance and the Risk Premium The Demand for Insurance and the Risk Premium Asymmetric Information and Insurance Asymmetric Information and Insurance The Value of Information and Decision Trees The Value of Information and Decision Trees Chapter Fifteen Tools for Describing Risky Outcomes Definition: A lottery is any event with an uncertain outcome Examples: Investment, Roulette, Football Game Definition: A probability of an outcome (of a lottery) is the likelihood that this outcome Example: The probability often is estimated by the historical frequency of the outcome Chapter Fifteen Copyright (c)2014 John Wiley & Sons, Inc occurs Probability Distribution Definition: The probability distribution of the lottery depicts all possible payoffs in the lottery and their associated probabilities • The probability of any particular outcome is between and • The sum of the probabilities of all possible outcomes equals Definition: Probabilities that reflect subjective beliefs about risky events are called subjective probabilities Chapter Fifteen Copyright (c)2014 John Wiley & Sons, Inc Property: Probability Distribution Probability 90 80 67% chance of losing 70 60 50 30 20 10 Payof $25 Chapter Fifteen Copyright (c)2014 John Wiley & Sons, Inc .40 Probability Distribution Probability 90 80 67% chance of losing 70 60 50 30 20 33% chance of winning 10 Payof $25 $100 Chapter Fifteen Copyright (c)2014 John Wiley & Sons, Inc .40 Expected Value Definition: Definition: The Theexpected expectedvalue valueofofaalottery lotteryisisaameasure measureofofthe theaverage averagepayoff payoffthat that the thelottery lotterywill willgenerate generate EV EV==Pr(A)xA Pr(A)xA++Pr(B)xB Pr(B)xB++Pr(C)xC Pr(C)xC Where: Where:Pr(.) Pr(.)isisthe theprobability probabilityofof(.)(.)A,B, A,B,and andCCare arethe thepayoffs payoffsififoutcome outcomeA,A,BBororCC Copyright (c)2014 John Wiley & Sons, Inc occurs occurs Chapter Fifteen Expected Value InInour ourexample examplelottery, lottery,which whichpays pays$25 $25with withprobability probability.67 67and and$100 $100 with withprobability probability0.33, 0.33,the theexpected expectedvalue valueis:is: EV EV==.67 67xx$25 $25++.33 33xx100 100==$50 $50 Notice Noticethat thatthe theexpected expectedvalue valueneed neednot notbe beone oneofofthe the Chapter Fifteen Copyright (c)2014 John Wiley & Sons, Inc outcomes outcomesofofthe thelottery lottery Variance & Standard Deviation Definition: The variance of a lottery is the sum of the probability-weighted squared deviations between the possible outcomes of the lottery and the expected value of the lottery It is a measure of the lottery's riskiness 2 Var = (A - EV) (Pr(A)) + (B - EV) (Pr(B)) + (C - EV) (Pr(C)) Copyright (c)2014 John Wiley & Sons, Inc Definition: The standard deviation of a lottery is the square root of the variance It is an alternative measure of risk Chapter Fifteen Variance & Standard Deviation For Forthe theexample examplelottery lottery The squared deviation of winning is: • 2 ($100 - $50) = 50 = 2500 The squared deviation of losing is: 2 ($25 - $50) = 25 = 625 Copyright (c)2014 John Wiley & Sons, Inc • The variance is: • (2500 x 33)+ (625 x 67) = 1250 Chapter Fifteen 10 The Demand for Insurance IfIfyou youare arerisk riskaverse, averse,you youprefer prefertotoinsure insurethis thisway wayover overno noinsurance insurance Why? Why? Full Fullcoverage coverage( (no norisk risksosoprefer preferall allelse elseequal) equal) Definition: Definition: AAfairly fairlypriced pricedinsurance insurancepolicy policyisisone oneininwhich whichthe theinsurance insurancepremium premium(price) (price) equals equalsthe theexpected expectedvalue valueofofthe thepromised promisedpayout payout.i.e.: i.e.: Copyright (c)2014 John Wiley & Sons, Inc 500 500==.05(10,000) 05(10,000)++.95(0) 95(0) Chapter Fifteen 31 The Supply of Insurance Insurance company expects to break even and assumes all risk – why would an insurance company ever offer this policy? Definition: Definition: Asymmetric AsymmetricInformation Informationisisaasituation situationininwhich whichone oneparty partyknows knows Copyright (c)2014 John Wiley & Sons, Inc more moreabout aboutits itsown ownactions actionsororcharacteristics characteristicsthan thananother anotherparty party Chapter Fifteen 32 Adverse Selection & Moral Hazard Definition: Definition: Adverse AdverseSelection Selectionisisopportunism opportunismcharacterized characterizedby byan aninformed informedperson's person'sbenefiting benefitingfrom fromtrading trading ororotherwise otherwisecontracting contractingwith withaaless lessinformed informedperson personwho whodoes doesnot notknow knowabout aboutan anunobserved unobservedcharacteristic characteristic ofofthe theinformed informedperson person Copyright (c)2014 John Wiley & Sons, Inc Definition: Definition:Moral MoralHazard Hazardisisopportunism opportunismcharacterized characterizedby byan aninformed informedperson's person'staking takingadvantage advantageofofaaless less informed informedperson personthrough throughan anunobserved unobservedaction action Chapter Fifteen 33 Adverse Selection & Market Failure Lottery: Lottery: •• $50,000 $50,000ififno noblindness blindness(p(p==.95) 95) •• $40,000 $40,000ififblindness blindness(1-p (1-p==.05) 05) •• EVEV==$49,500 $49,500 (fair) (fair)insurance: insurance: Chapter Fifteen Copyright (c)2014 John Wiley & Sons, Inc •• Coverage Coverage==$10,000 $10,000 •• Price Price==$500 $500 •• $500 $500==.05(10,000) 05(10,000)++.95(0) 95(0) 34 Adverse Selection & Market Failure Suppose Supposethat thateach eachindividual's individual'sprobability probabilityofofblindness blindnessdiffers differs∈∈[0,1] [0,1] Who Whowill willbuy buythis this policy? policy? Now, Now,p'p'==.10 10sosothat: that: EV EVofofpayout payout==.1(10,000) 1(10,000)++.9(0) 9(0)==$1000 $1000while whileprice priceofof policy policyisisonly only$500 $500.The Theinsurance insurance Copyright (c)2014 John Wiley & Sons, Inc company companyno nolonger longerbreaks breakseven even Chapter Fifteen 35 Adverse Selection & Market Failure Suppose Supposewe weraise raisethe theprice priceofofpolicy policytoto$1000 $1000 Now, Now,p'' p''==.20 20so sothat that EV EVofofpayout payout==.2(10,000) 2(10,000)++.8(0) 8(0)==$2000 $2000.So Sothe theinsurance insurancecompany companystill stilldoes does Chapter Fifteen Copyright (c)2014 John Wiley & Sons, Inc not notbreak breakeven evenand andthus thusthe theMarket MarketFails Fails 36 Decision Trees Definition: A decision tree is a diagram that describes the options available to a decision maker, as well as the risky events that can occur at each point in time Key Elements 1.1.Decision DecisionNodes Nodes 3.3.Probabilities Probabilities 4.4.Payoffs Payoffs We analyze decision problems by working backward along the decision tree to decide what the optimal decision would Be Chapter Fifteen 37 Copyright (c)2014 John Wiley & Sons, Inc 2.2.Chance ChanceNodes Nodes Copyright (c)2014 John Wiley & Sons, Inc Decision Trees Chapter Fifteen 38 Decision Trees Steps Stepsininconstructing constructingand andanalyzing analyzingthe thetree: tree: 1.1.Map Mapout outthe thedecision decisionand andevent eventsequence sequence 2.2.Identify Identifythe thealternatives alternativesavailable availablefor foreach eachdecision decision 3.3.Identify Identifythe thepossible possibleoutcomes outcomesfor foreach eachrisky riskyevent event 4.4.Assign Assignprobabilities probabilitiestotothe theevents events Copyright (c)2014 John Wiley & Sons, Inc 5.5.Identify Identifypayoffs payoffstotoall allthe thedecision/event decision/eventcombinations combinations 6.6.Find Findthe theoptimal optimalsequence sequenceofofdecisions decisions Chapter Fifteen 39 Perfect Information Definition: Definition:The Thevalue valueofofperfect perfectinformation informationisisthe theincrease increaseinin the thedecision decisionmaker's maker'sexpected expectedpayoff payoffwhen whenthe thedecision decisionmaker maker can can atatno nocost cost obtain obtaininformation informationthat thatreveals revealsthe theoutcome outcome Copyright (c)2014 John Wiley & Sons, Inc ofofthe therisky riskyevent event Chapter Fifteen 40 Perfect Information Example: • • Expected payoff to conducting test: $35M Expected payoff to not conducting test: $30M The value of information: $5M the conditions that will actually prevail in the future It should represent the agent's willingness to pay for a "crystal ball" Chapter Fifteen 41 Copyright (c)2014 John Wiley & Sons, Inc The value of information reflects the value of being able to tailor your decisions to Auctions - Types English Auction – An auction in which participants cry out their bids and each participant can increase his or her bid until the auction ends with the highest bidder winning the object being sold First-Price Sealed-Bid Auction – An auction in which each bidder submits one bid, not knowing the other bids The highest bidder wins the object and pays a price equal to his or her bid Second-Price Sealed-Bid Auction – An auction in which each bidder submits one bid, not knowing the other bids The highest Dutch Descending Auction – An auction in which the seller of the object announces a price which is then lowered until a buyer announces a desire to buy the item at that price Chapter Fifteen 42 Copyright (c)2014 John Wiley & Sons, Inc bidder wins the object but pays a price equal to the second-highest bid Auctions Private Values – A situation in which each bidder in an auction has his or her own personalized valuation of the object Revenue Equivalence Theorem – When participants in an auction have private values, any auction format will, on average, generate the same revenue for the seller Common Values – A situation in which an item being sold in an auction has the same intrinsic value to all buyers, but no buyer knows exactly what that value is Winner’s Curse – A phenomenon whereby the winning bidder in a common-values auction might bid an amount that exceeds Copyright (c)2014 John Wiley & Sons, Inc the item’s intrinsic value Chapter Fifteen 43 Summary We can think of risky decisions as lotteries We can think of individuals maximizing expected utility when faced with risk Individuals differ in their attitudes towards risk: those who prefer a sure thing are risk averse Those who are indifferent about risk are risk neutral Those who prefer risk are risk loving Copyright (c)2014 John Wiley & Sons, Inc Insurance can help to avoid risk The optimal amount to insure depends on risk attitudes Chapter Fifteen 44 Summary The provision of insurance by individuals does not require risk lovers Adverse Selection and Moral Hazard can cause inefficiency in insurance markets We can calculate the value of obtaining information in order to reduce risk by analyzing the expected payoff to eliminating risk from a decision tree and The main types of auctions are private values auctions and common values auctions Chapter Fifteen 45 Copyright (c)2014 John Wiley & Sons, Inc comparing this to the expected payoff of maintaining risk ... the likelihood that this outcome Example: The probability often is estimated by the historical frequency of the outcome Chapter Fifteen Copyright (c)2014 John Wiley & Sons, Inc occurs Probability... subjective probabilities Chapter Fifteen Copyright (c)2014 John Wiley & Sons, Inc Property: Probability Distribution Probability 90 80 67% chance of losing 70 60 50 30 20 10 Payof $25 Chapter Fifteen... $54,000 5xU($4,000) + 5xU($104,000) = 5(60) + 5(320) = 190 Chapter Fifteen 11 Evaluating Risky Outcomes Utility Utility function 104 Chapter Fifteen Income (000 $ per year) 12 Copyright (c)2014