1、Chapter 5,Uncertainty and Consumer Behavior,Chapter 5,2,Topics to be Discussed,Describing Risk Preferences Toward Risk Reducing Risk The Demand for Risky Assets,Chapter 5,3,Introduction,Choice with certainty is reasonably straightforward How do we make choices when certain variables such as income a

2、nd prices are uncertain (making choices with risk)?,Chapter 5,4,Describing Risk,To measure risk we must know: All of the possible outcomes The probability or likelihood that each outcome will occur,Chapter 5,5,Describing Risk,Interpreting Probability Objective Interpretation Based on the observed fr

3、equency of past events Subjective Interpretation Based on perception that an outcome will occur,Chapter 5,6,Interpreting Probability,Subjective Probability Different information or different abilities to process the same information can influence the subjective probability Based on judgment or exper

4、ience,Chapter 5,7,Describing Risk,With an interpretation of probability, must determine 2 measures to help describe and compare risky choices Expected value Variability,Chapter 5,8,Describing Risk,Expected Value The weighted average of the payoffs or values resulting from all possible outcomes Expec

5、ted value measures the central tendency; the payoff or value expected on average,Chapter 5,9,Expected Value An Example,Investment in offshore drilling exploration: Two outcomes are possible Success the stock price increases from $30 to $40/share Failure the stock price falls from $30 to $20/share,Ch

6、apter 5,10,Expected Value An Example,Objective Probability 100 explorations, 25 successes and 75 failures Probability (Pr) of success = 1/4 and the probability of failure = 3/4,Chapter 5,11,Expected Value An Example,Chapter 5,12,Expected Value,In general, for n possible outcomes: Possible outcomes h

7、aving payoffs X1, X2, , Xn Probabilities of each outcome is given by Pr1, Pr2, , Prn,Chapter 5,13,Describing Risk,Variability The extent to which possible outcomes of an uncertain event may differ How much variation exists in the possible choice,Chapter 5,14,Variability An Example,Suppose you are ch

8、oosing between two part-time sales jobs that have the same expected income ($1,500) The first job is based entirely on commission The second is a salaried position,Chapter 5,15,There are two equally likely outcomes in the first job: $2,000 for a good sales job and $1,000 for a modestly successful on

9、e The second pays $1,510 most of the time (.99 probability), but you will earn $510 if the company goes out of business (.01 probability),Variability An Example,Chapter 5,16,Variability An Example,Chapter 5,17,Variability An Example,Income from Possible Sales Job Job 1 Expected Income,Job 2 Expected

10、 Income,Chapter 5,18,Variability,While the expected values are the same, the variability is not Greater variability from expected values signals greater risk Variability comes from deviations in payoffs Difference between expected payoff and actual payoff,Chapter 5,19,Variability An Example,Chapter

11、5,20,Variability,Average deviations are always zero so we must adjust for negative numbers We can measure variability with standard deviation The square root of the average of the squares of the deviations of the payoffs associated with each outcome from their expected value,Chapter 5,21,Variability

12、,Standard deviation is a measure of risk Measures how variable your payoff will be More variability means more risk Individuals generally prefer less variability less risk,Chapter 5,22,Variability,The standard deviation is written:,Chapter 5,23,Standard Deviation Example 1,Chapter 5,24,Standard Devi

13、ation Example 1,Standard deviations of the two jobs are:,Chapter 5,25,Standard Deviation Example 1,Job 1 has a larger standard deviation and therefore it is the riskier alternative The standard deviation also can be used when there are many outcomes instead of only two,Chapter 5,26,Standard Deviatio

14、n Example 2,Job 1 is a job in which the income ranges from $1000 to $2000 in increments of $100 that are all equally likely Job 2 is a job in which the income ranges from $1300 to $1700 in increments of $100 that, also, are all equally likely,Chapter 5,27,Outcome Probabilities - Two Jobs,Income,0.1,

15、$1000,$1500,$2000,0.2,Job 1 has greater spread: greater standard deviation and greater risk than Job 2.,Probability,Chapter 5,28,Decision Making Example 1,What if the outcome probabilities of two jobs have unequal probability of outcomes? Job 1: greater spread and standard deviation Peaked distribut

16、ion: extreme payoffs are less likely that those in the middle of the distribution You will choose job 2 again,Chapter 5,29,Unequal Probability Outcomes,The distribution of payoffs associated with Job 1 has a greater spread and standard deviation than those with Job 2.,Income,0.1,$1000,$1500,$2000,0.

17、2,Probability,Chapter 5,30,Decision Making Example 2,Suppose we add $100 to each payoff in Job 1 which makes the expected payoff = $1600 Job 1: expected income $1,600 and a standard deviation of $500 Job 2: expected income of $1,500 and a standard deviation of $99.50,Chapter 5,31,Decision Making Exa

18、mple 2,Which job should be chosen? Depends on the individual Some may be willing to take risk with higher expected income Some will prefer less risk even with lower expected income,Chapter 5,32,Risk and Crime Deterrence,Attitudes toward risk affect willingness to break the law Suppose a city wants t

19、o deter people from double parking Monetary fines may be better than jail time,Chapter 5,33,Risk and Crime Deterrence,Costs of apprehending criminals are not zero, therefore Fines must be higher than the costs to society Probability of apprehension is actually less than one,Chapter 5,34,Risk and Cri

20、me Deterrence - Example,Assumptions: Double-parking saves a person $5 in terms of time spent searching for a parking space The driver is risk neutral Cost of apprehension is zero,Chapter 5,35,Risk and Crime Deterrence - Example,A fine greater than $5.00 would deter the driver from double parking Ben

21、efit of double parking ($5) is less than the cost ($6.00) equals a net benefit that is negative If the value of double parking is greater than $5.00, then the person would still break the law,Chapter 5,36,Risk and Crime Deterrence - Example,The same deterrence effect is obtained by either A $50 fine

22、 with a 0.1 probability of being caught resulting in an expected penalty of $5 or A $500 fine with a 0.01 probability of being caught resulting in an expected penalty of $5,Chapter 5,37,Risk and Crime Deterrence - Example,Enforcement costs are reduced with high fine and low probability Most effectiv

23、e if drivers dont like to take risks,Chapter 5,38,Preferences Toward Risk,Can expand evaluation of risky alternative by considering utility that is obtained by risk A consumer gets utility from income Payoff measured in terms of utility,Chapter 5,39,Preferences Toward Risk - Example,A person is earn

24、ing $15,000 and receiving 13.5 units of utility from the job She is considering a new, but risky job 0.50 chance of $30,000 0.50 chance of $10,000,Chapter 5,40,Preferences Toward Risk - Example,Utility at $30,000 is 18 Utility at $10,000 is 10 Must compare utility from the risky job with current uti

25、lity of 13.5 To evaluate the new job, we must calculate the expected utility of the risky job,Chapter 5,41,Preferences Toward Risk,The expected utility of the risky option is the sum of the utilities associated with all her possible incomes weighted by the probability that each income will occur,E(u

26、) = (Prob. of Utility 1) *(Utility 1) + (Prob. of Utility 2)*(Utility 2),Chapter 5,42,Preferences Toward Risk Example,The expected is: E(u) = (1/2)u($10,000) + (1/2)u($30,000) = 0.5(10) + 0.5(18) = 14 E(u) of new job is 14, which is greater than the current utility of 13.5 and therefore preferred,Ch

27、apter 5,43,Preferences Toward Risk,People differ in their preference toward risk People can be risk averse, risk neutral, or risk loving,Chapter 5,44,Preferences Toward Risk,Risk Averse A person who prefers a certain given income to a risky income with the same expected value The person has a dimini

28、shing marginal utility of income Most common attitude towards risk Ex: Market for insurance,Chapter 5,45,Risk Averse - Example,A person can have a $20,000 job with 100% probability and receive a utility level of 16 The person could have a job with a 0.5 chance of earning $30,000 and a 0.5 chance of

29、earning $10,000,Chapter 5,46,Risk Averse Example,Expected Income of Risky Job E(I) = (0.5)($30,000) + (0.5)($10,000) E(I) = $20,000 Expected Utility of Risky Job E(u) = (0.5)(10) + (0.5)(18) E(u) = 14,Chapter 5,47,Risk Averse Example,Expected income from both jobs is the same risk averse may choose

30、current job Expected utility is greater for certain job Would keep certain job Risk averse persons losses (decreased utility) are more important than risky gains,Chapter 5,48,Risk Averse,Can see risk averse choices graphically Risky job has expected income = $20,000 with expected utility = 14 Point

31、F Certain job has expected income = $20,000 with utility = 16 Point D,Chapter 5,49,Income ($1,000),Utility,The consumer is risk averse because she would prefer a certain income of $20,000 to an uncertain expected income = $20,000,Risk Averse Utility Function,Chapter 5,50,Preferences Toward Risk,A pe

32、rson is said to be risk neutral if they show no preference between a certain income, and an uncertain income with the same expected value Constant marginal utility of income,Chapter 5,51,Risk Neutral,Expected value for risky option is the same as utility for certain outcome E(I) = (0.5)($10,000) + (

33、0.5)($30,000) = $20,000 E(u) = (0.5)(6) + (0.5)(18) = 12 This is the same as the certain income of $20,000 with utility of 12,Chapter 5,52,Income ($1,000),10,20,Utility,0,30,The consumer is risk neutral and is indifferent between certain events and uncertain events with the same expected income.,Ris

34、k Neutral,Chapter 5,53,Preferences Toward Risk,A person is said to be risk loving if they show a preference toward an uncertain income over a certain income with the same expected value Examples: Gambling, some criminal activities Increasing marginal utility of income,Chapter 5,54,Risk Loving,Expect

35、ed value for risky option point F E(I) = (0.5)($10,000) + (0.5)($30,000) = $20,000 E(u) = (0.5)(3) + (0.5)(18) = 10.5 Certain income is $20,000 with utility of 8 point C Risky alternative is preferred,Chapter 5,55,Income ($1,000),Utility,0,10,20,30,The consumer is risk loving because she would prefe

36、r the gamble to a certain income.,Risk Loving,Chapter 5,56,Preferences Toward Risk,The risk premium is the maximum amount of money that a risk-averse person would pay to avoid taking a risk The risk premium depends on the risky alternatives the person faces,Chapter 5,57,Risk Premium Example,From the

37、 previous example A person has a .5 probability of earning $30,000 and a .5 probability of earning $10,000 The expected income is $20,000 with expected utility of 14,Chapter 5,58,Risk Premium Example,Point F shows the risky scenario the utility of 14 can also be obtained with certain income of $16,0

38、00 This person would be willing to pay up to $4000 (20 16) to avoid the risk of uncertain income Can show this graphically by drawing a straight line between the two points line CF,Chapter 5,59,Income ($1,000),Utility,0,10,16,Here, the risk premium is $4,000 because a certain income of $16,000 gives

39、 the person the same expected utility as the uncertain income with expected value of $20,000.,20,Risk Premium Example,Chapter 5,60,Risk Aversion and Income,Variability in potential payoffs increases the risk premium Example: A job has a .5 probability of paying $40,000 (utility of 20) and a .5 chanc

40、e of paying 0 (utility of 0).,Chapter 5,61,Risk Aversion and Income,Example (cont.): The expected income is still $20,000, but the expected utility falls to 10 E(u) = (0.5)u($0) + (0.5)u($40,000) = 0 + .5(20) = 10 The certain income of $20,000 has utility of 16 If person must take new job, their uti

41、lity will fall by 6,Chapter 5,62,Risk Aversion and Income,Example (cont.): They can get 10 units of utility by taking a certain job paying $10,000 The risk premium, therefore, is $10,000 (i.e. they would be willing to give up $10,000 of the $20,000 and have the same E(u) as the risky job,Chapter 5,6

42、3,Risk Aversion and Income,The greater the variability, the more the person would be willing to pay to avoid the risk, and the larger the risk premium,Chapter 5,64,Risk Aversion and Indifference Curves,Can describe a persons risk aversion using indifference curves that relate expected income to vari

43、ability of income (standard deviation) Since risk is undesirable, greater risk requires greater expected income to make the person equally well off Indifference curves are therefore upward sloping,Chapter 5,65,Risk Aversion and Indifference Curves,Standard Deviation of Income,Expected Income,Highly

44、Risk Averse: An increase in standard deviation requires a large increase in income to maintain satisfaction.,Chapter 5,66,Risk Aversion and Indifference Curves,Standard Deviation of Income,Expected Income,Slightly Risk Averse: A large increase in standard deviation requires only a small increase in

45、income to maintain satisfaction.,Chapter 5,67,Reducing Risk,Consumers are generally risk averse and therefore want to reduce risk Three ways consumers attempt to reduce risk are: Diversification Insurance Obtaining more information,Chapter 5,68,Reducing Risk,Diversification Reducing risk by allocati

46、ng resources to a variety of activities whose outcomes are not closely related Example: Suppose a firm has a choice of selling air conditioners, heaters, or both The probability of it being hot or cold is 0.5 How does a firm decide what to sell?,Chapter 5,69,Income from Sales of Appliances,Chapter 5

47、,70,Diversification Example,If the firm sells only heaters or air conditioners their income will be either $12,000 or $30,000 Their expected income would be: 1/2($12,000) + 1/2($30,000) = $21,000,Chapter 5,71,Diversification Example,If the firm divides their time evenly between appliances, their air

48、 conditioning and heating sales would be half their original values If it were hot, their expected income would be $15,000 from air conditioners and $6,000 from heaters, or $21,000 If it were cold, their expected income would be $6,000 from air conditioners and $15,000 from heaters, or $21,000,Chapt

49、er 5,72,Diversification Example,With diversification, expected income is $21,000 with no risk Better off diversifying to minimize risk Firms can reduce risk by diversifying among a variety of activities that are not closely related,Chapter 5,73,Reducing Risk The Stock Market,If invest all money in o

50、ne stock, then take on a lot of risk If that stock loses value, you lose all your investment value Can spread risk out by investing in many different stocks or investments Ex: Mutual funds,Chapter 5,74,Reducing Risk Insurance,Risk averse are willing to pay to avoid risk If the cost of insurance equa

51、ls the expected loss, risk averse people will buy enough insurance to recover fully from a potential financial loss,Chapter 5,75,The Decision to Insure,Chapter 5,76,Reducing Risk Insurance,For the risk averse consumer, guarantee of same income regardless of outcome has higher utility than facing the

52、 probability of risk Expected utility with insurance is higher than without,Chapter 5,77,The Law of Large Numbers,Insurance companies know that although single events are random and largely unpredictable, the average outcome of many similar events can be predicted When insurance companies sell many

53、policies, they face relatively little risk,Chapter 5,78,Reducing Risk Actuarially Fair,Insurance companies can be sure total premiums paid will equal total money paid out Companies set the premiums so money received will be enough to pay expected losses,Chapter 5,79,Reducing Risk Actuarially Fair,So

54、me events with very little probability of occurrence such as floods and earthquakes are no longer insured privately Cannot calculate true expected values and expected losses Governments have had to create insurance for these types of events Ex: National Flood Insurance Program,Chapter 5,80,The Value

55、 of Information,Risk often exists because we dont know all the information surrounding a decision Because of this, information is valuable and people are willing to pay for it,Chapter 5,81,The Value of Information,The value of complete information The difference between the expected value of a choic

56、e with complete information and the expected value when information is incomplete,Chapter 5,82,The Value of Information Example,Per capita milk consumption has fallen over the years The milk producers engaged in market research to develop new sales strategies to encourage the consumption of milk,Cha

57、pter 5,83,The Value of Information Example,Findings Milk demand is seasonal with the greatest demand in the spring Price elasticity of demand is negative and small Income elasticity is positive and large,Chapter 5,84,The Value of Information Example,Milk advertising increases sales most in the sprin

58、g Allocating advertising based on this information in New York increased profits by 9% or $14 million The cost of the information was relatively low, while the value was substantial (increased profits),Chapter 5,85,Demand for Risky Assets,Most individuals are risk averse and yet choose to invest mon

59、ey in assets that carry some risk Why do they do this? How do they decide how much risk to bear? Must examine the demand for risky assets,Chapter 5,86,The Demand for Risky Assets,Assets Something that provides a flow of money or services to its owner Ex: homes, savings accounts, rental property, shares of stock The flow of money or services can be explicit (dividends) or implicit (capital gain),Chapter 5,87,The Demand for Risky Assets,Capital Gain An increase in the value of an asset Capital loss A decrease in the value of an asset,Chapter 5,88,Risky and Riskless Ass