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Chapter 5 Uncertainty and Consumer Behavior. ©2005 Pearson Education, Inc.Chapter 52 Q: Value of Stock Investment in offshore drilling exploration: Two.

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Presentation on theme: "Chapter 5 Uncertainty and Consumer Behavior. ©2005 Pearson Education, Inc.Chapter 52 Q: Value of Stock Investment in offshore drilling exploration: Two."— Presentation transcript:

1 Chapter 5 Uncertainty and Consumer Behavior

2 ©2005 Pearson Education, Inc.Chapter 52 Q: Value of Stock 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

3 ©2005 Pearson Education, Inc.Chapter 53 Expected Value

4 ©2005 Pearson Education, Inc.Chapter 54 Expected Value In general, for n possible outcomes:  Possible outcomes having payoffs X 1, X 2, … X n  Probabilities of each outcome is given by Pr 1, Pr 2, … Pr n

5 ©2005 Pearson Education, Inc.Chapter 55 Describing Risk Variability  The extent to which possible outcomes of an uncertain event may differ  How much variation exists in the possible choice

6 ©2005 Pearson Education, Inc.Chapter 56 Q: Which Job? Suppose you are choosing 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 (almost) salaried position.  The third is a salaried position.

7 ©2005 Pearson Education, Inc.Chapter 57 There are two equally likely outcomes in the first job--$2,000 for a good sales job and $1,000 for a modestly successful one. 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). The third pays $1,500. Variability

8 ©2005 Pearson Education, Inc.Chapter 58 Variability Outcome 1Outcome 2 Prob.IncomeProb.Income Job 1: Commission.52000.51000 Job 2: Fixed Salary.991510.01510

9 ©2005 Pearson Education, Inc.Chapter 59 Variability Expected Income EV 1 = ½ $2,000 + ½ $1,000 = $1,500 EV 2 = (0.99)$1,510+(0.01)$510 = $1,500 EV 3 = $1,500

10 ©2005 Pearson Education, Inc.Chapter 510 Variability Greater variability from expected values signals greater risk. Variability comes from deviations in payoffs  Difference between expected payoff and actual payoff

11 ©2005 Pearson Education, Inc.Chapter 511 Variability – An Example Deviations from Expected Income ($) Outcome 1 DeviationOutcome 2 Deviation Job 1 $2000$500$1000-$500 Job 2 151010510-990

12 ©2005 Pearson Education, Inc.Chapter 512 Variability Average deviations are always zero. We must adjust for negative numbers We can measure variability with standard deviation

13 ©2005 Pearson Education, Inc.Chapter 513 Variability The standard deviation is written:

14 ©2005 Pearson Education, Inc.Chapter 514 Standard Deviation – Example 1 Deviations from Expected Income ($) Outcome 1 DeviationOutcome 2 Deviation Job 1 $2000$500$1000-$500 Job 2 151010510-990

15 ©2005 Pearson Education, Inc.Chapter 515 Standard Deviation – Example 1 Standard deviations of the two jobs are:

16 ©2005 Pearson Education, Inc.Chapter 516 Q: Revised What if the outcome probabilities of two jobs have unequal probability of outcomes  Job 1: greater spread & standard deviation  You will choose job 2 again

17 ©2005 Pearson Education, Inc.Chapter 517 Unequal Probability Outcomes Job 1 Job 2 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 0.2 Probability

18 ©2005 Pearson Education, Inc.Chapter 518 Q: Re-Revised Suppose we add $200 to each payoff in Job 1 which makes the expected payoff = $1700.  Job 1: expected income of $1,700 and a standard deviation of $500.  Job 2: expected income of $1,500 and a standard deviation of $99.50

19 ©2005 Pearson Education, Inc.Chapter 519 Unequal Probability Outcomes Job 1 Job 2 Income 0.1 $1000$1500$2000 0.2 Probability

20 ©2005 Pearson Education, Inc.Chapter 520 St. Petersburg Paradox Game: Toss a coin Payoff:  If H at the 1 st toss: 2 1 = 2  If H at the 2 nd toss: 2 2 = 4  …  If H at the n th toss: 2 n The fee for the game: 15 What is the EV of the game?

21 ©2005 Pearson Education, Inc.Chapter 521 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

22 ©2005 Pearson Education, Inc.Chapter 522 Example A person is earning $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

23 ©2005 Pearson Education, Inc.Chapter 523 Example Utility at $30,000 is 18 Utility at $10,000 is 10 Must compare utility from the risky job with current utility of 13.5 To evaluate the new job, we must calculate the expected utility of the risky job

24 ©2005 Pearson Education, Inc.Chapter 524 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) = (Prob. of Utility 1) *(Utility 1) + (Prob. of Utility 2)*(Utility 2)

25 ©2005 Pearson Education, Inc.Chapter 525 Example The Expected Utilility 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.

26 ©2005 Pearson Education, Inc. Example Chapter 526Chapter 526 Income ($1,000) Utility E 10 14 18 0 30 A 15 20 13.5

27 ©2005 Pearson Education, Inc. Example 2 Game: Toss a fair coin Game 1  H: +$100 T: -$0.5 Game 2  H: +$200 T: -$100 Game 3  H: +$20,000 T: -$10,000 Chapter 527

28 ©2005 Pearson Education, Inc. Chapter 528 Expected Values EV 1 = (1/2)$100 + (1/2)(-$0.5) = $49.75 EV 2 = (1/2)$200 + (1/2)(-$100) = $50 EV 3 = (1/2)$20,000 + (1/2)(-$10,000) = $5,000 Chapter 528

29 ©2005 Pearson Education, Inc. Chapter 529 Expected Utility Suppose U(M) = M 1/2, M = $10,000 U(M) = 10,000 1/2 = 100 EU 1 = (1/2) 10,100 1/2 + (1/2) 9,999.5 1/2 = 100.248 EU 2 = (1/2) 10,200 1/2 + (1/2) 9,900 1/2 = 100.247 EU 3 = (1/2) 30,000 1/2 + (1/2) 0 1/2 = 86.603 Chapter 529

30 ©2005 Pearson Education, Inc. Chapter 530 Example 3 Q: Your utility function is U(M) = M 1/2 and your initial wealth is 36. Will you play a gamble in which you win 13 with probability of ½ and lose 11 with probability of ½ ?  U(M) = 36 0.5 = 6  EV = ½ (36+13) + ½ (36-11) = 37  EU = ½ (36+13) 0.5 + ½ (36–11) 0.5 = ½ 7 + ½ 5 = 6 Chapter 530

31 ©2005 Pearson Education, Inc.Chapter 531 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 diminishing marginal utility of income  Most common attitude towards risk

32 ©2005 Pearson Education, Inc. Chapter 532 Risk Averse Chapter 532Chapter 532 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 E 10 14 18 0 30 A 20 16

33 ©2005 Pearson Education, Inc.Chapter 533 Preferences Toward Risk A person 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

34 ©2005 Pearson Education, Inc.Chapter 534 Income ($1,000) 1020 Utility 0 30 6 A E C 12 18 The consumer is risk neutral and is indifferent between certain events and uncertain events with the same expected income. Risk Neutral

35 ©2005 Pearson Education, Inc.Chapter 535 Income ($1,000) Utility 0 102030 The consumer is risk loving because she would prefer the gamble to a certain income. Risk Loving 3 A E C 8 18 F 10.5

36 ©2005 Pearson Education, Inc.Chapter 536 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.

37 ©2005 Pearson Education, Inc.Chapter 537 Risk Premium – Example From the 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.

38 ©2005 Pearson Education, Inc.Chapter 538 Risk Premium – Example Point F shows the risky scenario – the utility of 14 can also be obtained with certain income of $16,000 This person would be willing to pay up to $4000 (20 – 16) to avoid the risk of uncertain income.

39 ©2005 Pearson Education, Inc.Chapter 539 Income ($1,000) Utility 0 1016 Here, the risk premium is $4,000 because a certain income of $16,000 gives the person the same expected utility as the uncertain income with expected value of $20,000. 10 18 3040 14 A C E 20 Risk Premium F Risk Premium – Example

40 ©2005 Pearson Education, Inc.Chapter 540 Reducing Risk Consumers are generally risk averse and therefore want to reduce risk Three ways consumers attempt to reduce risk are: 1.Diversification 2.Insurance 3.Obtaining more information

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