Uncertainty and Consumer Behavior Chapter 5 Chapter Outline Describing Risk Preferences Toward Risk Reducing Risk Describing Risk probability Likelihood that a given outcome will occur Subjective probability is the perception that an outcome will occur expected value Probability weighted average of the payoffs associated with all possible outcomes payoff Value associated with a possible outcome The expected value measures the central tendency E X Pr 1X1 Pr2X2 the payoff or value that we would expect on average E X Pr1X1 Pr2X2 PrnXn Describing Risk variability Extent to which possible outcomes of an uncertain event differ Income from Sales Jobs OUTCOME 1 Job 1 Commission Job 2 Fixed Salary deviation OUTCOME 2 Probability Income Probability Income 5 2000 5 1000 99 1510 01 510 Expected Income 1500 1500 Difference between expected payoff and actual payoff Deviations from Expected Income Deviation Job 1 Outcome 1 Deviation 2000 Outcome 2 500 1000 500 Job 2 1510 10 510 990 standard deviation Square root of the weighted average of the squares of the deviations of the payoffs associated with each outcome from their expected values Describing Risk Calculating Variance Job 1 Job 2 Outcome 1 2000 1510 Deviatio n Squared 250 000 100 Outcome 2 1000 510 Weighted Deviatio Average Deviatio n n Squared Squared 250 000 250 000 980 100 9900 Standar d Deviatio 500 n 99 50 Describing Risk Calculating Variance Outcome Probabilities for Two Jobs Job 1 income ranging from 1000 to 2000 with 100 increments all of them equally likely Job 2 incomes from 1300 to 1700 with 100 increments all of them equally likely The distribution of payoffs associated with Job 1 has a greater spread and a greater standard deviation than the distribution of payoffs associated with Job 2 Both distributions are flat because all outcomes are equally likely Describing Risk Unequal Probability Outcomes The distribution of payoffs associated with Job 1 has a greater spread and a greater standard deviation than the distribution of payoffs associated with Job 2 Both distributions are peaked because the extreme payoffs are less likely than those near the middle of the distribution Decision Making Incomes from Sales Jobs Modified Outcome 1 Job 1 2100 Job 2 1510 Deviatio n Squared 250 000 100 Outcome 2 1100 Deviatio n Squared 250 000 Expecte d Income 1600 510 980 100 1500 Payoff of job 1 2100 with probability 0 5 1100 with probability 0 5 Payoff of job 2 1510 with probability 0 99 510 with probability 0 01 Standar d Deviatio 500 n 99 50 Different preferences toward risk risk averse Condition of preferring a certain income to a risky income with the same expected value risk neutral Condition of being indifferent between a certain income and an uncertain income with the same expected value risk loving Condition of preferring a risky income to a certain income with the same expected value Preferences toward risk Marginal utility diminishes as income increases The consumer is risk averse because she would prefer a certain income of 20 000 with a utility of 16 to a gamble with a 5 probability of 10 000 and a 5 probability of 30 000 and expected utility of 14 A certain income of 16 000 at point C gives her the same expected utility 14 as the uncertain income a 5 probability of being at point A and a 5 probability of being at point E that has an expected value of 20 000 30 Different preferences toward risk risk premium Maximum amount of money that a riskaverse person will pay to avoid taking a risk The risk premium CF measures the amount of income that an individual would give up to leave her indifferent between a risky choice and a certain one Here the risk premium is 4000 Preferences toward risk In b the consumer is risk loving She would prefer the same gamble with expected utility of 10 5 to the certain income with a utility of 8 Finally the consumer in c is risk neutral and indifferent between certain and uncertain events with the same expected income ACTIVE LEARNING Lottery with three possible outcomes 125 will be received with probability 2 100 will be received with probability 3 50 will be received with probability 5 A What is the expected value of the lottery B What is the variance of the outcome C What would a risk neutral person pay to play the lottery 13 ACTIVE LEARNING Answers A EV 0 2 125 0 3 100 0 5 50 80 B Variance 0 2 125 80 2 0 3 100 80 2 0 5 50 8 2 975 A A risk neutral person would pay the expected value of the lottery 80 14 Different preferences toward risk The extent of an individual s risk aversion depends on the nature of the risk and on the person s income Other things being equal risk averse people prefer a smaller variability of outcomes The greater the variability of income the more the person would be willing to pay to avoid the risky situation Risk Aversion and Indifference Curves Part a applies to a person who is highly risk averse An increase in this individual s standard deviation of income requires a large increase in expected income if he or she is to remain equally well off Part b applies to a person who is only slightly risk averse An increase in the standard deviation of income requires only a small increase in expected income if he or she is to remain equally well off Reducing Risk diversification insurance obtaining more information