Uncertainty and Consumer BehaviorChapter OutlineDescribing RiskSlide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12A C T I V E L E A R N I N G Lottery with three possible outcomesA C T I V E L E A R N I N G AnswersSlide 15Slide 16Reducing RiskUncertainty and Consumer BehaviorChapter 5Chapter OutlineDescribing RiskPreferences Toward RiskReducing RiskDescribing 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—the payoff or value that we would expect on average.E(X) = Pr1X1 + Pr2X2E(X) = Pr1X1 + Pr2X2 + . . . + PrnXn● variability Extent to which possible outcomes of an uncertain event differ.● deviation Difference between expected payoff and actual payoff.OUTCOME 1 OUTCOME 2Probability Income ($)Probability Income ($)ExpectedIncome ($)Job 1: CommissionJob 2: Fixed Salary.5.99200015101000510.5.0115001500Income from Sales JobsDeviations from Expected Income ($)Outcome 1 Deviation Outcome 2 DeviationJob 1Job 220001510500101000510500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 RiskOutcome 1DeviationSquaredDeviationSquaredOutcome 2DeviationSquaredWeighted AverageStandardDeviationJob 1Job 220001510250,0001001000510250,000980,100250,0009900 500 99.50Calculating Variance ($)Describing RiskCalculating Variance ($)Outcome Probabilities for Two JobsJob 1: income ranging from 1000 to 2000 with 100 increments, all of them equally likelyJob 2: incomes from 1300 to 1700 with 100 increments, all of them equally likelyThe 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 RiskUnequal Probability OutcomesThe 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.Describing RiskIncomes from Sales Jobs—Modified ($)Outcome 1DeviationSquaredDeviationSquaredOutcome 2StandardDeviationExpectedIncomeJob 1Job 221001510250,0001001100510250,000980,100 500 99.5016001500Decision MakingPayoff 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● 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.Different preferences toward riskMarginal 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.Preferences toward risk30● risk premium Maximum amount of money that a risk-averse 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.Different preferences toward riskIn (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.Preferences toward riskA C T I V E L E A R N I N G A C T I V E L E A R N I N G Lottery with three possible Lottery with three possible outcomesoutcomes$125 will be received with probability .2$100 will be received with probability .3$50 will be received with probability .5A. 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?13A C T I V E L E A R N I N G A C T I V E L E A R N I N G AnswersAnswers14A. EV = 0.2*125 + 0.3*100 + 0.5*50 = 80B. Variance = 0.2*(125-80)2 + 0.3*(100-80)2 +0.5*(50-8-)2 = 975A. A risk-neutral person would pay the expected value of the lottery: 80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.Different preferences toward riskPart (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.Risk Aversion and Indifference CurvesPart (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