CHAPTER • Uncertainty and Consumer Behavior 161 Regardless of the interpretation of probability, it is used in calculating two important measures that help us describe and compare risky choices One measure tells us the expected value and the other the variability of the possible outcomes Expected Value The expected value associated with an uncertain situation is a weighted average of the payoffs or values associated with all possible outcomes The probabilities of each outcome are used as weights Thus the expected value measures the central tendency—the payoff or value that we would expect on average Our offshore oil exploration example had two possible outcomes: Success yields a payoff of $40 per share, failure a payoff of $20 per share Denoting “probability of” by Pr, we express the expected value in this case as • expected value Probabilityweighted average of the payoffs associated with all possible outcomes • payoff Value associated with a possible outcome Expected value = Pr(success)($40/share) + Pr(failure)($20/share) = (1/4)($40/share) + (3/4)($20/share) = $25/share More generally, if there are two possible outcomes having payoffs X1 and X2 and if the probabilities of each outcome are given by Pr1 and Pr2, then the expected value is E(X) = Pr1X1 + Pr2X2 When there are n possible outcomes, the expected value becomes E(X) = Pr1X1 + Pr2X2 + c + PrnXn Variability Variability is the extent to which the possible outcomes of an uncertain situation differ To see why variability is important, suppose you are choosing between two part-time summer sales jobs that have the same expected income ($1500) The first job is based entirely on commission—the income earned depends on how much you sell There are two equally likely payoffs for this job: $2000 for a successful sales effort and $1000 for one that is less successful The second job is salaried It is very likely (.99 probability) that you will earn $1510, but there is a 01 probability that the company will go out of business, in which case you would earn only $510 in severance pay Table 5.1 summarizes these possible outcomes, their payoffs, and their probabilities Note that these two jobs have the same expected income For Job 1, expected income is 5($2000) ϩ 5($1000) ϭ $1500; for Job 2, it is 99($1510) ϩ 01($510) ϭ $1500 However, the variability of the possible payoffs is different We measure TABLE 5.1 INCOME FROM SALES JOBS OUTCOME OUTCOME PROBABILITY INCOME ($) EXPECTED INCOME ($) 2000 1000 1500 1510 01 510 1500 PROBABILITY INCOME ($) Job 1: Commission Job 2: Fixed Salary 99 • variability Extent to which possible outcomes of an uncertain event differ