(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 186

CHAPTER 5 • 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 1

OUTCOME 2
PROBABILITY

INCOME ($)

EXPECTED
INCOME ($)

2000

.5

1000

1500

1510

.01

510

1500

PROBABILITY

INCOME ($)

Job 1: Commission

.5

Job 2: Fixed Salary

.99

• variability Extent to which
possible outcomes of an
uncertain event differ.