6.7 Attitudes to risk and expected value
can see from Figure 6.4 that our individual derives great utility from increases in days
of holiday at the lower end but, as more days are obtained, the additional utility given
by each extra day diminishes. Figure 6.4 raises the question of how utility is measured,
and how we actually draw such a graph in practice. In fact, utility is not a readily meas-
urable factor and therefore graphs of it are difficult to construct. Utility is in the mind
of the individual.
Utility theory has been criticised for the fact that utility is difficult to measure. Most
observers agree, however, that the notions represented in the theory have an inex-
orable logic. For our present purposes it is sufficient that we accept these notions; we
shall not need to concern ourselves further than that.6.7 Attitudes to risk and expected value
Let us now go back to expected value and the other reason why it is apparently not as
useful as it might be to decision makers in businesses.
Like the attitude of our individual to holidays, depicted in Figure 6.4, most
people’s attitude to wealth varies with the amount of it that they have. On the face of
it, a rational person would pay to enter the expected value of a risky venture. For
example, the expected value of a wager on the spin of a fair coin that pays out £200 for
a head and nothing for a tail is £100 [that is, (£200 ×0.5) +(0 ×0.5)]. We might expect
that a rational person would be prepared to pay £100 to take part in this wager. In fact
it would appear that only a minority of people would be prepared to risk losing £100
in order to stand a one in two chance of winning £200. This is because most of us are
risk-averse.Figure 6.4
Utility function
of a particular
individual for going
away on holiday
Increasing days of holiday will give this individual more and more satisfaction. Each additional
day gives a decreasing amount of additional satisfaction, however.‘