Economists
today generally treat utility numbers ordinally measureable. Though unable to
be added together, ordinal numbers can be ranked. Ranking is a kind of measure.
Non-additive ranking means that the intervals between numbers are not
comparable. 101 is bigger than 99, while 99 is bigger than 89. The interval
between the former is 2 while the interval between the latter is 10. But since
they are not cardinal measures, we cannot say the interval between the latter
is five times that of the former.
Let’s cite
a few examples. In Miss Hong Kong Beauty Pageant, the winner has 88 points, the
first runner-up 82, and the second runner-up 79. The positions are ranked, yet
it cannot be said that the difference between the winner and the first
runner-up is twice the difference between the first runner-up and the second runner-up.
Another example is about school examination where the teacher arbitrarily uses
marks to rank. When I was studying at the University of California, Los Angeles
(UCLA), a student asked the teacher how examination marks were calculated. The
reply was: “Examination marks are only arbitrarily ranked. Otherwise, the
teacher will be too foolish to teach at the UCLA.” Examination marks of essay
questions are ordinal measures.
Using
ordinal measure to rank utility has no logical problem. When a certain person
prefers A to B, the reason is A’s utility number bigger than B’s. And if the
associated constraints are properly handled, this person’s behavior will be
explained. However, in using ordinal measure to gauge utility, we will never
comprehend what the difference between A and B represents, nor what usage this
person’s total utility number has. More than twenty years ago, I received a
call from the father of a Hong Kong high school student. He said that there was
a question in his son’s examination asking for the usage of total utility. His
son did not know how to answer and thus failed in the examination. This father
asked me for the answer, and I asked back, “Does your son really not know?” “He
doesn’t.” “Then your son knows much more than the teacher!”
In 1892,
Irving Fisher (1867 – 1947), who subsequently became the greatest economist of
the twentieth century, published his doctoral thesis. Part of the thesis was on
the utility theory. This thesis shows how talented Fisher was. One of the key
points in that was from the perspective of explaining behavior, cardinal
measure of utility is not necessary. Since cardinal measure is no different
from ordinal measure at the margin, thus in explaining behavior, viewing purely
at the “margin” is sufficient. “Marginal” utility refers to the change in
utility number by having a little more or a little less of a good. Viewing at
the margin, nothing needs to be added together, nor is comparison of the
intervals between utility numbers required.
William
Stanley Jevons (1835 – 1882) incubated the argument that to explain behavior,
one only has to start working from changes at the margin. This idea, valued by
Fisher, was succeeded by others. In 1946, Stigler pointed out that if a
production process simultaneously produced two products, the average cost of
each product would not be known, yet we would know the change in marginal cost.
In explaining production behavior, there is no need to know the average cost.
When I
subsequently worked on transaction costs, I started purely from marginal
changes. It is no easy matter to measure transaction costs in the real world. A
commendable approach in explaining behavior is to determine whether transaction
costs will increase or decrease under different circumstances. Change is “marginal”,
and if there are no changes, behavior cannot be explained. In applying this
marginal changes approach to handle transaction cost, whether the cost measure
is cardinal or ordinal makes no difference. We cannot assume cardinal measure
is any more accurate, since the accuracy of a measure depends on the observer’s
recognition instead of the number’s thoroughness.
Let me
reiterate. Utility is only a random assignment of numbers to arbitrarily rank
options for explaining choice behavior. This is what my teacher Alchian said.
Stigler said: “In our postulate, regardless of whether a person strives to
maximize wealth, religiosity, eliminate people who sing love songs, or his own
waistline, from the strict perspective of the demand theory, there are no differences.”
Robert Henry Strotz said: “Clearly we do not have to determine if utility
measure is supported by money, loose time, octave or inch. And we do not need
to conceive utility measure as a psychological unit.” These are wisdoms of the
1950s.
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