Indifference Curves
Economists write the notion that using goods and services
helps people achieve goals (attain utility) as a
mathematical function, or
U = f( x1, x2, . . . xn)
One can represent this equation with a
table that gives a "map" of consumer preferences.
However, there are two problems with tables of this sort.
First, they assume an independence between goods that seems
unlikely. The added utility of a shirt depends only on the
number of previous shirts that have been bought, and not at
all on the number of hamburgers. If shirts and hamburgers
are either substitutes or complements, this independence
should not exist. However, tables can easily be made that
will avoid this problem.
The second problem is more serious and has led economists
to avoid tables (except for explanatory purposes) when
discussing utility theory. A table with numbers to represent
utility assumes that utility can be measured. Because
utility refers to the extent that goals are accomplished,
there is no way of knowing whether any measurement is
arbitrary or not. This problem can be overcome by using
graphs or mathematics.
At first glance, using a graph instead of a table may not
seem like a good way to proceed. Discussion of maximizing
utility must involve at least three variables: the amount of
good A, the amount of good B, and the level of
utility. Graphs have only two axes, and three variables seem
to require a threedimensional construction rather than a
twodimensional one. However, there is a way around this
problem, one that geographers use when they draw contour
maps showing the three variables of longitude, latitude, and
altitude. They show altitude with a series of lines or
topographic contours such as those in the map below, which
shows a hilly section of West Virginia.
The same method of construction can be used to show a
utility map. A line will connect all possible combinations
of good A and good B that show the same level
of utility. This line is called an isoutility
(iso is Greek and means "the same" or "equal") line
or, more commonly, an indifference curve. In general,
these isoutility lines will be curved, as in the graph
below, if diminishing
returns hold.
One does not need to measure utility in order to draw a
graph such as that in the graph above. All one needs is the
ability to order different levels of utility; that
is, to say that bundle A is preferred to bundle
B, or that bundle B is preferred to bundle
A, or that the chooser is indifferent between the two
bundles.
Indifference curves assume that individuals are
consistent. If Jane prefers option A to option
B, and if she also prefers option B to option
C, then she should prefer option A to option
C. People with inconsistent behavior will not attain
their goals as well as they could, and if behavior is too
inconsistent, their behavior may show few regularities or
predictable patterns.
Next we see how demand
curves come out of indifference curves and budget
lines.
Copyright
Robert Schenk
