Lecture notes companion 6'—Indifference Curves
The type of analysis of consumer behavior we’ve done so far is known as partial equilibrium analysis. Typified by demand
and supply analysis, it studies the effect of a change in price of a single good without reference to the feedback effects from
other markets. It’s most closely associated with the work of Alfred Marshall. In recent years, however, economists have
th
increasingly turned to what’s known as general equilibrium analysis. Pioneered by the 19 century French economist Léon
Walras (pronounced väl’ rä—please don’t say walrus), this attempts to show how a change in the price of a single good runs
across different markets and back into the market in which the price change originally occurred.
Graphically, general equilibrium analysis requires the use of what are known as indifference curves. Let’s see how they
work.
Assume a market in which—
1. There are two goods (for simplicity)
2. Consumers know their preferences. They might not be able to assign utility values to different goods they
consume, but they know which goods they like more and which ones they like less. (Technically speaking,
consumers are aware of ordinal utility, i.e., rankings, but not cardinal utility, i.e, utils. This is a lot more realistic and
lets us avoid the problems associated with the concept of utility.)
3. Buyers prefer more to less—that is, given a choice between two eggs and three eggs, the consumer would
always choose three. Higher indifference curves—those farther from the origin—represent higher levels of
consumption and hence are preferred to lower ones.
4. Goods are substitutable—i.e., if happy meals for the kids become too expensive, you can always feed them at
home and spend the difference on stuffed animals. (Not to eat, of course.) As a result, indifference curves always
slope downward to the right.
5. People prefer variety in consumption. That is, the more of a good one consumes, the less one prefers to have
another extra unit of it. As a result, indifference curves are convex viewed from the origin. (Economists sometimes
speak of people as having “convex preferences,” which means the same thing.) The slope of the indifference curve
is called the marginal rate of substitution, the rate at which a consumer is just willing to trade one unit of a good for
the other. (Note that this concept is analogous to diminishing marginal utility from partial equilibrium analysis!)
6. Indifference curves are everywhere dense. There aren’t any gaps in the indifference map, as it is called, so
there is an infinity of indifference curves on a given indifference map.
7. Indifference curves never intersect. If so, people would have inconsistent preferences. I’ll explain.
On each indifference curve, we have an infinity of combinations of the two goods, each of which makes the consumer
equally well off. He thus does not prefer any one combination to any other, and so is—indifferent among those choices,
hence the name. So all combinations of the two goods that exist on any single indifference curve are, from the consumer’s
standpoint, the same. (For this reason, we sometimes call indifference curves isoutility curves. Recall that the Greek prefix
iso- means “same.”)
Now for an example—Say that you have a limited budget of $40 a week to spend (sorry), and that you can only purchase 2
goods, bread and beer (not sorry). Say that bread is priced at $2 per loaf , and beer is $1 per pint. Your maximum
consumption levels of the two goods are, respectively, 20 loaves of bread or 40 pints of beer, provided you only purchase
one good. But, since you prefer variety in consumption (see #5 above), you will choose some combination of the two. But
which combination makes you best off?
Refer to Figure 1 at right. I’ve sketched three (of the
infinity of) indifference curves as I1, I2, and I3. BB is the
budget line. Note that its slope is -2, since the price of
bread is 2 times that of beer, i.e., you can buy twice as
much beer as bread with your budget. Now, we need to
determine your optimal consumption bundle, i.e., that set
of goods that you prefer most highly. (In partial equilibrium
terms, this would be the set of goods that maximizes your
total utility.
Let’s see:
1. We know for sure that you won’t choose point V, 4
breads and 23 beers, because you haven’t spent all your
budget (4*$2 + 23*$1 = $31). You can therefore increase
your consumption and move to a higher indifference curve
(more preferred, i.e., more utility) by spending more.
Remember assumption #3—more is preferred to less.
2. You won’t choose point W, either. Here, at 16 breads
and 8 beers, you’re spending the whole wad (16*$2 + 8*$1
= $40), but you’re still on the same indifference curve as
Beer
40
Figure 1.
B
30
Z
V
X
20
Y
I3
10
W
I2
B I1
Bread
10
20
30 point V. I.e., you’re spending more money, but you’re no better off. Given your preferences (which, by the way I’ve drawn
the indifference curves, I’ve tilted somewhat toward beer) all that extra bread isn’t enough to offset the loss of the 15 beers.
3. Point X—here it is! You’re maximizing your utility here. Why? Because, first, at 9 breads and 22 beers, your total
expenditure is 9*$2 + 22*$1 = $40, i.e., your entire budget. And point X lies on indifference curve IC2, which is further from
the origin than IC1. Note further that at point X, IC2 is just tangent to the budget line. The next highest indifference curve,
then, would not intersect the budget line at all, and hence would be unaffordable. Thus IC2 is highest indifference curve you
can (just barely) reach, and so point X is the optimal consumption bundle. (Note also that you can’t afford any other point on
IC2.)
4. So what’s wrong with points Y and Z? Y is on the same indifference curve as X, but it costs more (too much bread), and
so it’s outside the budget line. You can’t afford it, and you wouldn’t choose it even if you could, because you can choose
point X for less money but the same utility. Point Z is on a higher indifference curve, and is preferred to point X, that’s for
sure, but it’s outside the budget line, too. You can’t afford it.
Now—let’s say that you get a nice little raise. You now have
a monthly budget of $56, represented by the new budget line
B’B’ in Figure 2, which means you can afford either 56 pints
or 28 loaves, or some combination of the two totaling $56.
Now, the optimal bundle is point Z, at 24 beers and 16
breads. You’re now able to attain indifference curve IC3,
which is preferred to IC2. (Remember that this is the point
you couldn’t afford in Figure 1.) Note that a change in the
budget is represented by a parallel shift in the budget line.
Beer
Figure 2.
B’
50
40
Finally, let’s go back to our original budget of $40. (ECO231
review question: Say that the raise was really just a one-time
bonus payment. According to the permanent income
hypothesis, would you likely have spent the whole $56, or
would you have saved some to smooth out your consumption
over time?) Now, let the price of bread rise to $4 a loaf due
to a plague of locusts. As Figure 3 shows, this change in the
price ratio swings the budget line inward, since you can now
afford only 10 loaves instead of 20, so it rotates, anchored to
the beer axis, to the new budget line BB”. As a result, our
optimal bundle is now point V, which is less preferred than
point X. Our total utility has fallen. Bah.
B
30
Z
V
X
20
Y
IC3 10
W
IC2 B B’ IC1 Bread
Beer 10
B’ 20 30 Figure 3.
Deriving the demand curve for bread
Note also that, as we move from point X to point V, that the
quantity of bread consumed has fallen, from 9 loaves to 5. So
we have two prices and two quantities demanded for bread,
which means we can plot a demand curve, as in Figure 4.
Whee, this is
fun.
50 40 B B’’ 30 V
Figure 4.
P
Z
$5
X
20 4
Y
I3
10 W
B’’ 5
I2
B I1 9
10 Bread
20 30 P
$4
2
Qd
5
9
3
2
1
D
Q
1 3 5 7 9