Chapter 3
NAME
Preferences
Introduction.
In the previous section you learned how to use graphs to
show the set of commodity bundles that a consumer can afford. In this
section, you learn to put information about the consumer’s preferences on
the same kind of graph. Most of the problems ask you to draw indifference
curves.
Sometimes we give you a formula for the indifference curve.
Then
all you have to do is graph a known equation. But in some problems, we
give you only “qualitative” information about the consumer’s preferences
and ask you to sketch indifference curves that are consistent with this
information. This requires a little more thought. Don’t be surprised or
disappointed if you cannot immediately see the answer when you look
at a problem, and don’t expect that you will find the answers hiding
somewhere in your textbook. The best way we know to find answers is to
“think and doodle.” Draw some axes on scratch paper and label them,
then mark a point on your graph and ask yourself, “What other points on
the graph would the consumer find indifferent to this point?” If possible,
draw a curve connecting such points, making sure that the shape of the
line you draw reﬂects the features required by the problem.
This gives
you one indifference curve. Now pick another point that is preferred to
the first one you drew and draw an indifference curve through it.
Example:
Jocasta loves to dance and hates housecleaning. She has strictly
convex preferences. She prefers dancing to any other activity and never
gets tired of dancing, but the more time she spends cleaning house, the less
happy she is. Let us try to draw an indifference curve that is consistent
with her preferences.
There is not enough information here to tell us
exactly where her indifference curves go, but there is enough information
to determine some things about their shape.
Take a piece of scratch
paper and draw a pair of axes. Label the horizontal axis “Hours per day of
housecleaning.” Label the vertical axis “Hours per day of dancing.” Mark
a point a little ways up the vertical axis and write a 4 next to it. At this
point, she spends 4 hours a day dancing and no time housecleaning. Other
points that would be indifferent to this point would have to be points
where she did more dancing
and
more housecleaning.
The pain of the
extra housekeeping should just compensate for the pleasure of the extra
dancing.
So an indifference curve for Jocasta must be upward sloping.
Because she loves dancing and hates housecleaning, it must be that she
prefers all the points above this indifference curve to all of the points on
or below it.
If Jocasta has strictly convex preferences, then it must be
that if you draw a line between any two points on the same indifference
curve, all the points on the line (except the endpoints) are preferred to
the endpoints. For this to be the case, it must be that the indifference
curve slopes upward ever more steeply as you move to the right along it.
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 Summer '09
 JOHNG.SESSIONS
 Microeconomics, Convex preferences

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