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APPENDIX
Marginal Utility and
Indifference Curves
8
After studying this chapter you will be able to
Explain the connection between utility and indifference
curves
Explain why maximizing utility is the same as choosing
the best affordable point
Explain why utility exists
Two Ways of Describing Preferences
–The marginal utility model describes preferences
by using the concept of utility.
–The indifference curve model describes
preferences by using the concepts of preference
and indifference.
–Figure A8.1 on the next slide illustrates the
connection between these two ways of describing
preferences.
Two Ways of Describing Preferences
In part (a), you can see the
levels of utility derived from
each quantity of movies
and soda.
Three combinations
generate 331 units of utility
and two combinations
generate 313 units of utility.
Indifference curves pass
through these points.
Maximizing Utility is Choosing the Best
Affordable Point
Call the marginal utility of movies MUM .
Call the marginal utility of soda MUS .
Call the price of movies PM .
Call the price of soda PS .
The marginal utility per dollar from movies is MUM/PM .
The marginal utility per dollar from soda is MUS/PS.
Utility is maximized when
MUM/PM = MUS/PS.
Maximizing Utility is Choosing the Best
Affordable Point
Call the marginal rate of substitution of movies for soda
MRS.
The consumer is at the best affordable point on the
budget line when
MRS = PM/PS.
Maximizing Utility is Choosing the Best
Affordable Point
To see that maximizing utility is the same as choosing the
best affordable point, begin with
MUM/PM = MUS/PS
and multiply both sides of this equation by PM and divide
both sides by MUS to get
MUM/MUS = PM/PS.
Maximizing Utility is Choosing the Best
Affordable Point
Because the best affordable point is when MRS = PM/PS,
it must be the case that
MUM/MUS = MRS.
To see that this proposition is true, note first that
U = MUM  QM + MUS  QS .
But along an indifference curve, which is where we
measure MRS, U = 0, so
0 = MUM  QM + MUS  QS .
Maximizing Utility is Choosing the Best
Affordable Point
Because
0 = MUM  QM + MUS  QS
we know that
MUM  QM = –MUS  QS .
Now divide both sides of this equation by MUS and by
QM to obtain
MUM / MUS = –QS /QM .
Maximizing Utility is Choosing the Best
Affordable Point
But –QS /QM—rise over run—is the slope of the
indifference curve and removing the minus sign, it is the
marginal rate of substitution.
So
MRS = MUM / MUS = QS /QM .
The two models of consumer choice give the same
answer.
One implies the other.
Utility Exists!
The indifference curve model is powerful because it
enables us to derive the downward-sloping demand curve
from the assumption of diminishing marginal rate of
substitution.
The model is also powerful because it implies that utility
exists.
By observing incomes and prices and the quantities bought
at those prices, we can infer a person’s utility schedule and
the marginal utilities at each quantity combination.
THE END