Download Ch08A-7e[1]

MARGINAL
UTILITY AND
INDIFFERENCE
CURVES
8
APPENDIX
Objectives
After studying this appendix, you will 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 spent on movies is MUM/PM
The marginal utility per dollar spent on 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.
But the best affordable point is when MRS = PM/PS.
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.
Consumption Possibilities
A household’s real income is the income expressed as a
quantity of goods the household can afford to buy.
Lisa’s real income in terms of soda is the point on her
budget line where it meets the y-axis.
A relative price is the price of one good divided by the
price of another good.
It is the magnitude of the slope of the budget line
The relative price shows how many sodas must be
forgone to see an additional movie.
THE END