2. Utility Maximization
Learning Objective
• How do economists model consumer
choice?
• Define what economists mean by utility.
• Distinguish between the concepts of total
utility and marginal utility.
• State the law of diminishing marginal
utility and illustrate it graphically.
• State, explain, and illustrate algebraically
the utility-maximizing condition.
4. Budget or Feasible Set
Learning Objective
• How does income limit choice?
5. Consumer Choice
• Suppose that a consumer has a fixed
amount of money to spend, M.
• There are two goods X and Y, with
associated prices pX and pY.
• The feasible choices that the consumer can
make satisfy pXx+pYy≤M
6. Figure 12.1. Budget set
• The budget line
• The boundary of the
budget set, and it
consists of the goods
that just exhaust the
consumer’s budget
7. Figure 12.2. Effect of an increase in
price on the budget
• An increase in the
price of one good
pivots or rotates the
budget line.
• Increasing prices and
income by the same
multiplicative factor
leaves the feasible set
unchanged.
8. 3.1 The Budget Line
EQUATION 3.1 PX QX + PY QY ≤ M
7
Unattainable The combination in the
6 combinations region above the budget
D
5 line are unattainable,
given Ms. Bain’s budget
4 The budget line
constraint
graphically shows the
3 combinations of two
2 goods a consumer can
Budget
Ms. Bain’s budget allows her line buy with a given budget
1 to purchase any combination
m
D
on or below the budget line.
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EQUATION 3.2 M / PS
Slope = −
M / PH
EQUATION 3.3 M PH P
Slope = − × =− H
PS M PS
9. Revealed preference
• Can we determine preferences just from
the budget and from peoples choices? Or
do we have to ask people to state their
preferences in order to discover their
preferences?
• Revealed versus stated preferences
10. Revealed preference
Suppose you are observed to
Choose A, A is then revealed to be preferred
to all other points on or below the same budget line
M/py
A
Now if py increases and px falls
B so the budget line goes though B, you will
Be worse of at B
11. Revealed preference
Suppose C is chosen then
C is revelaed preferred to A
M/py
A
D
But if D is chosen over C
Then D is reveled
preferred to C
C
B
12. Revealed preferences
• If some bundles are chosen over others at
the same budget and prices then this
demonstrates that people prefer that
bundle to the alternatives they are offered
14. Utility
• Refers not to usefulness but to the flow of
pleasure or happiness that a person enjoys
—some measure of the satisfaction a
person experiences.
• Usefulness might contribute to utility, but
so does style, fashion, or even whimsy.
15. Utility
• Suppose there are two goods, X and Y.
• Suppose the consumer is both hungry and
thirsty, and the goods are pizza and beer.
– The consumer would like more of both,
reflected in greater pleasure for greater
consumption.
– Items that one might consume are generally
known as “bundles,” as in bundles of goods
and services
16. Isoquants
Learning Objectives
• What is an isoquant?
• Why does it help to analyze consumer
choice?
17. Isoquants
• Meaning “equal quantity,” are also known
as indifference curves and represent sets
of points holding utility constant.
• They are analogous to production
isoquants.
18. Figure 12.4. Indifference curves
• Each curve represents one
level of utility.
• Higher utilities occur to the
northeast, farther away from
the origin.
• As with production isoquants,
the slope of the indifference
curves has the interpretation of
the trade-off between the two
goods.
• The amount of Y that the
consumer is willing to give up,
in order to obtain an extra bit
of X, is the slope of the
indifference curve.
19. Figure 12.5. Convex preferences
• Convex preferences mean
that a consumer prefers a
mix to any two equally
valuable extremes.
• Thus, if the consumer
likes black coffee and also
likes drinking milk, then
the consumer prefers
some of each—not
necessarily mixed—to
only drinking coffee or
only drinking milk.
20. 3.2 Indifference Curves
The marginal rate of
substitution is the
maximum amount of one
good a consumer would
be willing to give up in
order to obtain an
additional unit of another
21. Marginal Rate of Substitution
• (MRS) The amount extra of one good
needed to make up for a decrease in
another good, staying on an indifference
curve. is the extra amount of one good
needed to make up for a decrease in
another good, staying on an indifference
curve
33. Utility maximization
• Utility maximization is a matter of selecting a
combination of two goods that satisfy two conditions
– The point at which utility is maximized must be
within the attainable region defined by the
budget line.
– The point at which utility is maximized must be
on the highest indifference curve consistent with
condition 1.
EQUATION 3.4 P
MRS X ,Y = X
PY
43. What about y?
But So
Once again you can
solve this in WolframAlpha.
Hint: Break the problem into steps!
44. Satiation
• The point at which increased consumption
does not increase utility.—the point at
which increased consumption does not
increase utility—would set in at some
point.
• How many pizzas can you eat per month?
How much beer can you drink?
45. Figure 12.8. Isoquants for a bliss point
• A bliss point, or
satiation, is a point at
which further
increases in
consumption reduce
utility.
46. Substitution Effects
Learning Objective
• When prices change, how do consumers
change their behavior?
47. Changes in Consumer Behavior
• An increase in the price of a good is really a
composition of two effects: an increase in the relative
price of the good and a decrease in the purchasing
power of money
• The substitution effect is the change in consumption
resulting from a price change keeping utility constant.
The substitution effect always involves a reduction in the
good whose price increased.
• The amount of money required to keep the consumer’s
utility constant from an infinitesimal price increase is
precisely the amount required to let him or her buy his
or her old bundle at the new prices.
48. Figure 12.9. Substitution with an
increase in price
• An increase in the price
of Y causes the budget
line to pivot around the
intersection on the x-axis
• Since the amount of X
that can be purchased
hasn’t changed. In this
case, the quantity y of Y
demanded rises.
49. Figure 12.10. Substitution effect
• The effect on
consumption of a
change in the relative
price, with a sufficient
change in income to
keep the consumer on
the same utility
isoquant.
• The income effect
changes only income.
50. Income Effects
Learning Objective
• How do consumers change their
purchases when their income rises or
falls?
51. Income effect on Consumer
Behavior
• When an increase in income causes a
consumer to buy more of a good, that
good is called a normal good for that
consumer.
• When the consumer buys less, the good is
called an inferior good. At a sufficiently
high income, most goods become inferior.
52. Figure 12.11. Engel curve
• The curve that shows
the path of
consumption as
income changes,
holding prices
constant, is known as
an Engel curve
53. Figure 12.12. Backward bending— Figure 12.13. Income and substitution
inferior good effects
54. Price and Income effects
• The effect of a price increase decomposes
into two effects: a decrease in real income
and a substitution effect from the change
in the price ratio. For normal goods, a
price increase decreases quantity. For
inferior goods, a price increase decreases
quantity only if the substitution effect is
larger than the income effect.
55. Mathematical Cleanup
Learning Objectives
• Are there important details that haven’t
been addressed in the presentation of
utility maximization?
• What happens when consumers buy none
of a good?
56. • Conditions are available that ensure that
the first-order conditions produce a utility
maximum.
• With convex preferences, zero
consumption of one good arises when
utility is decreasing in the consumption of
one good, spending the rest of income on
the other good.
