Utility Maximization: Equalizing
Marginal Utility per Dollar
Spending the Marginal Dollar
• Sammy’s optimal consumption choice is
found by finding his total utility he receives
from each consumption bundle on his budget
line and then choosing the bundle at which
total utility is maximized.
• Now, use marginal analysis
• Sammy’s problem of finding his optimal
consumption choice into a “how much”
problem
Spending the Marginal Dollar
• The way to do this is by choosing an optimal
consumption bundle as a problem of how
much to spend on each good.
• To find the optimal consumption bundle, we
have to see whether Sammy will make
himself better off by spending a little bit
more of his income on clams and less on
potatoes, or the opposite, more on potatoes
and less on clams
Spending the Marginal Dollar
• Marginal decisions is a question of how
to spend the marginal dollar—how to
allocate an additional dollar between
clams and potatoes in a way that
maximizes utility
• Is Sammy better off by spending an
additional $1 on either good, and if so,
by how much is he better off?
Marginal Utility per Dollar
• To answer the question on Sammy, need to
calculate the marginal utility dollar spend on
either clams or potatoes
– How much additional utility Sammy gets from
spending an additional dollar on either good
Sammy’s Marginal Utility per Dollar
Optimal Consumption
• Optimal consumption rule says that when a
consumer maximizes utility, the marginal
utility per dollar spent must be the same for
all goods and services in the consumption
bundle.
• General rule applied to all goods and services
• In the consumption bundle, the marginal
utilities per dollar spent for each and every
good or service in that bundle are equal
Marginal Utility per Dollar
Total utility (utils)
If Sammy has,
in fact,
chosen his
optimal
consumption
bundle, his
marginal
utility per
dollar spent
on clams and
potatoes
must be
equal.
At the optimal consumption
bundle, the marginal utility per
dollar spent on clams is equal
to the marginal utility per
dollar spent on potatoes.
6
5
MU / P
P P
4
B
C
3
C
2
1
MU
B
P
C
0
1
2
3
Quantity of clams (pounds)
4
5
10
8
6
4
Quantity of potatoes (pounds)
2
0
/P
C
Marginal Utility and the Law of
Demand
• Price of fried claims rises.
• Doesn’t change the marginal utility a
consumer gets from an additional pound of
clams at any given level of clam consumption
• But….it reduces the marginal utility per dollar
spent on fried clams
• The decrease in marginal utility per dollar
spent on clams gives the consumer an
incentive to consume fewer clams when the
price of clams rises
Marginal Utility and the Law of
Demand
• Why?
• A utility-maximizing consumer chooses a
consumption bundle for which the marginal
utility per dollar spent on all goods is the
same
• If the MU per dollar spent on clams falls
because the price of clams rises, the
consumer can increase his or her utility by
purchasing fewer clams and more of other
goods
Marginal Utility and the Law of
Demand
• The opposite happens also, if the price of
clams fell
• If that happens, marginal utility per dollar
spend on clams, increases at any given level
of clam consumption
• Consumers can increase his or her utility by
purchasing more clams and less of other
goods when the price of clam falls
Marginal Utility and the Law of
Demand
• When the price of a good increases, an
individual will normally consume less of that
good and more of other goods
• When a price of a good decreases, an
individual will normally consume more of
that good and less of other goods
Utility Maximization: Equalizing
Marginal Utility per Dollar Notes
Spending the Marginal Dollar
• Sammy’s optimal consumption choice is
found by
• Now, we will use marginal analysis
Spending the Marginal Dollar
• To find the optimal consumption bundle, we
have to see whether Sammy will make
himself better off by spending a little bit
more of his income on clams and less on
potatoes, or the opposite, more on potatoes
and less on clams
Spending the Marginal Dollar
• Marginal decisions is a question of how to
spend the marginal
• Is Sammy better off by spending an
additional $1 on either good, and if so, by
how much is he better off?
Marginal Utility per Dollar
• To answer the question on Sammy, need to
calculate the marginal utility dollar spend on
either clams or potatoes
Sammy’s Marginal Utility per Dollar
Optimal Consumption
• Optimal consumption rule says that when a
consumer maximizes utility, the marginal
utility per dollar spent must be the same for
all goods and services in the consumption
bundle.
• General rule applied to all goods and services
• In the consumption bundle, the marginal
utilities per dollar spent for each and every
good or service in that bundle are equal
Marginal Utility per Dollar
Total utility (utils)
MU / P
P P
6
5
4
B
C
3
C
2
1
MU
B
P
C
0
1
2
3
Quantity of clams (pounds)
4
5
10
8
6
4
Quantity of potatoes (pounds)
2
0
/P
C
Marginal Utility and the Law of
Demand
• Price of fried claims rises.
• Doesn’t change the marginal utility a
consumer gets from an additional pound of
clams at any given level of clam consumption
• But….
• The decrease in marginal utility per dollar
spent on clams
Marginal Utility and the Law of
Demand
• Why?
• If the MU per dollar spent on clams falls
because the price of clams rises, the
consumer can increase his or her utility by
purchasing fewer clams and more of other
goods
Marginal Utility and the Law of
Demand
• The opposite happens also, if the price of
clams fell
• If that happens, marginal utility per dollar
spend on clams, increases at any given level
of clam consumption
• Consumers can increase his or her utility by
purchasing more clams and less of other
goods when the price of clam falls
Marginal Utility and the Law of
Demand
• When the price of a good increases,
• When a price of a good decreases,