Utility Maximization: Equalizing Marginal Utility per Dollar

1
Utility Maximization Equalizing Marginal Utility
per Dollar
2
Spending the Marginal Dollar

• Sammys 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
• Sammys problem of finding his optimal
  consumption choice into a how much problem

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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

4
Spending the Marginal Dollar

• Marginal decisions is a question of how to spend
  the marginal dollarhow 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?

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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

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Sammys Marginal Utility per Dollar
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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

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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.
MU
/
P
P
P
6
5
4
3
C
2
1
5
4
3
2
1
0
Quantity of clams (pounds)
0
2
4
6
8
10
Quantity of potatoes (pounds)
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Marginal Utility and the Law of Demand

• Price of fried claims rises.
• Doesnt 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

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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

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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

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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

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Utility Maximization Equalizing Marginal Utility
per Dollar Notes
14
Spending the Marginal Dollar

• Sammys optimal consumption choice is found by
• Now, we will use marginal analysis

15
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

16
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?

17
Marginal Utility per Dollar

• To answer the question on Sammy, need to
  calculate the marginal utility dollar spend on
  either clams or potatoes

18
Sammys Marginal Utility per Dollar
19
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

20
Marginal Utility per Dollar
Total utility (utils)

MU
/
P
P
P
6
5
4
3
C
2
1
5
4
3
2
1
0
Quantity of clams (pounds)
0
2
4
6
8
10
Quantity of potatoes (pounds)
21
Marginal Utility and the Law of Demand

• Price of fried claims rises.
• Doesnt 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

22
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

23
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

24
Marginal Utility and the Law of Demand

• When the price of a good increases,
• When a price of a good decreases,