Utility Maximization: Equalizing Marginal Utility per Dollar.

Utility Maximization: Equalizing Utility Maximization: Equalizing Marginal Utility per DollarMarginal Utility per Dollar

Spending the Marginal DollarSpending the Marginal Dollar• Sammy’s optimal consumption choice is found Sammy’s optimal consumption choice is found

by finding his total utility he receives from each by finding his total utility he receives from each consumption bundle on his budget line and then consumption bundle on his budget line and then choosing the bundle at which total utility is choosing the bundle at which total utility is maximized.maximized.

• Now, use marginal analysisNow, use marginal analysis• Sammy’s problem of finding his optimal Sammy’s problem of finding his optimal

consumption choice into a “how much” problemconsumption choice into a “how much” problem

Spending the Marginal DollarSpending the Marginal Dollar

• The way to do this is by choosing an optimal The way to do this is by choosing an optimal consumption bundle as a problem of how consumption bundle as a problem of how much to spend on each good.much to spend on each good.

• To find the optimal consumption bundle, we To find the optimal consumption bundle, we have to see whether Sammy will make have to see whether Sammy will make himself better off by spending a little bit himself better off by spending a little bit more of his income on clams and less on more of his income on clams and less on potatoes, or the opposite, more on potatoes potatoes, or the opposite, more on potatoes and less on clamsand less on clams


• Marginal decisions is a question of how Marginal decisions is a question of how to spend the marginal dollar—how to to spend the marginal dollar—how to allocate an additional dollar between allocate an additional dollar between clams and potatoes in a way that clams and potatoes in a way that maximizes utilitymaximizes utility

• Is Sammy better off by spending an Is Sammy better off by spending an additional $1 on either good, and if so, additional $1 on either good, and if so, by how much is he better off?by how much is he better off?

Marginal Utility per DollarMarginal Utility per Dollar

• To answer the question on Sammy, need to To answer the question on Sammy, need to calculate the marginal utility dollar spend on calculate the marginal utility dollar spend on either clams or potatoeseither clams or potatoes– How much additional utility Sammy gets from How much additional utility Sammy gets from

spending an additional dollar on either goodspending an additional dollar on either good

Sammy’s Marginal Utility per DollarSammy’s Marginal Utility per Dollar

Optimal ConsumptionOptimal Consumption

• Optimal consumption rule says that when a Optimal consumption rule says that when a consumer maximizes utility, the marginal consumer maximizes utility, the marginal utility per dollar spent must be the same for utility per dollar spent must be the same for all goods and services in the consumption all goods and services in the consumption bundle.bundle.

• General rule applied to all goods and servicesGeneral rule applied to all goods and services• In the consumption bundle, the marginal In the consumption bundle, the marginal

utilities per dollar spent for each and every utilities per dollar spent for each and every good or service in that bundle are equalgood or service in that bundle are equal


If Sammy has, If Sammy has, in fact, in fact,

chosen his chosen his optimal optimal

consumption consumption bundle, his bundle, his marginal marginal utility per utility per

dollar spent dollar spent on clams and on clams and

potatoes potatoes must be must be equal.equal.

6

5

4

3

2

1

BC

BP

MUC

/ PC

MUP/ P

P

C

543210

0246810

Total utility (utils)

Quantity of clams (pounds)

Quantity of potatoes (pounds)

At the optimal consumption At the optimal consumption bundle, the marginal utility per bundle, the marginal utility per dollar spent on clams is equal dollar spent on clams is equal

to the marginal utility per to the marginal utility per dollar spent on potatoes.dollar spent on potatoes.

Marginal Utility and the Law of Marginal Utility and the Law of DemandDemand

• Price of fried claims rises.Price of fried claims rises.• Doesn’t change the marginal utility a Doesn’t change the marginal utility a

consumer gets from an additional pound of consumer gets from an additional pound of clams at any given level of clam consumptionclams at any given level of clam consumption

• But….it reduces the marginal utility per dollar But….it reduces the marginal utility per dollar spent on fried clamsspent on fried clams

• The decrease in marginal utility per dollar The decrease in marginal utility per dollar spent on clams gives the consumer an spent on clams gives the consumer an incentive to consume fewer clams when the incentive to consume fewer clams when the price of clams risesprice of clams rises


• Why?Why?• A utility-maximizing consumer chooses a A utility-maximizing consumer chooses a

consumption bundle for which the marginal consumption bundle for which the marginal utility per dollar spent on all goods is the utility per dollar spent on all goods is the samesame

• If the MU per dollar spent on clams falls If the MU per dollar spent on clams falls because the price of clams rises, the because the price of clams rises, the consumer can increase his or her utility by consumer can increase his or her utility by purchasing fewer clams and more of other purchasing fewer clams and more of other goodsgoods


• The opposite happens also, if the price of The opposite happens also, if the price of clams fellclams fell

• If that happens, marginal utility per dollar If that happens, marginal utility per dollar spend on clams, increases at any given level spend on clams, increases at any given level of clam consumptionof clam consumption

• Consumers can increase his or her utility by Consumers can increase his or her utility by purchasing more clams and less of other purchasing more clams and less of other goods when the price of clam fallsgoods when the price of clam falls


• When the price of a good increases, an When the price of a good increases, an individual will normally consume less of that individual will normally consume less of that good and more of other goodsgood and more of other goods

• When a price of a good decreases, an When a price of a good decreases, an individual will normally consume more of individual will normally consume more of that good and less of other goodsthat good and less of other goods

Utility Maximization: Equalizing Utility Maximization: Equalizing Marginal Utility per Dollar NotesMarginal Utility per Dollar Notes


• Sammy’s optimal consumption choice is Sammy’s optimal consumption choice is found byfound by

• Now, we will use marginal analysisNow, we will use marginal analysis


• To find the optimal consumption bundle, we To find the optimal consumption bundle, we have to see whether Sammy will make have to see whether Sammy will make himself better off by spending a little bit himself better off by spending a little bit more of his income on clams and less on more of his income on clams and less on potatoes, or the opposite, more on potatoes potatoes, or the opposite, more on potatoes and less on clamsand less on clams


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

• Is Sammy better off by spending an Is Sammy better off by spending an additional $1 on either good, and if so, by additional $1 on either good, and if so, by how much is he better off?how much is he better off?


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

Sammy’s Marginal Utility per DollarSammy’s Marginal Utility per Dollar

Optimal ConsumptionOptimal Consumption

• Optimal consumption rule says that when a Optimal consumption rule says that when a consumer maximizes utility, the marginal consumer maximizes utility, the marginal utility per dollar spent must be the same for utility per dollar spent must be the same for all goods and services in the consumption all goods and services in the consumption bundle.bundle.

• General rule applied to all goods and servicesGeneral rule applied to all goods and services• In the consumption bundle, the marginal In the consumption bundle, the marginal

utilities per dollar spent for each and every utilities per dollar spent for each and every good or service in that bundle are equalgood or service in that bundle are equal


6

5

4

3

2

1

BC

BP

MUC

/ PC

MUP/ P

P

C

543210

0246810

Total utility (utils)

Quantity of clams (pounds)

Quantity of potatoes (pounds)


• Price of fried claims rises.Price of fried claims rises.• Doesn’t change the marginal utility a Doesn’t change the marginal utility a

consumer gets from an additional pound of consumer gets from an additional pound of clams at any given level of clam consumptionclams at any given level of clam consumption

• But….But….

• The decrease in marginal utility per dollar The decrease in marginal utility per dollar spent on clams spent on clams


• Why?Why?

• If the MU per dollar spent on clams falls If the MU per dollar spent on clams falls because the price of clams rises, the because the price of clams rises, the consumer can increase his or her utility by consumer can increase his or her utility by purchasing fewer clams and more of other purchasing fewer clams and more of other goodsgoods


• The opposite happens also, if the price of The opposite happens also, if the price of clams fellclams fell

• If that happens, marginal utility per dollar If that happens, marginal utility per dollar spend on clams, increases at any given level spend on clams, increases at any given level of clam consumptionof clam consumption

• Consumers can increase his or her utility by Consumers can increase his or her utility by purchasing more clams and less of other purchasing more clams and less of other goods when the price of clam fallsgoods when the price of clam falls


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

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

Utility Maximization: Equalizing Marginal Utility per Dollar.

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