econ 2020ch7

ECON 2020Priniciples of MicroeconomicsChapter 7: Utility Maximization

Hyeon Joon Shin

Assistant Professor of EconomicsThe Falls School of Business, Anderson University

Semester II, 2014-15

Shin (FSB, Anderson Univ.) Semester II, 2014-15 1 / 19

Understanding Consumer Behavior

ProblemWhy do business people have to understand consumer behavior?

Each �rm produces its good or service and sell it to consumers in orderto maximize its pro�t.Consumers purchase their optimal bundle set among many goods andservices.When a �rm�s good or service is not chosen by consumers anymore, the�rm should go out of business.Thus, each �rm has to keep abreast of trends in consumer demand tosurvive in businees and maximize its pro�t.Therefore, understanding the microeconomics of consumer behavior isthe �rst step in managing �rms.

Each �rm produces its good or service and sell it to consumers in orderto maximize its pro�t.

Consumers purchase their optimal bundle set among many goods andservices.When a �rm�s good or service is not chosen by consumers anymore, the�rm should go out of business.Thus, each �rm has to keep abreast of trends in consumer demand tosurvive in businees and maximize its pro�t.Therefore, understanding the microeconomics of consumer behavior isthe �rst step in managing �rms.

Each �rm produces its good or service and sell it to consumers in orderto maximize its pro�t.Consumers purchase their optimal bundle set among many goods andservices.

When a �rm�s good or service is not chosen by consumers anymore, the�rm should go out of business.Thus, each �rm has to keep abreast of trends in consumer demand tosurvive in businees and maximize its pro�t.Therefore, understanding the microeconomics of consumer behavior isthe �rst step in managing �rms.

Each �rm produces its good or service and sell it to consumers in orderto maximize its pro�t.Consumers purchase their optimal bundle set among many goods andservices.When a �rm�s good or service is not chosen by consumers anymore, the�rm should go out of business.

Thus, each �rm has to keep abreast of trends in consumer demand tosurvive in businees and maximize its pro�t.Therefore, understanding the microeconomics of consumer behavior isthe �rst step in managing �rms.

Each �rm produces its good or service and sell it to consumers in orderto maximize its pro�t.Consumers purchase their optimal bundle set among many goods andservices.When a �rm�s good or service is not chosen by consumers anymore, the�rm should go out of business.Thus, each �rm has to keep abreast of trends in consumer demand tosurvive in businees and maximize its pro�t.

Therefore, understanding the microeconomics of consumer behavior isthe �rst step in managing �rms.

Basic Assumptions of Consumer Theory

Utility The satisfaction that each consumer obtains fromconsuming goods and services

Rational Behavior Each consumer is a rational, self-interested personwho tries to use his/her income to obtain the maximumutility from consuming goods and services.

Preferences Each consumer has clear-cut preferences for certaingoods and services that are available in the market.

Each rational and self-interested consumer prefers a certain good orservice that gives him/her higher utility to other goods or services.

Basic Assumptions of Consumer Theory (cont�d)

Budget Constraint The limited income that each consumer spends ongoods and services.

Each consumer uses all his/her income up for his/her consumption,without borrowing or saving.

Prices The prices of goods and services are determined by themarket supply and demand.

Each consumer�s choice cannot a¤ect the prices.

TheoremGiven the prices of goods and services, each consumer chooses the optimalbundle set that maximizes his/her utility, subject to his/her budgetconstraint.

Utility

De�nition

Utility Consumers�satisfaction obtained from consumption

Utility is not a synonym for "usefulness."

ExampleA ticket to a Colts game gives us utility, but it is useless functionally.

The utility of a good or service may vary from person to person.

ExampleAn economics textbook may have greater utility to business students thanto medical students.

Utility is assumed to be measure with units called utils.

ExampleYou may get 100 utils from a donation and 50 utils from a Colts game.

Utility

De�nition

Utility

De�nition

Utility

De�nition

Utility

De�nition

Utility

De�nition

Utility

De�nition

Utility

De�nition

Utility

The Law of Diminishing Marginal Utility

Total Utility The total amount of utility obtained from consumingsome speci�c quantity of a good or service.

Marginal Utility The extra amount of utility obtained from consumingan additional unit of a good or service.

Marginal utility is the change in total utility that results from theconsumption of one more unit of a good or service.

TheoremAs a consumer increases consumption of a good or service, the marginalutility of that good or service declines.

Utility

The Law of Diminishing Marginal Utility (cont�d)

Total and Marginal Utility of Consuming Taco (Figure 7.1)

As more of a product is consumed, total utility increases at adiminishing rate, reaches a maximum, and then declines.As more of a product is consumed, marginal utility continues todecrease, reaches zero at the maximum of total utility, and turns to benegative.

Utility

As more of a product is consumed, total utility increases at adiminishing rate, reaches a maximum, and then declines.

As more of a product is consumed, marginal utility continues todecrease, reaches zero at the maximum of total utility, and turns to benegative.

Utility

ProblemUsing graphs, illustrate how total utility and marginal utility change as theconsumption of taco changes.

Total Utility Curve and Marginal Utility Curve:

Utility

The Law of Diminishing Marginal Utility (cont�d)Total and Marginal Utility of Consuming Taco (Figure 7.1)

Utility

Utility Maximization

Utility-Maximizing Rule

TheoremWhen the prices of goods and services are given, each consumer choosesthe optimal bundle set that maximizes his/her utility, subject to his/herbudget constraint.

Utility-Maximizing Rule To maximize utility, each consumer shouldallocate his/her income so that the last dollar spent oneach good yields the same amount of marginal utility.

ProblemFor simplicity, suppose there are only two goods, apple and orange. Whatis meant by this utility-maximizing rule? How does this rule work?

1 The sum of dollars spent on two goods should be equal to income.2 Marginal utilities per dollar of two goods should be equal.

1 The sum of dollars spent on two goods should be equal to income.

2 Marginal utilities per dollar of two goods should be equal.

Marginal Utility per Dollar

ProblemA pizza will give you 36 utils and cost you $12. A movie which costs you$6 will give you 24 utils. What do you choose, a pizza or a movie?

If you are rational, you would choose the movie rather than the pizza!

The marginal utility per dollar spent on the movie would be 4 utils�= 24 utils

The marginal utility per dollar spent on the pizza would be 3 utils�= 36 utils

The rational consumer must compare the marginal utility from eachproduct with its added cost.To make the amounts of marginal utility derived from di¤erently pricedgoods comparable, marginal utilities must be put on a per-dollar-spentbasis.

The rational consumer must compare the marginal utility from eachproduct with its added cost.

To make the amounts of marginal utility derived from di¤erently pricedgoods comparable, marginal utilities must be put on a per-dollar-spentbasis.

Utility Maximization: A Numerical Example

Problem(1) Find all possible combinations of apples and oranges obtainable withan income of $10.

Utility Maximization: A Numerical Example

Problem(1) Find all possible combinations of apples and oranges obtainable withan income of $10.

Utility Maximization: A Numerical Example (cont�d)

Problem(2) Find the utility-maximizing combination among them, using theutility-maximizing rule.

Problem(3) Make sure if your utility-maximizing combination achieves the highesttotal utility.

Algebraic Generalization

The utility-maximizing rule can be represented by the following twoequations:

(PA �QA) + (PB �QB ) = I (1)

MUA of QAPA

=MUB of QB

PA = Price of APB = Price of BQA = Quantity of AQB = Quantity of BI = Income

(PA �QA) + (PB �QB ) = I (1)

MUA of QAPA

=MUB of QB

(PA �QA) + (PB �QB ) = I (1)

MUA of QAPA

=MUB of QB

PA = Price of A

PB = Price of BQA = Quantity of AQB = Quantity of BI = Income

(PA �QA) + (PB �QB ) = I (1)

MUA of QAPA

=MUB of QB

PA = Price of APB = Price of B

QA = Quantity of AQB = Quantity of BI = Income

(PA �QA) + (PB �QB ) = I (1)

MUA of QAPA

=MUB of QB

PA = Price of APB = Price of BQA = Quantity of A

QB = Quantity of BI = Income

(PA �QA) + (PB �QB ) = I (1)

MUA of QAPA

=MUB of QB

PA = Price of APB = Price of BQA = Quantity of AQB = Quantity of B

I = Income

(PA �QA) + (PB �QB ) = I (1)

MUA of QAPA

=MUB of QB

Algebraic Generalization (cont�d)

We found out that the utility-maximizing combination of apples andoranges with an income of $10 is:

2 apples and 4 oranges.

Case (1): If the consumer spent $10 on 0 apples and 5 oranges, then

MUA of QAPA

>MUB of QB

The consumer should consume more apples and less oranges tomaximize utility.

Case (2): if the consumer spent $10 on 4 apples and 3 oranges, then

MUA of QAPA

<MUB of QB

The consumer should consume less apples and more oranges tomaximize utility.

MUA of QAPA

>MUB of QB

MUA of QAPA

<MUB of QB

MUA of QAPA

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MUA of QAPA

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MUA of QAPA

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MUA of QAPA

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MUA of QAPA

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MUA of QAPA

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MUA of QAPA

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MUA of QAPA

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Utility Maximization and the Demand Curve

Assume that, other things being equal, the price of oranges falls to $1.

Marginal utilities per dollar of oranges will double.

Apple (Price = $1) Orange (Price = $1)Unit MU MU/$ MU MU/$1 10 10 24 242 8 8 20 203 7 7 18 184 6 6 16 165 5 5 12 126 4 4 6 67 3 3 4 4

ProblemFind the utility-maximizing combination of apples and oranges, and �ndout how the price decrease in oranges changes the utility-maximizingquantity of oranges.

Utility Maximization and the Demand CurveAssume that, other things being equal, the price of oranges falls to $1.

Utility Maximization and the Demand Curve (cont�d)

Let�s derive an individual demand curve for oranges:

By looking at the individual demand for oranges, we can make sure ofthe law of demand.

Substitution E¤ect and Income E¤ect

This increase in the quantity demanded of oranges can be explained bytwo e¤ects: substitution e¤ect and income e¤ect.

Substitution E¤ect The e¤ect of a change in the relative price oforanges to apples on a change in the quantity demandedof oranges

When the price of oranges falls from $2 to $1, the relative price oforanges to apples also falls from $2 to $1.After this relative price change,

MUA of QAPA

<MUB of QB

This caused the consumer to switch his/her consumption from applestoward oranges.

MUA of QAPA

<MUB of QB

MUA of QAPA

<MUB of QB

When the price of oranges falls from $2 to $1, the relative price oforanges to apples also falls from $2 to $1.

After this relative price change,

MUA of QAPA

<MUB of QB

MUA of QAPA

<MUB of QB

MUA of QAPA

<MUB of QB

Substitution E¤ect and Income E¤ect (cont�d)

Income E¤ect The e¤ect of a change in the price of oranges on theconsumer�s real income and thus on the quantitydemanded of oranges

When the price of oranges falls from $2 to $1,

(PA �QA) + (PB �QB ) < I .

This real income increase caused the consumers to buy more oranges.

(PA �QA) + (PB �QB ) < I .

econ 2020ch7

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