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Section 2 - Consumer Theory

• Consumer theory attempts to explain why consumers choose one good or bundle of goods over another good or bundle of goods.

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Section 2 - Consumer Theory

• In Consumer Theory we will discuss:

–Consumer Utility (Chapter 3)

–Utility and Constraints (Chapter 4)

–Utility and the Demand Curve (Chapter 5)

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Chapter 3 – Consumer Preferences and the Concept of Utility

• Every day, people make choices about what they prefer:

–Buy a red car with a sunroof or a green truck with 4 wheel drive

–Buy Edo and a chocolate milk or MacDonalds and a Diet Coke

–Buy a computer with a 24” LCD screen and windows or a computer with a 21” screen with an apple on it

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Chapter 3 – Consumer Preferences and the Concept of Utility

• In this chapter we will study:

3.1 Preferences and Ranking

3.2 Utility Functions

3.3 Indifference Curves

3.4 Marginal Rates of Substitution

3.5 Special Utility Functions

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3.1 Preference Definitions

• Basket (bundle) – any combination of goods and services–3 hot dogs, 2 pop and 1 ice cream–Haircut, manicure and 20 min massage–2 punches in the gut, 1 kick in the groin

• Consumer preferences – any ranking of two baskets–I prefer 2 hot dogs and a coke to a hot

dog, coke and ice cream

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Preference Assumptions

1) Preferences are complete

- A consumer can always rank preferences:

a) A is preferred to B: A B

b) B is prefered to A: B A

c) A consumer is indifferent between A and B: A ≈ B

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Preference Example

1)Preferences are complete- “I would rather go to a movie with Bobby than go skiing with Mark.” (valid)-“I prefer a computer with a good video card and large screen to a computer with a good sound card and good speakers.” (valid)- “I hate everyone equally!” (valid)- “I can’t decide whether Ruth or Victoria is hotter!” (invalid)

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Preference Assumptions

2) Preferences are transitive

- Choices are consistent:

If

a) A is preferred to B: A B

b) B is preferred to C: B C

then

a) A is preferred to C: A C

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Preference Example

2) Choices are transitive

- “I would rather see the movie Star Wars than Tears and Feelings. I prefer seeing Oceans 13 to Star Wars. Therefore, I prefer Oceans 13 to Tears and Feelings.” (valid)-“Ruth is hotter than Victoria and Susan is cuter than Ruth. Victoria is more attractive than Susan, however.” (invalid)

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Preference Assumptions

3) More is better- A consumer always prefers having

more of a goodExamples:

-“I prefer seven hot dogs to 3.”

-“It’s better to have loved and lost than never to have loved at all!”

-“2 heads are better than 1.”

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Ranking

Ordinal Ranking-baskets are ordered or compared to each

other without any quantitative information or intensity of preference-ie: “I like dogs more than cats.”

Cardinal Ranking-baskets are quantitatively compared

-ie: “I like dogs ten times more than cats.”

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3.2 Utility

• utility: a number that represents the level of satisfaction that the consumer derives from consuming a specific quantity of a good.

•util: unit of pleasure.

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Total Utility, Marginal Utility• TU (total utility):

–the total amount of satisfaction that you get from consuming a product.

• MU (marginal utility):–the increase in TU that comes about as a result of consuming one more unit of the product.

–The slope of the total utility function

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Marginal Utility• If one more unit of a good is consumed, the

marginal utility is equal to the increased utility from that extra good

• If more than one additional good is consumed:

Goods

UtilityMU

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Law of Diminishing MU

• The MU (marginal utility) of a good or service will decline as more units of that good or service are consumed.

•Marginal utility is what counts for rational consumer decisions.

• The “More is Better” assumption is violated if MU ever becomes negative (ie: eating 23 pieces of pizza)

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Maximizing Unconstrained Utility

Performances per Week

Mar

gina

l Util

ity (

utils

per

wee

k)0

3 4 5 6 7

2

4

6

8

10

Performances per Week

To

tal U

tility

(u

tils

pe

r w

eek)

0 2 3 4 5 6 7 8

22

28

34Total utility ismaximized...

…where marginalutility equals zero.

2

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Marginal Utility Example• Let Utility (U) depend on how much pizza you

eat (P), therefore

• Therefore the first piece of pizza gives you 2 “utils” of pleasure, but 4 pieces of pizza give you 4 “utils” of pleasure, not 10….marginal utility is diminishing:

P2 U(P)

P

1MU(P)

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Utility With 2 or More Goods

• Utility and 1 good can be measured on a 2-dimensional graph

• Utility and 2 goods must be measured on a 3-dimensional graph

• Here Marginal Utility uses the ceteris paribus assumption: how does utility change when 1 good changes, everything else held constant?

constant held x yX

UMU

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Marginal Utility Example

• Let Utility (U) depend on how much pizza (P) and hot dogs (H) you eat, therefore

• If hot dogs are held constant, each additional pizza yields less utility:

PH2 U(P)

PMU(P)

H

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3.3 Indifference Curves

• 3 dimensional graphs are difficult to graph and understand

• In practice, consumer preference is graphed using 2 goods on the X and Y axis and INDIFFERENCE CURVES

• Each INDIFFERENCE CURVE plots all the goods combinations that yield the same utility; that a person is indifferent between

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U=√2

U=2

x

y

Consider the utility function U=(xy)1/2. Each indifference curve below shows all the baskets of a given utility level. Consumers are indifferent between baskets along the same curve.

•

•

•

•

0 1 2 4

1

2

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U=√2

U=2

x

y

From the indifference curves, we know that: A ≈ B, C ≈ D

C A & C B,

D A & D B

•

•

•

•

0 1 2 4

1

2A

B

C

D

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1). Completeness => each basket lies on only one indifference curve

2). Transitivity => indifference curves do not cross

3). Negative Slope => when a consumer likes both goods (MUa and MUb are positive), the indifference curve is downward sloping

4). Thin curves => indifference curves are not “thick”

24x

y

•A•

B

•

IC1IC2

C

B A. (different indifference curves)A ≈ C (same indifference curve)B ≈ C (same indifference curve)

Therefore:B ≈ A by transitivityContradiction!

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IC1

x

y

I: Preferred to A

•AII: Less preferred

More of any good is more preferred and less of a good is less preferred, so an indifference curve cannot extend into areas I or II; it must slope downward

26x

y

Since more is better, baskets B and C should be preferred to basket A

BUT

they all lie on the same indifferencecurve, implying indifference.

• ••

0 1 2 4

1

2A

B

C

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Renegade Indifference Curves

• Note that some specialized models produce indifference curves that violate one or more of our assumptions

• These models may still be useful, but their violations must always be kept in mind

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UniversityOf Alberta

IC1

IC2

IC3

North

East

•••

C

BA

Example of “more is better” violation

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Example: Goods people don’t care about  Are these curves Complete?

Yes Are these curves Transitive?

YesDo these curves have Negative Slope?No

Movies watched

Cat

fish

in t

he

city

IC1 IC2 IC3 IC4

Preference direction

0

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3.4 Marginal Rate of Substitution (MRS)

• All along an individual’s indifference curve, an individual consumes different baskets of goods while remaining at the same utility

• The individual is willing to SUBSTITUTE one good for another

• An individual must be compensated by an increase in one good if the other good decreases– Ie) if Bob is equally happy with 3 hot dogs and 1

soda or 2 hot dogs and 2 soda, he is willing to give up 1 hot dog for 1 soda or 1 soda for 1 hot dog

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Marginal Rate of Substitution (MRS)• The marginal rate of substitution (MRS) is the change

(loss) in one good needed to offset the change (gain) in another good– In this case, MRS is the trade-off (loss) of y for a

small increase in x-”The Marginal Rate of Substitution of x for y”-x is gained, so how much y must be given up-alternately, if x is given up, how much y can we get?

• The MRS is equal to the SLOPE of the indifference curve (slope of the tangent to the indifference curve)

constantutility , x

yMRS yx

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Marginal Rate of Substitution (MRS)

yx

y

yx

MRSxy

xy

yx

yMUxMUU

,y

xconstantutility

constantutility y

x

x

curve, ceindifferen thealong moves one as 0U sincebut

MUMU

MUMU

MUMU-

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MRS Example

x

y MRS

y2

1x2

1

MU

MUMRS

y2

1MU ,

x2

1MU

xyLet Utilit

yx,

y

xyx,

yx

y

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Diminishing MRS

• In general, people tend to value more what they have less of:

– Ie) If Frank has 30 chicken wings and 1 Pepsi, he is very willing to give up wings for another Pepsi. If Frank has 10 chicken wings and 2 Pepsi’s, he is less willing to give up wings for Pepsi

• Therefore MRSx,y diminishes as x increases along the indifference curve

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Diminishing Marginal Utility

IC1

Wings

Pepsi

Very willing to give up Pepsi for wings(steep slope=high MRS)

Less willing to give up Pepsi for wings(flat slope = low MRS)

•

•

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Diminishing MRS

• Due to Diminishing MRS, most indifference curves are “bowed” towards the origin (0,0)

– As seen in the above graph

• If Diminishing MRS does not hold (ie: trading quarters for loonies), the graph is not bowed towards the origin

Exercise: Let Utility=(Pepsi)(Wings). For a utility level of 16, sketch the graph and see if Diminishing MRS applies.

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3.4 Special Utility Functions

• In Economics, utility functions dealing with 2 categories of goods create unique indifferent curves:

– Perfect Substitutes

– Perfect Compliments

• Furthermore, 2 utility functions are widely used by Economists for their desirable properties:

– Cobb-Douglas Utility Function

– Quasi-Linear Utility Function

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Perfect Substitutes

• Goods that are perfect substitutes can always be substituted for each other on a 1-to-1 basis

– If a restaurant doesn’t carry Pepsi, you order a Coke instead

– Therefore, MRSCoke, Pepsi=1 and MUCoke/MUPepsi

=1

– In general, MRS=a constant, and indifference curves are a straight line

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Perfect Substitutes: U = Ax + By

Where: A, B positive constants  MUx = A MUy = B  MRSx,y = A/B

1 unit of x is equal to B/A units of y everywhere (constant MRS).

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Example: Perfect Substitutes (Tylenol, Extra-Strength Tylenol)

x0

y

IC1IC2 IC3

Slope = -A/B

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Perfect Compliments

• Some goods are only useful in a set ratio to each other; extra of one good is useless without extra of the other:

– Shoes: 1 Left shoe for every Right shoe

– Cars: 4 full-size tires for every car

– Kraft Dinner: 6 cups of water for every packet

– Marriage: 1 Bride for Every Groom

• Indifference curves are right angles

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3. Perfect Complements: U = A min(x,y) where: A is a positive constant.  MUX = 0 or A MUY = 0 or A  MRSX,Y is 0 (horizontal)

or infinite (vertical) or undefined (at corner)

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Example: Perfect Complements (nuts and bolts)

x0

y

IC1

IC2

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Cobb-Douglas Utility Function

• The Cobb-Douglas Utility function is the holy grail of economic models for a variety of reasons:

– It’s straightforward

– It’s easily modified to suit the model

– It has desirable mathematical properties

• The Cobb-Douglas Utility function also yields “STANDARD” indifference curves

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1. Cobb-Douglas: U = Axy

where: + = 1; A, , positive constants

MUX =Ax-1y (Positive)

MUY =Axy-1 (Positive)

 

MRSx,y = (y)/(x)

“Standard” case: Downward sloping IC, diminishing MRS

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Example: Cobb-Douglas (speed vs. maneuverability)

IC1

IC2

x

y

Preference direction

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Quasi-Linear Utility Function

• Quasi-Linear Utility Functions often explain consumer behavior without an overly complex model

– It’s effective

– It’s simple

– It has a catchy name – “Quasi”

• In a Quasi-Linear Utility Function, MRS is equal for all points above and below each other:

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U = v(x) + Ay

Where: A is a positive constant. 

MUx = v’(x) = V(x)/x, where smallMUy = A

Example: U=4(x)1/2+2yMUx=2/(x) ½ MUy=2

-Useful if one good’s consumption changes little (ie:soap)-linear in Y, non-linear in X (hence quasi-linear)

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Example: Quasi-linear Preferences (movies and toothpaste)

••

IC’s have same slopes on anyvertical line

toothpaste

movies

0

IC2

IC1

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Chapter 3 Key Concepts

PreferencesPreference Assumptions

UtilityMarginal UtilityDiminishing Marginal Utility

Indifference CurvesIndifference Curve Properties

Marginal Rate of SubstitutionDiminishing MRS

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Chapter 3 Key Concepts

Special Utility FunctionsPerfect SubstitutesPerfect ComplimentsCobb-DouglasQuasi-Linear