Chapter 3: Preferences

Morimitsu Kurino

U. of Tsukuba and VJU

Spring 2017

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

1 / 16

3.1 Consumer Preferences

Given any two consumption bundles x = (x1 , x2 ) and y = (y1 , y2 ), the

consumers can rank them as to their desirability using preference

relations.

(y1 , y2 ): The consumer strictly prefers (x1 , x2 ) to (y1 , y2 ).

1

(x1 , x2 )

2

(x1 , x2 ) : (y1 , y2 ): The consumer is indiﬀerent between (x1 , x2 ) and

(y1 , y2 ).

3

(x1 , x2 ) ⌫ (y1 , y2 ): The consumer weakly prefers (x1 , x2 ) to (y1 , y2 ).

Or she has (x1 , x2 ) at least as good as (y1 , y2 ).

These are related “relations”:

x ⌫ y and y ⌫ x , x : y

x ⌫ y and (not x : y ) , x

y

When we talk about the “preference relations” or “preferences,” we

usually mean the “at-least-as-good-as” relation. Other relations can be

derived from it.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

2 / 16

3.2 Assumptions about Preferences

1

2

3

Completeness.

It is always possible to rank-order any two bundles x and y by

preference.

Thus, we have either x ⌫ y or y ⌫ x.

Reflexivity.

Any bundle is at least as good as itself.

x ⌫ x.

Transitivity.

If x is at least as good as y and y is at least as good as z, then x is at

least as good as z.

x ⌫ y and y ⌫ z ) x ⌫ z.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

3 / 16

ndifference Curves

3.3 Indiﬀerence Curves (1)

It isItconvenient

to to

describe

preferences

is convenient

describe

preferencesgraphically

graphicallyusing

using aa

construction

known

as

indifference

curves.

construction known as indiﬀerence curves.

An indifference

curve) of

of bundles

bundlesthat

thatare

are

An indiﬀerencecurve

curveisis the

the set

set (or curve)

indifferent

to

each

other.

indiﬀerent to each other.

Indiﬀerence

curve

Indifference

curve

at at

(x1(x

, x12, )x2 ):

¨Kurino“Micro

Utku

Theory”

MoriUnver

(U. of

Tsukuba(BC)

and VJU)

Preferences

Chap

2: Preferences

VJU

74 // 20

16

ndifference Curves-2

3.3 Indiﬀerence Curves (2)

z

z

y

y

x

z.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

5 / 16

3.3 Indiﬀerence Curves (3)

Claim

Indiﬀerence curves of a single consumer cannot intersect each other.

Indifference Curves-3

Why?

Indifference curves of a single consumer cannot intersect each other.

Proof. Why?

Suppose for a contradiction that they did.

Suppose they did:

x

y x

z but y

z; contradicting transitivity of

¨ : “Micro

M. Utku

Theory”not

(BC) (y : z);

Preferences

9 / 20

x : y and

xUnver

z but

contradicting the transitivity

of :.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

6 / 16

3.4 Examples of Preferences (1): Perfect Substitutes

Examples of Preferences

Perfect Substitutes: The consumer is willing to substitute one good

for Perfect

anotherSubstitutes:

at a constant

Therate.

consumers are willing to substitute one

for another

constant rate.

Thegood

simplest

case at

is aone-to-one

basis.

The simplest case is one to one basis.

The indifference curves have constant slopes and moreover they all

have the same

slope.

The indiﬀerence

curves

have constant slopes and moreover they all have

The

slope

does

not need to be -1, that is: these items need not be

the same slope.

substituted at one-to-one basis!

The slope does not need to Preferences

be -1, that is, these items need 10not

be

/ 20

substituted at one-to-one basis!

¨

M. Utku Unver

“Micro Theory” (BC)

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

7 / 16

3.4 Examples of Preferences (2): Perfect Complements

Perfect Complements: Goods that are always consumed together in

Perfect Complements: Goods that are always consumed together in

fixed proportions.

fixed proportions.

For example left shoe, right shoe.

For example, left shoe and right shoe.

Indifference Curves

These proportions do not need to be one-to-one!

These proportions do not need to be one-to-one!

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

8 / 16

3.4 Examples of Preferences (3): Bads

Bads: A commodity that a consumer does not like.

Bads: A commodity that a consumer does not like.

Example: Indiﬀerence curves for One Good and One Bad.

Example indifference curves for One Good and One Bad

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

9 / 16

3.4 Examples of Preferences (4): Neutrals

Neutrals: A commodity that a consumer does not care for one way or

Neutrals: A commodity that a consumer does not care for one way

another.

or another.

Indiﬀerence curves are always like this for one Neutral and one Good.

Indifference curves are always like this for one Neutral and one Good

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

10 / 16

3.4 Examples of Preferences (5): Satiation

Satiation:

There

is an

overallbest

bestbundle

bundlefor

forthe

the consumer

consumer and

and the

Satiation:

There

is an

overall

the

closer

he

is

to

the

best

bundle,

the

better

oﬀ

he

is.

closer he is to the best bundle, the better off he is.

Example:

Example:

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

11 / 16

3.5 Well-Behaved Preferences (1): Monotonicity

In general it will be convenient to focus on a few general shapes of

indiﬀerence curves.

We will often assume that more is better (so we will be talking about

goods rather than bads).

Definition (Monotonic Preferences)

If x = (x1 , x2 ) and y = (y1 , y2 ) are such that x1

then (x1 , x2 ) (y1 , y2 ).

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

y1 , x 2

y2 , and x 6= y ,

VJU

12 / 16

3.5 Well-Behaved Preferences (2): Monotonicity

Monotonicity implies that indifference curves are negatively sloped (or zero

sloped).

Monotonicity implies that indiﬀerence curves are negatively sloped.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

13 / 16

3.5 Well-Behaved Preferences (3): Convex Preferences

We will often assume that averages are weakly preferred to extremes.

Example: (little food, much water) could be indiﬀerent to (much

Convex Preferences:

food, little water). But both are worth than (some food, some water).

We will often assume that averages are weakly preferred to extremes.

Example:

(littleprefences)

food, a lot of water) could be indifferent to (a lot of

Definition

(Convex

food, little water). But both are worse than (some food, some water).

SupposeDefinition:

(x1 , x2 ) :Suppose

(y1 , y2()x and

0 <(yt, <

1. Then(0, 1). Then

1 , x2 )

1 y2 ) and t

(tx1(tx

+1 (1

+ (1 t)y

t )1y,1tx

, tx22 +

+ (1

(1 tt)y

)y2 )2 ) ⌫(x(x

12,)x2 ).

1, x

¨ of Tsukuba

Mori Kurino

(U.

and VJU)

M. Utku

Unver

“Micro Theory”

(BC)

Chap

2: Preferences

Preferences

VJU

17

/ 20

14 / 16

3.6 The Marginal Rate of Substitution

The Marginal Rate of Substitution (MRS)

The slope of an indiﬀerence curve is known as the marginal rate of

substitution

(MRS).

The slope of

an indifference curve is known as the marginal rate of

substitution

MRS

measures (MRS).

the rate at which the consumer is willing to substitute

MRS

measures

the rate at which the consumer is willing to substitute

one good for another.

one good for another.

Here xx21 is the rate at which the consumer is willing to substitute

goodx22 for good 1. The slope is negative. MRS is usually a negative

Here

x1 is the rate at which the consumer is willing to substitute

number.

good 2 for good 1. The slope

is negative. MRS is usually a 18negative

Preferences

/ 20

number.

¨

M. Utku Unver

“Micro Theory” (BC)

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

15 / 16

Properties of Preferences and MRS

1

2

Monotonic preferences ) MRS < 0.

Strictly convex preferences ) diminishing marginal rate of

substitution.

That is, as we increase x1 , the slope of the indiﬀerence curve decreases

in absolute value. This means that the amount of good 2 the person is

willing to substitute for good 1 is decreasing as you increase the

amount of good 1 consumed.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

16 / 16

Morimitsu Kurino

U. of Tsukuba and VJU

Spring 2017

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

1 / 16

3.1 Consumer Preferences

Given any two consumption bundles x = (x1 , x2 ) and y = (y1 , y2 ), the

consumers can rank them as to their desirability using preference

relations.

(y1 , y2 ): The consumer strictly prefers (x1 , x2 ) to (y1 , y2 ).

1

(x1 , x2 )

2

(x1 , x2 ) : (y1 , y2 ): The consumer is indiﬀerent between (x1 , x2 ) and

(y1 , y2 ).

3

(x1 , x2 ) ⌫ (y1 , y2 ): The consumer weakly prefers (x1 , x2 ) to (y1 , y2 ).

Or she has (x1 , x2 ) at least as good as (y1 , y2 ).

These are related “relations”:

x ⌫ y and y ⌫ x , x : y

x ⌫ y and (not x : y ) , x

y

When we talk about the “preference relations” or “preferences,” we

usually mean the “at-least-as-good-as” relation. Other relations can be

derived from it.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

2 / 16

3.2 Assumptions about Preferences

1

2

3

Completeness.

It is always possible to rank-order any two bundles x and y by

preference.

Thus, we have either x ⌫ y or y ⌫ x.

Reflexivity.

Any bundle is at least as good as itself.

x ⌫ x.

Transitivity.

If x is at least as good as y and y is at least as good as z, then x is at

least as good as z.

x ⌫ y and y ⌫ z ) x ⌫ z.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

3 / 16

ndifference Curves

3.3 Indiﬀerence Curves (1)

It isItconvenient

to to

describe

preferences

is convenient

describe

preferencesgraphically

graphicallyusing

using aa

construction

known

as

indifference

curves.

construction known as indiﬀerence curves.

An indifference

curve) of

of bundles

bundlesthat

thatare

are

An indiﬀerencecurve

curveisis the

the set

set (or curve)

indifferent

to

each

other.

indiﬀerent to each other.

Indiﬀerence

curve

Indifference

curve

at at

(x1(x

, x12, )x2 ):

¨Kurino“Micro

Utku

Theory”

MoriUnver

(U. of

Tsukuba(BC)

and VJU)

Preferences

Chap

2: Preferences

VJU

74 // 20

16

ndifference Curves-2

3.3 Indiﬀerence Curves (2)

z

z

y

y

x

z.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

5 / 16

3.3 Indiﬀerence Curves (3)

Claim

Indiﬀerence curves of a single consumer cannot intersect each other.

Indifference Curves-3

Why?

Indifference curves of a single consumer cannot intersect each other.

Proof. Why?

Suppose for a contradiction that they did.

Suppose they did:

x

y x

z but y

z; contradicting transitivity of

¨ : “Micro

M. Utku

Theory”not

(BC) (y : z);

Preferences

9 / 20

x : y and

xUnver

z but

contradicting the transitivity

of :.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

6 / 16

3.4 Examples of Preferences (1): Perfect Substitutes

Examples of Preferences

Perfect Substitutes: The consumer is willing to substitute one good

for Perfect

anotherSubstitutes:

at a constant

Therate.

consumers are willing to substitute one

for another

constant rate.

Thegood

simplest

case at

is aone-to-one

basis.

The simplest case is one to one basis.

The indifference curves have constant slopes and moreover they all

have the same

slope.

The indiﬀerence

curves

have constant slopes and moreover they all have

The

slope

does

not need to be -1, that is: these items need not be

the same slope.

substituted at one-to-one basis!

The slope does not need to Preferences

be -1, that is, these items need 10not

be

/ 20

substituted at one-to-one basis!

¨

M. Utku Unver

“Micro Theory” (BC)

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

7 / 16

3.4 Examples of Preferences (2): Perfect Complements

Perfect Complements: Goods that are always consumed together in

Perfect Complements: Goods that are always consumed together in

fixed proportions.

fixed proportions.

For example left shoe, right shoe.

For example, left shoe and right shoe.

Indifference Curves

These proportions do not need to be one-to-one!

These proportions do not need to be one-to-one!

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

8 / 16

3.4 Examples of Preferences (3): Bads

Bads: A commodity that a consumer does not like.

Bads: A commodity that a consumer does not like.

Example: Indiﬀerence curves for One Good and One Bad.

Example indifference curves for One Good and One Bad

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

9 / 16

3.4 Examples of Preferences (4): Neutrals

Neutrals: A commodity that a consumer does not care for one way or

Neutrals: A commodity that a consumer does not care for one way

another.

or another.

Indiﬀerence curves are always like this for one Neutral and one Good.

Indifference curves are always like this for one Neutral and one Good

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

10 / 16

3.4 Examples of Preferences (5): Satiation

Satiation:

There

is an

overallbest

bestbundle

bundlefor

forthe

the consumer

consumer and

and the

Satiation:

There

is an

overall

the

closer

he

is

to

the

best

bundle,

the

better

oﬀ

he

is.

closer he is to the best bundle, the better off he is.

Example:

Example:

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

11 / 16

3.5 Well-Behaved Preferences (1): Monotonicity

In general it will be convenient to focus on a few general shapes of

indiﬀerence curves.

We will often assume that more is better (so we will be talking about

goods rather than bads).

Definition (Monotonic Preferences)

If x = (x1 , x2 ) and y = (y1 , y2 ) are such that x1

then (x1 , x2 ) (y1 , y2 ).

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

y1 , x 2

y2 , and x 6= y ,

VJU

12 / 16

3.5 Well-Behaved Preferences (2): Monotonicity

Monotonicity implies that indifference curves are negatively sloped (or zero

sloped).

Monotonicity implies that indiﬀerence curves are negatively sloped.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

13 / 16

3.5 Well-Behaved Preferences (3): Convex Preferences

We will often assume that averages are weakly preferred to extremes.

Example: (little food, much water) could be indiﬀerent to (much

Convex Preferences:

food, little water). But both are worth than (some food, some water).

We will often assume that averages are weakly preferred to extremes.

Example:

(littleprefences)

food, a lot of water) could be indifferent to (a lot of

Definition

(Convex

food, little water). But both are worse than (some food, some water).

SupposeDefinition:

(x1 , x2 ) :Suppose

(y1 , y2()x and

0 <(yt, <

1. Then(0, 1). Then

1 , x2 )

1 y2 ) and t

(tx1(tx

+1 (1

+ (1 t)y

t )1y,1tx

, tx22 +

+ (1

(1 tt)y

)y2 )2 ) ⌫(x(x

12,)x2 ).

1, x

¨ of Tsukuba

Mori Kurino

(U.

and VJU)

M. Utku

Unver

“Micro Theory”

(BC)

Chap

2: Preferences

Preferences

VJU

17

/ 20

14 / 16

3.6 The Marginal Rate of Substitution

The Marginal Rate of Substitution (MRS)

The slope of an indiﬀerence curve is known as the marginal rate of

substitution

(MRS).

The slope of

an indifference curve is known as the marginal rate of

substitution

MRS

measures (MRS).

the rate at which the consumer is willing to substitute

MRS

measures

the rate at which the consumer is willing to substitute

one good for another.

one good for another.

Here xx21 is the rate at which the consumer is willing to substitute

goodx22 for good 1. The slope is negative. MRS is usually a negative

Here

x1 is the rate at which the consumer is willing to substitute

number.

good 2 for good 1. The slope

is negative. MRS is usually a 18negative

Preferences

/ 20

number.

¨

M. Utku Unver

“Micro Theory” (BC)

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

15 / 16

Properties of Preferences and MRS

1

2

Monotonic preferences ) MRS < 0.

Strictly convex preferences ) diminishing marginal rate of

substitution.

That is, as we increase x1 , the slope of the indiﬀerence curve decreases

in absolute value. This means that the amount of good 2 the person is

willing to substitute for good 1 is decreasing as you increase the

amount of good 1 consumed.

Mori Kurino (U. of Tsukuba and VJU)

Chap 2: Preferences

VJU

16 / 16

## Enterprise Mac Managed Preferences

## MODELLING IMPORTANCE PREFERENCES IN CUSTOMER SATISFACTION SURVEYS

## Mạng điện tử chap3

## Chap3-4

## chap3

## Compositing Preferences

## Delivering Managed Preferences

## Enforcing Managed Preferences

## Preference Manifests and “Raw” Preferences

## Troubleshooting Managed Preferences

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