Lecture 3

LECTURE 3

CONSUMPTION

4-2

Outline

1. Preferences.

2. Utility.

3. Budget Constraint.

4. Constrained Consumer Choice.

5. Behavioral Economics.

4-3

Premises of Consumer Behavior

Individual preferences determine the

amount of pleasure people derive from

the goods and services they consume.

Consumers face constraints or limits

on their choices.

Consumers maximize their well-being

or pleasure from consumption, subject

to the constraints they face.

4-4

Properties of Consumer Preferences

We start from a set of fundamental axioms,

that is assumptions assumed to be true about

consumer preferences that form the basis on

which we build the model of consumer’s

behaviour.

Completeness

Transitivity

Non-satiation

4-5


Completeness - when facing a choice

between any two bundles of goods, a

consumer can rank them so that one

and only one of the following

relationships is true: The consumer

prefers the first bundle to the second,

prefers the second to the first, or is

indifferent between them.

4-6


Transitivity - a consumer’s preferences

over bundles is consistent in the sense

that, if the consumer weakly prefers

Bundle z to Bundle y (likes z at least as

much as y) and weakly prefers Bundle y

to Bundle x, the consumer also weakly

prefers Bundle z to Bundle x.

4-7


More Is Better - all else being the

same, more of a commodity is better

than less of it (always wanting more is

known as nonsatiation).

Good - a commodity for which more is

preferred to less, at least at some levels of

consumption

Bad - something for which less is preferred

to more, such as pollution

4-8

Preference Maps

Indifference curve - the set of all

bundles of goods that a consumer views

as being equally desirable.

Indifference map - a complete set of

indifference curves that summarize a

consumer’s tastes or preferences

4-9

Figure 4.1 Bundles of Pizzas and

Burritos Lisa Might Consume B

, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15

Z , Pizzas per semester

25

20

15

10

5

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d

e

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d

e

Which of these

two bundles

would be

preferred by

Lisa?

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d

e

Which of these

two bundles

would be

preferred by

Lisa?

Lisa prefers

bundle e over

bundle d, since e

has more of both

goods: Pizza and

Burritos

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d

e

B

Which of these

two bundles

would be

preferred by

Lisa?

Lisa prefers

bundle e over

bundle d, since e

has more of both

goods: Pizza and

Burritos

Lisa prefers

bundle e to any

bundle in area B

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d

e

f

B

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d

e

f

B

Which of these

two bundles

would be

preferred by

Lisa?

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d

e

f

B

Which of these

two bundles

would be

preferred by

Lisa?

Lisa prefers

bundle f over

bundle e, since f

has more of both

goods: Pizza and

Burritos

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d

e

f

A

B

Which of these

two bundles

would be

preferred by

Lisa?

Lisa prefers

bundle f over

bundle e, since f

has more of both

goods: Pizza and

Burritos

Lisa prefers any

bundle in area A

over e

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d

e

f

A

B

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d a

e

c

f

A

B

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d a

e

c

f

A

B

If Lisa is indifferent

between bundles e, a,

and c …..

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d a

e

c

f

A

B

B ,

Bur r

ito

s p

er

se

me

ste

r

(b)

30 25 15


25

20

15

10

a

e

c



and c …..

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d a

e

c

f

A

B

B ,

Bur r

ito

s p

er

se

me

ste

r

(b)

30 25 15


25

20

15

10

a

I 1

e

c



and c …..

4-9



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d a

e

c

f

A

B

B ,

Bur r

ito

s p

er

se

me

ste

r

(b)

30 25 15


25

20

15

10

a

I 1

e

c



and c …..

we can draw an

indifferent curve over

those three points

4-10



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d a

e

c

f

A

B

B ,

Bur r

ito

s p

er

se

me

ste

r

(c)

30 25 15


25

20

15

10

a

I 1

e

c

f

we can draw an


those three points

4-10



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d a

e

c

f

A

B

B ,

Bur r

ito

s p

er

se

me

ste

r

(c)

30 25 15


25

20

15

10

a

I 1

e

c

f

we can draw an


those three points

I2

4-10



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d a

e

c

f

A

B

B ,

Bur r

ito

s p

er

se

me

ste

r

(c)

30 25 15


25

20

15

10 d

a

I 1

e

c

f

we can draw an


those three points

I2

4-10



, B

ur r

ito

s p

er

se

me

ste

r

(a)

30 25 15


25

20

15

10

5

d a

e

c

f

A

B

B ,

Bur r

ito

s p

er

se

me

ste

r

(c)

30 25 15


25

20

15

10 d

a

I 1

e

c

f

we can draw an


those three points

I2

I0

4-11

Properties of Indifference Maps

1. Bundles on indifference curves farther

from the origin are preferred to those

on indifference curves closer to the

origin.

2. There is an indifference curve through

every possible bundle.

3. Indifference curves cannot cross.

4. Indifference curves slope downward.

4-12

Impossible Indifference Curves

B ,

Bu

r r ito

s p

er

se

me

ste

r


I 1

I 0

a

b

e

4-12


Lisa is indifferent between e and a, and also between e and b…

B ,

Bu

r r ito

s p

er

se

me

ste

r


I 1

I 0

a

b

e

4-12


Lisa is indifferent between e and a, and also between e and b… so by transitivity she

should also be

indifferent between a

and b…

B ,

Bu

r r ito

s p

er

se

me

ste

r


I 1

I 0

a

b

e

4-12



should also be


and b…

but this is impossible,

since b must be

preferred to a given it has more of both goods.

B ,

Bu

r r ito

s p

er

se

me

ste

r


I 1

I 0

a

b

e

4-12



should also be


and b…


since b must be


B ,

Bu

r r ito

s p

er

se

me

ste

r


I 1

I 0

a

b

e

4-12



should also be


and b…


since b must be


B ,

Bu

r r ito

s p

er

se

me

ste

r


I 1

I 0

a

b

e

4-13


B ,

Bu

r r ito

s p

er

se

me

ste

r


I

a

b

4-13


Lisa is indifferent between b and a since both points are in the same indifference curve…

B ,

Bu

r r ito

s p

er

se

me

ste

r


I

a

b

4-13


Lisa is indifferent between b and a since both points are in the same indifference curve… But this contradicts

the “more is better” assumption. Can you tell why?

B ,

Bu

r r ito

s p

er

se

me

ste

r


I

a

b

4-13


Lisa is indifferent between b and a since both points are in the same indifference curve… But this contradicts

the “more is better” assumption. Can you tell why?

Yes, b has more of both and hence it should be preferred over a.

B ,

Bu

r r ito

s p

er

se

me

ste

r


I

a

b

4-14

Solved Problem 4.1

Can indifference curves be thick?

Answer:

Draw an indifference curve that is at least

two bundles thick, and show that a

preference property is violated

4-15

Solved Problem 4.1

B ,

Bu

r r ito

s p

er

se

me

ste

r

a

b


I

4-15

Solved Problem 4.1

Consumer is

indifferent between b

and a since both

points are in the same

indifference curve…

B ,

Bu

r r ito

s p

er

se

me

ste

r

a

b


I

4-15

Solved Problem 4.1

Consumer is

indifferent between b

and a since both

points are in the same

indifference curve…

But this contradicts the

“more is better”

assumption since b

has more of both and

hence it should be

preferred over a.

B ,

Bu

r r ito

s p

er

se

me

ste

r

a

b


I

4-16

Willingness to Substitute Between

Goods

marginal rate of substitution (MRS) - the

maximum amount of one good a consumer will

sacrifice to obtain one more unit of another

good.

The slope of the indifference curve!

Z

BMRS

4-17

Convex indifference curve B

, B

ur r

ito

s p

er

se

me

ste

r

3

8

2

0 3 5 6


a

I

4-17


, B

ur r

ito

s p

er

se

me

ste

r

3

8

2

0 3 5 6


a

I

4-17


, B

ur r

ito

s p

er

se

me

ste

r

3

8

2

0 3 5 6


a

b

I

4-17


, B

ur r

ito

s p

er

se

me

ste

r

5

3

8

2

0 3 4 5 6


a

b

I

4-17


, B

ur r

ito

s p

er

se

me

ste

r

5

3

8

2

0 3 4 5 6


a

b

I

4-17

From bundle a to bundle b, Lisa

is willing to give up 3 Burritos in

exchange for 1 more Pizza…


, B

ur r

ito

s p

er

se

me

ste

r

5

3

8

1

2

0

–3

3 4 5 6


a

b

I

4-17


, B

ur r

ito

s p

er

se

me

ste

r

5

3

8

1

2

0

–3

3 4 5 6


a

b

c

I

4-17

From bundle b to bundle c,

Lisa is willing to give up 2

Burritos in exchange for 1

more Pizza…


, B

ur r

ito

s p

er

se

me

ste

r

5

3

8

1

1

2

0

-2

–3

3 4 5 6


a

b

c

I

4-17


, B

ur r

ito

s p

er

se

me

ste

r

5

3

8

1

1

2

0

-2

–3

3 4 5 6


a

b

c

d

I

4-17

From bundle c to bundle d,

Lisa is willing to give up 1

Burritos in exchange for 1

more Pizza…


, B

ur r

ito

s p

er

se

me

ste

r

5

3

8

1

-1 1

1 2

0

-2

–3

3 4 5 6


a

b

c

d

I

4-17


, B

ur r

ito

s p

er

se

me

ste

r

5

3

8

1

-1 1

1 2

0

-2

–3

3 4 5 6


a

b

c

d

I

The MRS from bundle a to bundle b is -3. This is the same as the

slope of the indifference curve between those two points.

4-17


, B

ur r

ito

s p

er

se

me

ste

r

5

3

8

1

-1 1

1 2

0

-2

–3

3 4 5 6


a

b

c

d

I

The MRS from bundle a to bundle b is -3. This is the same as the

slope of the indifference curve between those two points.

From b to c, MRS = -2.

This is the same as the slope of the indifference curve between those two points.

4-18

Concave indifference curve

B , B

ur r

itos p

er

sem

este

r

5

7

1

1

2

0

– 2

– 3

3 4 5 6


a

b

c

I

4-18

Concave indifference curve

From bundle a to bundle b, Lisa is willing to give up 2 Pizzas for 1 Burrito. Nevertheless, from

b to c she is willing to give up 3 Pizzas for 1 burrito.

This is very unlikely Could you think

why?

B , B

ur r

itos p

er

sem

este

r

5

7

1

1

2

0

– 2

– 3

3 4 5 6


a

b

c

I

4-19

Curvature of Indifference Curves

In general we can have both convex or

concave indifference curves.

But casual observation suggests that most

people’s indifference curves are convex.

This implies a diminishing marginal rate of

substitution (also knows as law of diminishing

marginal utility).

The marginal rate of substitution approaches zero

as we move down and to the right along an

indifference curve.

4-20

Law of diminishing marginal utility

The increase in utility from one additional unit

of a good is lower the larger is the total

available amount of that good.

Examples:

Food: the first forkful of pasta al pesto is heaven, the 10th

is very good, the 50th is ok, the 300th I’m getting sick.

Chocolate?

Counter-examples:

Antibiotics

Pringles?

Sunbathing

4-21

Two extreme cases

Perfect substitutes - goods that a

consumer is completely indifferent as to

which to consume.

Perfect complements - goods that a

consumer is interested in consuming only

in fixed proportions

4-22

Perfect Substitutes

Co

k e

, C

ans p

er w

ee

k

P epsi, Cans per w eek

0

4-22

Perfect Substitutes

Bill views Coke and Pepsi as perfect substitutes: can you tell how his indifference curves would look like?

Co

k e

, C

ans p

er w

ee

k


0

4-22

Perfect Substitutes

Bill views Coke and Pepsi as perfect substitutes: can you tell how his indifference curves would look like? Straight, parallel lines

with an MRS (slope) of −1.

Bill is willing to exchange one can of Coke for one can of Pepsi.

Co

k e

, C

ans p

er w

ee

k


0

4-22

Perfect Substitutes




Co

k e

, C

ans p

er w

ee

k

1


1

0

I 1

4-22

Perfect Substitutes




Co

k e

, C

ans p

er w

ee

k

1 2


1

0

2

I 1 I 2

4-22

Perfect Substitutes




Co

k e

, C

ans p

er w

ee

k

1 2 3 4


1

0

2

3

4

I 1 I 2 I 3 I 4

4-23

Perfect Complements Ic

e c

ream

, S

coops p

er w

ee

k

Pi e , Slices per w eek

0

4-23


e c

ream

, S

coops p

er w

ee

k


0

If she has only one

piece of pie, she

gets as much

pleasure from it

and one scoop of

ice cream, a,

4-23


e c

ream

, S

coops p

er w

ee

k

1


1

0

a

If she has only one

piece of pie, she

gets as much

pleasure from it

and one scoop of

ice cream, a,

4-23


e c

ream

, S

coops p

er w

ee

k

1


1

2

0

a

d

If she has only one

piece of pie, she

gets as much

pleasure from it

and one scoop of

ice cream, a,

as from it and two

scoops, d,

4-23


e c

ream

, S

coops p

er w

ee

k

1


1

2

3

0

a

d

e

If she has only one

piece of pie, she

gets as much

pleasure from it

and one scoop of

ice cream, a,

as from it and two

scoops, d,

or as from it and

three scoops, e.

4-23


e c

ream

, S

coops p

er w

ee

k

1


1

2

3

0

I 1 a

d

e

If she has only one

piece of pie, she

gets as much

pleasure from it

and one scoop of

ice cream, a,

as from it and two

scoops, d,

or as from it and

three scoops, e.

4-23


e c

ream

, S

coops p

er w

ee

k

1 2


1

2

3

0

I 1

I 2

a

d

e

b

If she has only one

piece of pie, she

gets as much

pleasure from it

and one scoop of

ice cream, a,

as from it and two

scoops, d,

or as from it and

three scoops, e.

4-23


e c

ream

, S

coops p

er w

ee

k

1 2 3


1

2

3

0

I 1

I 2

I 3

a

d

e c

b

If she has only one

piece of pie, she

gets as much

pleasure from it

and one scoop of

ice cream, a,

as from it and two

scoops, d,

or as from it and

three scoops, e.

4-24

Imperfect Substitutes

B , B

ur r

itos p

er

se

meste

r


I

4-24


The standard-shaped, convex indifference curve lies between these two extreme examples.

B , B

ur r

itos p

er

se

meste

r


I

4-24


The standard-shaped, convex indifference curve lies between these two extreme examples. Convex indifference

curves show that a consumer views two goods as imperfect substitutes.

B , B

ur r

itos p

er

se

meste

r


I

4-25

Application: Indifference Curves

Between Food and Clothing

4-26

Utility

Ordinal utility function: from the completeness

axiom we know that we can rank all possible

bundles of goods. We have an ordinal

measure of preferences. Only relative

comparisons can be made.

Cardinal utility function: we assign a numerical

value to each bundle. Absolute comparisons

can be made.

4-27

Utility

Utility - a set of numerical values that

reflect the relative rankings of various

bundles of goods.

utility function - the relationship

between utility values and every

possible bundle of goods.

U(B, Z)

4-28

Utility Function: Example

Question: Can determine whether Lisa would be

happier if she had Bundle x with 9 burritos and 16

pizzas or Bundle y with 13 of each?

Answer: The utility she gets from x is 12utils. The

utility she gets from y is 13utils. Therefore, she

prefers y to x.U= BZ.

BZu

4-29

Utility Function: 3D plot

4-30

Utility Function: 3D plot

4-31

Marginal utility

marginal utility - the extra utility that a

consumer gets from consuming the last unit of

a good.

the slope of the utility function as we hold the

quantity of the other good constant.

Marginal Utility of good Z is:

Z

UMUZ

4-32

Utility and

Marginal Utility

U ,

Utils

Utility function, U (10, Z )

10 9 8 7 6 5 4 3 2 1


0

350

(a) Utility

230

4-32

Utility and

Marginal Utility

U ,

Utils


10 9 8 7 6 5 4 3 2 1


0

350

250

(a) Utility

230

4-32

Utility and

Marginal Utility

As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases…

U ,

Utils


10 9 8 7 6 5 4 3 2 1


0

350

250

(a) Utility

230

4-32

Utility and

Marginal Utility


U ,

Utils

U = 20


Z = 1

10 9 8 7 6 5 4 3 2 1


0

350

250

(a) Utility

230

4-32

Utility and

Marginal Utility


U ,

Utils

U = 20


Z = 1

10 9 8 7 6 5 4 3 2 1


0

350

250

(a) Utility

230

Z

UMUZ

4-32

Utility and

Marginal Utility


and her marginal utility of pizza, MUZ, decreases (though it remains positive).

U ,

Utils

U = 20


Z = 1

10 9 8 7 6 5 4 3 2 1


0

350

250

(a) Utility

230

Z

UMUZ

4-32

Utility and

Marginal Utility



U ,

Utils

U = 20


Z = 1

10 9 8 7 6 5 4 3 2 1


0

350

250

(a) Utility

230

Z

UMUZ

4-32

Utility and

Marginal Utility



MU

Z , M

arg

inal u

tilit

y o

f p

izza

MU Z

10 9 8 7 6 5 4 3 2 1


0

130

(b) Marginal Utility

U ,

Utils

U = 20


Z = 1

10 9 8 7 6 5 4 3 2 1


0

350

250

(a) Utility

230

Z

UMUZ

4-32

Utility and

Marginal Utility



MU

Z , M

arg

inal u

tilit

y o

f p

izza

MU Z

10 9 8 7 6 5 4 3 2 1


0

130


20

U ,

Utils

U = 20


Z = 1

10 9 8 7 6 5 4 3 2 1


0

350

250

(a) Utility

230

Z

UMUZ

4-32

Utility and

Marginal Utility



Marginal utility is the slope of the utility function as we hold the quantity of the other good constant.

MU

Z , M

arg

inal u

tilit

y o

f p

izza

MU Z

10 9 8 7 6 5 4 3 2 1


0

130


20

U ,

Utils

U = 20


Z = 1

10 9 8 7 6 5 4 3 2 1


0

350

250

(a) Utility

230

Z

UMUZ

4-32

Utility and

Marginal Utility



Marginal utility is the slope of the utility function as we hold the quantity of the other good constant.

MU

Z , M

arg

inal u

tilit

y o

f p

izza

MU Z

10 9 8 7 6 5 4 3 2 1


0

130


20

U ,

Utils

U = 20


Z = 1

10 9 8 7 6 5 4 3 2 1


0

350

250

(a) Utility

230

Z

UMUZ

4-33

Utility and Marginal Rates of

Substitution

4-33


Substitution

The MRS is the negative of the ratio of the

marginal utility of another pizza to the

marginal utility of another burrito.

4-33


Substitution

The MRS is the negative of the ratio of the

marginal utility of another pizza to the

marginal utility of another burrito.

Formally,

B

Z

MU

MU

Z

BMRS

4-34

Budget Constraint

4-34

Budget Constraint

budget line (or budget constraint) - the

bundles of goods that can be bought if

the entire budget is spent on those

goods at given prices.

4-34

Budget Constraint

budget line (or budget constraint) - the

bundles of goods that can be bought if

the entire budget is spent on those

goods at given prices.

opportunity set - all the bundles a

consumer can buy, including all the

bundles inside the budget constraint and

on the budget constraint

4-35

Budget Constraint

4-35

Budget Constraint

If Lisa spends all her budget, Y, on pizza and

burritos, then

4-35

Budget Constraint


burritos, then

pBB + pZZ = Y

where pBB is the amount she spends on burritos

and pZZ is the amount she spends on pizzas.

4-35

Budget Constraint


burritos, then

pBB + pZZ = Y

where pBB is the amount she spends on burritos

and pZZ is the amount she spends on pizzas.

This equation is her budget constraint.

It shows that her expenditures on burritos and pizza use

up her entire budget.

4-36

Budget Constraint (cont).

4-36


How many burritos can Lisa buy?

To answer solve budget constraint for B (quantity of

burritos):

4-36


How many burritos can Lisa buy?

To answer solve budget constraint for B (quantity of

burritos):

B

Z

ZB

ZB

P

ZPYB

ZPYBP

YZPBP

4-37


From previous slide we have:

If pZ = $1, pB = $2, and Y = $50, then:

B

Z

P

ZPYB

4-37


From previous slide we have:

If pZ = $1, pB = $2, and Y = $50, then:

B

Z

P

ZPYB

$50 ($1 )25 0.5

$2

ZB Z

4-38

Budget Constraint

From previous slide we have

that if:

– pZ = $1, pB = $2, and Y = $50,

then the budget constraint,

L1, is:

$50 ($1 )25 0.5

$2

ZB Z

B , B

ur r

ito

s p

er

se

me

ste

r

0


4-38

Budget Constraint


that if:

– pZ = $1, pB = $2, and Y = $50,


L1, is:

$50 ($1 )25 0.5

$2

ZB Z

B , B

ur r

ito

s p

er

se

me

ste

r

L 1

0


4-38

Budget Constraint


that if:

– pZ = $1, pB = $2, and Y = $50,


L1, is:

$50 ($1 )25 0.5

$2

ZB Z

B , B

ur r

ito

s p

er

se

me

ste

r

L 1

25 = Y / p B

0


a

4-38

Budget Constraint


that if:

– pZ = $1, pB = $2, and Y = $50,


L1, is:

$50 ($1 )25 0.5

$2

ZB Z

B , B

ur r

ito

s p

er

se

me

ste

r

L 1

25 = Y / p B

0


a

Amount of Burritos

consumed if all income

is allocated for

Burritos.

4-38

Budget Constraint


that if:

– pZ = $1, pB = $2, and Y = $50,


L1, is:

$50 ($1 )25 0.5

$2

ZB Z

B , B

ur r

ito

s p

er

se

me

ste

r

50 = Y / p Z

L 1

25 = Y / p B

0


a

d

Amount of Burritos


is allocated for

Burritos.

4-38

Budget Constraint


that if:

– pZ = $1, pB = $2, and Y = $50,


L1, is:

$50 ($1 )25 0.5

$2

ZB Z

B , B

ur r

ito

s p

er

se

me

ste

r

50 = Y / p Z

L 1

25 = Y / p B

0


a

d

Amount of Burritos


is allocated for

Burritos.

Amount of Pizza


is allocated for Pizza.

4-38

Budget Constraint


that if:

– pZ = $1, pB = $2, and Y = $50,


L1, is:

$50 ($1 )25 0.5

$2

ZB Z

B , B

ur r

ito

s p

er

se

me

ste

r

50 = Y / p Z

L 1

25 = Y / p B

20

10 0


a

b

d

Amount of Burritos


is allocated for

Burritos.

Amount of Pizza



4-38

Budget Constraint


that if:

– pZ = $1, pB = $2, and Y = $50,


L1, is:

$50 ($1 )25 0.5

$2

ZB Z

B , B

ur r

ito

s p

er

se

me

ste

r

50 = Y / p Z

L 1

25 = Y / p B

20

10

10 0 30


a

b

c

d

Amount of Burritos


is allocated for

Burritos.

Amount of Pizza



4-38

Budget Constraint


that if:

– pZ = $1, pB = $2, and Y = $50,


L1, is:

$50 ($1 )25 0.5

$2

ZB Z

B , B

ur r

ito

s p

er

se

me

ste

r

Opportunity set

50 = Y / p Z

L 1

25 = Y / p B

20

10

10 0 30


a

b

c

d

Amount of Burritos


is allocated for

Burritos.

Amount of Pizza



4-39

The Slope of the Budget Constraint

We have seen that the budget constraint for Lisa is

given by the following equation:

ZP

P

P

YB

B

Z

B

4-39




ZP

P

P

YB

B

Z

B

Slope = B/Z = MRT

4-39




The slope of the budget line is also called the marginal rate of

transformation (MRT)

rate at which Lisa can trade burritos for pizza in the marketplace

ZP

P

P

YB

B

Z

B

Slope = B/Z = MRT

4-40

Allocations of a $50 Budget Between

Burritos and Pizza

4-41

Changes in the Budget Constraint: An

increase in the Price of Pizzas. B

, B

ur r

ito

s p

er

se

me

ste

r

50

L 1 ( p Z = $1)

25

0


B = Y PB

- PZ = $1

PB

Z Slope = -$1/$2 = -0.5

4-41



, B

ur r

ito

s p

er

se

me

ste

r

50

L 1 ( p Z = $1)

25

0


B = Y PB

- PZ = $1

PB

Z

If the price of Pizza

doubles, (increases

from $1 to $2) the

slope of the budget

line increases

$2 Slope = -$1/$2 = -0.5

4-41



, B

ur r

ito

s p

er

se

me

ste

r

50

L 1 ( p Z = $1)

L2 (pZ = $2)

25

25 0


B = Y PB

- PZ = $1

PB

Z


doubles, (increases

from $1 to $2) the

slope of the budget

line increases

$2 Slope = -$1/$2 = -0.5

4-41



, B

ur r

ito

s p

er

se

me

ste

r

50

L 1 ( p Z = $1)

L2 (pZ = $2)

25

25 0


B = Y PB

- PZ = $1

PB

Z


doubles, (increases

from $1 to $2) the

slope of the budget

line increases

$2 Slope = -$1/$2 = -0.5

Slope = -$2/$2 = -1

4-41



, B

ur r

ito

s p

er

se

me

ste

r

Loss

50

L 1 ( p Z = $1)

L2 (pZ = $2)

25

25 0


B = Y PB

- PZ = $1

PB

Z


doubles, (increases

from $1 to $2) the

slope of the budget

line increases

$2 Slope = -$1/$2 = -0.5

Slope = -$2/$2 = -1

4-41



, B

ur r

ito

s p

er

se

me

ste

r

Loss

50

L 1 ( p Z = $1)

L2 (pZ = $2)

25

25 0


B = Y PB

- PZ = $1

PB

Z


doubles, (increases

from $1 to $2) the

slope of the budget

line increases

This area represents

the bundles she can

no longer afford!!!

$2 Slope = -$1/$2 = -0.5

Slope = -$2/$2 = -1

4-42

Changes in the Budget Constraint:

Increase in Income (Y)

L 1 ( Y = $50)

0

B = $50 PB

- PZ

PB

Z

50


B, B

urr

ito

s p

er

se

me

ste

r

25

4-42



L 1 ( Y = $50)

0

B = $50 PB

- PZ

PB

Z

If Lisa’s income

increases by $50 the

budget line shifts to

the right (with the

same slope!)

50


B, B

urr

ito

s p

er

se

me

ste

r

25

4-42



L 1 ( Y = $50)

0

B = $50 PB

- PZ

PB

Z

If Lisa’s income



the right (with the

same slope!)

$100

50


B, B

urr

ito

s p

er

se

me

ste

r

25

4-42



L 3 ( Y = $100)

L 1 ( Y = $50)

0

B = $50 PB

- PZ

PB

Z

If Lisa’s income



the right (with the

same slope!)

$100

100 50


B, B

urr

ito

s p

er

se

me

ste

r

50

25

4-42



Gain

L 3 ( Y = $100)

L 1 ( Y = $50)

0

B = $50 PB

- PZ

PB

Z

If Lisa’s income



the right (with the

same slope!)

$100

100 50


B, B

urr

ito

s p

er

se

me

ste

r

50

25

4-42



Gain

L 3 ( Y = $100)

L 1 ( Y = $50)

0

B = $50 PB

- PZ

PB

Z

If Lisa’s income



the right (with the

same slope!)

$100

This area represents

the new consumption

bundles she can now

afford!!!

100 50


B, B

urr

ito

s p

er

se

me

ste

r

50

25

Constrained optimization

Now we combine together the two tools we

introduced: indifference curve and budget

constraint (preferences and scarce

resources).

So, the consumer faces a constrained

maximization problem (maximize utility

subject to available income).

We will find the solution of the consumer’s

problem graphically, and show that the

solution can be of two types.

4-43

4-44

Consumer Maximization: Interior

Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I 3

4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I 3

4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I 3

4-44


Solution

Would Lisa be able to

consume any bundle

along I3 (i.e. bundle f)?

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I 3

f

4-44


Solution


consume any bundle


No! Lisa does not have

enough income to afford

any bundle along I3

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I 3

f

4-44


Solution


consume any bundle


No! Lisa does not have

enough income to afford

any bundle along I3

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I1

I 3

f

4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I1

I 3

f

Would Lisa be able to consume any bundle along I1?

4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I1

I 3

d

f c

a

Would Lisa be able to consume any bundle along I1?

4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I1

I 3

d

f c

a

Would Lisa be able to consume any bundle along I1? Yes; she could afford bundles

d, c, and a.

4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I1

I 3

d

f c

a


d, c, and a.

Nevertheless, there are other affordable bundles that should be preferred and affordable.

4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I1

I 3

d

f c

e

a


d, c, and a.

Nevertheless, there are other affordable bundles that should be preferred and affordable.

4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I1

I 3

d

f c

e

a


d, c, and a.

Nevertheless, there are other affordable bundles that should be preferred and affordable. For instance bundle e

4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I1

I 3

d

f c

e

a

B


d, c, and a.


4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I1

I 3

d

f c

e

a A

B


d, c, and a.


4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I1

I2

I 3

d

f c

e

a A

B


d, c, and a.


4-44


Solution

B , B

ur r

ito

s p

er

se

me

ste

r

10

20

25

50 30 10 0


I1

I2

I 3

d

f c

e

a A

B

Bundle e is called a consumer’s optimum.

If Lisa is consuming this

bundle, she has no

incentive to change her

behavior by substituting

one good for another.

4-45


Solution B

, B

ur r

ito

s p

er

se

me

ste

r

25

50 0


I2

e

4-45

The budget constraint and the indifference curve

have the same slope at the point e where they

touch.

Therefore, at point e:


Solution B

, B

ur r

ito

s p

er

se

me

ste

r

25

50 0


I2

e

4-45



touch.



Solution B

, B

ur r

ito

s p

er

se

me

ste

r

25

50 0


I2

e

MRTP

P

MU

MUMRS

B

Z

B

Z

4-45



touch.


Slope of I2


Solution B

, B

ur r

ito

s p

er

se

me

ste

r

25

50 0


I2

e

MRTP

P

MU

MUMRS

B

Z

B

Z

4-45



touch.


Slope of I2


Solution B

, B

ur r

ito

s p

er

se

me

ste

r

25

50 0


I2

e

MRTP

P

MU

MUMRS

B

Z

B

Z

Slope of BL

4-46

Consumer Maximization: Corner

Solution B

, B

ur r

ito

s p

er

se

me

ste

r

Budget line

25

50


I 1

I 2

I 3

e

4-47

Optimal Bundles on Convex Sections

of Indifference Curves

4-48

Solved Problem 4.4

Alexx doesn’t care about where he lives, but he does care about what he eats. Alexx spends all his money on restaurant meals at either American or French restaurants. His firm offers to transfer him from its Miami office to its Paris office, where he will face different prices. The firm will pay him a salary in euros such that he can buy the same bundle of goods in Paris that he is currently buying in Miami.11 Will Alexx benefit by moving to Paris?

4-49

Solved Problem 4.4

4-50

Behavioral Economics

Recent field of economics that takes insights

from psychology and empirical research on

human cognition and emotional biases and

study their effect on individual choice, and

how it deviates from the rational model of

behaviour.

Examples: transitivity failure, endowment

effect, bounded rationality, rules of thumb.

Documents

Lecture 3