lecture 3
DESCRIPTION
lec 3TRANSCRIPT
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
Properties of Consumer Preferences
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
Properties of Consumer Preferences
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
Properties of Consumer Preferences
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
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
d
e
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
d
e
Which of these
two bundles
would be
preferred by
Lisa?
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
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
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
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
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
d
e
f
B
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
d
e
f
B
Which of these
two bundles
would be
preferred by
Lisa?
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
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
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
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
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
d
e
f
A
B
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
d a
e
c
f
A
B
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
d a
e
c
f
A
B
If Lisa is indifferent
between bundles e, a,
and c …..
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
d a
e
c
f
A
B
B ,
Bur r
ito
s p
er
se
me
ste
r
(b)
30 25 15
Z , Pizzas per semester
25
20
15
10
a
e
c
If Lisa is indifferent
between bundles e, a,
and c …..
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
d a
e
c
f
A
B
B ,
Bur r
ito
s p
er
se
me
ste
r
(b)
30 25 15
Z , Pizzas per semester
25
20
15
10
a
I 1
e
c
If Lisa is indifferent
between bundles e, a,
and c …..
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
d a
e
c
f
A
B
B ,
Bur r
ito
s p
er
se
me
ste
r
(b)
30 25 15
Z , Pizzas per semester
25
20
15
10
a
I 1
e
c
If Lisa is indifferent
between bundles e, a,
and c …..
we can draw an
indifferent curve over
those three points
4-10
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
d a
e
c
f
A
B
B ,
Bur r
ito
s p
er
se
me
ste
r
(c)
30 25 15
Z , Pizzas per semester
25
20
15
10
a
I 1
e
c
f
we can draw an
indifferent curve over
those three points
4-10
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
d a
e
c
f
A
B
B ,
Bur r
ito
s p
er
se
me
ste
r
(c)
30 25 15
Z , Pizzas per semester
25
20
15
10
a
I 1
e
c
f
we can draw an
indifferent curve over
those three points
I2
4-10
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
d a
e
c
f
A
B
B ,
Bur r
ito
s p
er
se
me
ste
r
(c)
30 25 15
Z , Pizzas per semester
25
20
15
10 d
a
I 1
e
c
f
we can draw an
indifferent curve over
those three points
I2
4-10
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
d a
e
c
f
A
B
B ,
Bur r
ito
s p
er
se
me
ste
r
(c)
30 25 15
Z , Pizzas per semester
25
20
15
10 d
a
I 1
e
c
f
we can draw an
indifferent curve over
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
Z , Pizzas per semester
I 1
I 0
a
b
e
4-12
Impossible Indifference Curves
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
Z , Pizzas per semester
I 1
I 0
a
b
e
4-12
Impossible Indifference Curves
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
Z , Pizzas per semester
I 1
I 0
a
b
e
4-12
Impossible Indifference Curves
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…
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
Z , Pizzas per semester
I 1
I 0
a
b
e
4-12
Impossible Indifference Curves
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…
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
Z , Pizzas per semester
I 1
I 0
a
b
e
4-12
Impossible Indifference Curves
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…
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
Z , Pizzas per semester
I 1
I 0
a
b
e
4-13
Impossible Indifference Curves
B ,
Bu
r r ito
s p
er
se
me
ste
r
Z , Pizzas per semester
I
a
b
4-13
Impossible Indifference Curves
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
Z , Pizzas per semester
I
a
b
4-13
Impossible Indifference Curves
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
Z , Pizzas per semester
I
a
b
4-13
Impossible Indifference Curves
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
Z , Pizzas per semester
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
Z , Pizzas per semester
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
Z , Pizzas per semester
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
Z , Pizzas per semester
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
Z , Pizzas per semester
a
I
4-17
Convex indifference curve B
, B
ur r
ito
s p
er
se
me
ste
r
3
8
2
0 3 5 6
Z , Pizzas per semester
a
I
4-17
Convex indifference curve B
, B
ur r
ito
s p
er
se
me
ste
r
3
8
2
0 3 5 6
Z , Pizzas per semester
a
b
I
4-17
Convex indifference curve B
, B
ur r
ito
s p
er
se
me
ste
r
5
3
8
2
0 3 4 5 6
Z , Pizzas per semester
a
b
I
4-17
Convex indifference curve B
, B
ur r
ito
s p
er
se
me
ste
r
5
3
8
2
0 3 4 5 6
Z , Pizzas per semester
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…
Convex indifference curve B
, B
ur r
ito
s p
er
se
me
ste
r
5
3
8
1
2
0
–3
3 4 5 6
Z , Pizzas per semester
a
b
I
4-17
Convex indifference curve B
, B
ur r
ito
s p
er
se
me
ste
r
5
3
8
1
2
0
–3
3 4 5 6
Z , Pizzas per semester
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…
Convex indifference curve B
, B
ur r
ito
s p
er
se
me
ste
r
5
3
8
1
1
2
0
-2
–3
3 4 5 6
Z , Pizzas per semester
a
b
c
I
4-17
Convex indifference curve B
, B
ur r
ito
s p
er
se
me
ste
r
5
3
8
1
1
2
0
-2
–3
3 4 5 6
Z , Pizzas per semester
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…
Convex indifference curve B
, 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
Z , Pizzas per semester
a
b
c
d
I
4-17
Convex indifference curve B
, 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
Z , Pizzas per semester
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
Convex indifference curve B
, 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
Z , Pizzas per semester
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
Z , Pizzas per semester
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
Z , Pizzas per semester
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
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? 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
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? 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
1
P epsi, Cans per w eek
1
0
I 1
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
1 2
P epsi, Cans per w eek
1
0
2
I 1 I 2
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
1 2 3 4
P epsi, Cans per w eek
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
Perfect Complements Ic
e c
ream
, S
coops p
er w
ee
k
Pi e , Slices per w eek
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
Perfect Complements Ic
e c
ream
, S
coops p
er w
ee
k
1
Pi e , Slices per w eek
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
Perfect Complements Ic
e c
ream
, S
coops p
er w
ee
k
1
Pi e , Slices per w eek
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
Perfect Complements Ic
e c
ream
, S
coops p
er w
ee
k
1
Pi e , Slices per w eek
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
Perfect Complements Ic
e c
ream
, S
coops p
er w
ee
k
1
Pi e , Slices per w eek
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
Perfect Complements Ic
e c
ream
, S
coops p
er w
ee
k
1 2
Pi e , Slices per w eek
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
Perfect Complements Ic
e c
ream
, S
coops p
er w
ee
k
1 2 3
Pi e , Slices per w eek
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
Z , Pizzas per semester
I
4-24
Imperfect Substitutes
The standard-shaped, convex indifference curve lies between these two extreme examples.
B , B
ur r
itos p
er
se
meste
r
Z , Pizzas per semester
I
4-24
Imperfect Substitutes
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
Z , Pizzas per semester
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
Z , Pizzas per semester
0
350
(a) Utility
230
4-32
Utility and
Marginal Utility
U ,
Utils
Utility function, U (10, Z )
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
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
Utility function, U (10, Z )
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
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
U = 20
Utility function, U (10, Z )
Z = 1
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
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
U = 20
Utility function, U (10, Z )
Z = 1
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
0
350
250
(a) Utility
230
Z
UMUZ
4-32
Utility and
Marginal Utility
As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases…
and her marginal utility of pizza, MUZ, decreases (though it remains positive).
U ,
Utils
U = 20
Utility function, U (10, Z )
Z = 1
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
0
350
250
(a) Utility
230
Z
UMUZ
4-32
Utility and
Marginal Utility
As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases…
and her marginal utility of pizza, MUZ, decreases (though it remains positive).
U ,
Utils
U = 20
Utility function, U (10, Z )
Z = 1
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
0
350
250
(a) Utility
230
Z
UMUZ
4-32
Utility and
Marginal Utility
As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases…
and her marginal utility of pizza, MUZ, decreases (though it remains positive).
MU
Z , M
arg
inal u
tilit
y o
f p
izza
MU Z
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
0
130
(b) Marginal Utility
U ,
Utils
U = 20
Utility function, U (10, Z )
Z = 1
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
0
350
250
(a) Utility
230
Z
UMUZ
4-32
Utility and
Marginal Utility
As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases…
and her marginal utility of pizza, MUZ, decreases (though it remains positive).
MU
Z , M
arg
inal u
tilit
y o
f p
izza
MU Z
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
0
130
(b) Marginal Utility
20
U ,
Utils
U = 20
Utility function, U (10, Z )
Z = 1
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
0
350
250
(a) Utility
230
Z
UMUZ
4-32
Utility and
Marginal Utility
As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases…
and her marginal utility of pizza, MUZ, decreases (though it remains positive).
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
Z , Pizzas per semester
0
130
(b) Marginal Utility
20
U ,
Utils
U = 20
Utility function, U (10, Z )
Z = 1
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
0
350
250
(a) Utility
230
Z
UMUZ
4-32
Utility and
Marginal Utility
As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases…
and her marginal utility of pizza, MUZ, decreases (though it remains positive).
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
Z , Pizzas per semester
0
130
(b) Marginal Utility
20
U ,
Utils
U = 20
Utility function, U (10, Z )
Z = 1
10 9 8 7 6 5 4 3 2 1
Z , Pizzas per semester
0
350
250
(a) Utility
230
Z
UMUZ
4-33
Utility and Marginal Rates of
Substitution
4-33
Utility and Marginal Rates of
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
Utility and Marginal Rates of
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
If Lisa spends all her budget, Y, on pizza and
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
If Lisa spends all her budget, Y, on pizza and
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
Budget Constraint (cont).
How many burritos can Lisa buy?
To answer solve budget constraint for B (quantity of
burritos):
4-36
Budget Constraint (cont).
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
Budget Constraint (cont).
From previous slide we have:
If pZ = $1, pB = $2, and Y = $50, then:
B
Z
P
ZPYB
4-37
Budget Constraint (cont).
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
Z , Pizzas per semester
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
L 1
0
Z , Pizzas per semester
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
L 1
25 = Y / p B
0
Z , Pizzas per semester
a
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
L 1
25 = Y / p B
0
Z , Pizzas per semester
a
Amount of Burritos
consumed if all income
is allocated for
Burritos.
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
50 = Y / p Z
L 1
25 = Y / p B
0
Z , Pizzas per semester
a
d
Amount of Burritos
consumed if all income
is allocated for
Burritos.
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
50 = Y / p Z
L 1
25 = Y / p B
0
Z , Pizzas per semester
a
d
Amount of Burritos
consumed if all income
is allocated for
Burritos.
Amount of Pizza
consumed if all income
is allocated for Pizza.
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
50 = Y / p Z
L 1
25 = Y / p B
20
10 0
Z , Pizzas per semester
a
b
d
Amount of Burritos
consumed if all income
is allocated for
Burritos.
Amount of Pizza
consumed if all income
is allocated for Pizza.
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
50 = Y / p Z
L 1
25 = Y / p B
20
10
10 0 30
Z , Pizzas per semester
a
b
c
d
Amount of Burritos
consumed if all income
is allocated for
Burritos.
Amount of Pizza
consumed if all income
is allocated for Pizza.
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
Opportunity set
50 = Y / p Z
L 1
25 = Y / p B
20
10
10 0 30
Z , Pizzas per semester
a
b
c
d
Amount of Burritos
consumed if all income
is allocated for
Burritos.
Amount of Pizza
consumed if all income
is allocated for 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
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
Slope = B/Z = MRT
4-39
The Slope of the Budget Constraint
We have seen that the budget constraint for Lisa is
given by the following equation:
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
Z , Pizzas per semester
B = Y PB
- PZ = $1
PB
Z Slope = -$1/$2 = -0.5
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
Z , Pizzas per semester
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
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)
L2 (pZ = $2)
25
25 0
Z , Pizzas per semester
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
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)
L2 (pZ = $2)
25
25 0
Z , Pizzas per semester
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
Slope = -$2/$2 = -1
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
Loss
50
L 1 ( p Z = $1)
L2 (pZ = $2)
25
25 0
Z , Pizzas per semester
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
Slope = -$2/$2 = -1
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
Loss
50
L 1 ( p Z = $1)
L2 (pZ = $2)
25
25 0
Z , Pizzas per semester
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
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
Z , Pizzas per semester
B, B
urr
ito
s p
er
se
me
ste
r
25
4-42
Changes in the Budget Constraint:
Increase in Income (Y)
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
Z , Pizzas per semester
B, B
urr
ito
s p
er
se
me
ste
r
25
4-42
Changes in the Budget Constraint:
Increase in Income (Y)
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!)
$100
50
Z , Pizzas per semester
B, B
urr
ito
s p
er
se
me
ste
r
25
4-42
Changes in the Budget Constraint:
Increase in Income (Y)
L 3 ( Y = $100)
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!)
$100
100 50
Z , Pizzas per semester
B, B
urr
ito
s p
er
se
me
ste
r
50
25
4-42
Changes in the Budget Constraint:
Increase in Income (Y)
Gain
L 3 ( Y = $100)
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!)
$100
100 50
Z , Pizzas per semester
B, B
urr
ito
s p
er
se
me
ste
r
50
25
4-42
Changes in the Budget Constraint:
Increase in Income (Y)
Gain
L 3 ( Y = $100)
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!)
$100
This area represents
the new consumption
bundles she can now
afford!!!
100 50
Z , Pizzas per semester
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
Z , Pizzas per semester
I 3
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
Z , Pizzas per semester
I 3
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
Z , Pizzas per semester
I 3
4-44
Consumer Maximization: Interior
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
Z , Pizzas per semester
I 3
f
4-44
Consumer Maximization: Interior
Solution
Would Lisa be able to
consume any bundle
along I3 (i.e. bundle f)?
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
Z , Pizzas per semester
I 3
f
4-44
Consumer Maximization: Interior
Solution
Would Lisa be able to
consume any bundle
along I3 (i.e. bundle f)?
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
Z , Pizzas per semester
I1
I 3
f
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
Z , Pizzas per semester
I1
I 3
f
Would Lisa be able to consume any bundle along I1?
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
Z , Pizzas per semester
I1
I 3
d
f c
a
Would Lisa be able to consume any bundle along I1?
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
Z , Pizzas per semester
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
Consumer Maximization: Interior
Solution
B , B
ur r
ito
s p
er
se
me
ste
r
10
20
25
50 30 10 0
Z , Pizzas per semester
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.
Nevertheless, there are other affordable bundles that should be preferred and affordable.
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
Z , Pizzas per semester
I1
I 3
d
f c
e
a
Would Lisa be able to consume any bundle along I1? Yes; she could afford bundles
d, c, and a.
Nevertheless, there are other affordable bundles that should be preferred and affordable.
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
Z , Pizzas per semester
I1
I 3
d
f c
e
a
Would Lisa be able to consume any bundle along I1? Yes; she could afford bundles
d, c, and a.
Nevertheless, there are other affordable bundles that should be preferred and affordable. For instance bundle e
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
Z , Pizzas per semester
I1
I 3
d
f c
e
a
B
Would Lisa be able to consume any bundle along I1? Yes; she could afford bundles
d, c, and a.
Nevertheless, there are other affordable bundles that should be preferred and affordable. For instance bundle e
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
Z , Pizzas per semester
I1
I 3
d
f c
e
a A
B
Would Lisa be able to consume any bundle along I1? Yes; she could afford bundles
d, c, and a.
Nevertheless, there are other affordable bundles that should be preferred and affordable. For instance bundle e
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
Z , Pizzas per semester
I1
I2
I 3
d
f c
e
a A
B
Would Lisa be able to consume any bundle along I1? Yes; she could afford bundles
d, c, and a.
Nevertheless, there are other affordable bundles that should be preferred and affordable. For instance bundle e
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
Z , Pizzas per semester
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
Consumer Maximization: Interior
Solution B
, B
ur r
ito
s p
er
se
me
ste
r
25
50 0
Z , Pizzas per semester
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:
Consumer Maximization: Interior
Solution B
, B
ur r
ito
s p
er
se
me
ste
r
25
50 0
Z , Pizzas per semester
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:
Consumer Maximization: Interior
Solution B
, B
ur r
ito
s p
er
se
me
ste
r
25
50 0
Z , Pizzas per semester
I2
e
MRTP
P
MU
MUMRS
B
Z
B
Z
4-45
The budget constraint and the indifference curve
have the same slope at the point e where they
touch.
Therefore, at point e:
Slope of I2
Consumer Maximization: Interior
Solution B
, B
ur r
ito
s p
er
se
me
ste
r
25
50 0
Z , Pizzas per semester
I2
e
MRTP
P
MU
MUMRS
B
Z
B
Z
4-45
The budget constraint and the indifference curve
have the same slope at the point e where they
touch.
Therefore, at point e:
Slope of I2
Consumer Maximization: Interior
Solution B
, B
ur r
ito
s p
er
se
me
ste
r
25
50 0
Z , Pizzas per semester
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
Z , Pizzas per semester
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.