SI 425: Introduction to User Modeling
Lecture B1: Consumer Choice
Tanya Rosenblat
University of Michigan
Introduction
Consumers face tradeoffs:
I
Buying more of one good leaves less income for other goods
⇒ budget constraint.
I
Working more hours means more income and more
consumption, but less leisure time.
I
Reducing saving allows more consumption today but reduces
future consumption.
Consumer theory provides a framework to explore how consumers
make choices like these
Quality 16 tickets and iTunes rentals
Example: Alice divides her semester movie entertainment budget of
$150 between Quality 16 tickets (where she watches new releases
with random friends on a large screen) and iTunes rentals (where
she watches older releases with her room mates on her laptop).
I
A consumption bundle is a particular combination of the
goods, e.g., 30 tickets and 20 rentals.
I
Budget constraint: the limit on the consumption bundles that
a consumer can afford
Budget Constraint
Alice’s income: $150
Prices: $6.25 per ticket, $5 per rental
A. If Alice spends all her income on rentals, how many rentals
does she buy?
B. If Alice spends all her income on tickets, how many tickets
does she buy?
B. If Alice buys 10 rentals, how many tickets can she buy?
Budget Constraint
A. $150/$5 = 30
tickets
B. $150/$6.25 =
24 tickets
B. 10 rentals cost
$50, $100 left
buys 16 tickets
Quality 16
C
24
20
B
16
12
8
4
0
0
5
10
15
20
25
A
30 iTunes
The Slope of the Budget Constraint
From C to D:
I
“rise” = -4
tickets
I
“run” = +5
rentals
I
Slope = - 0.8
Alice must give
up 4 tickets to
get 5 rentals:
4×$6.25 = 5×$5
Quality 16
24
20
C
16
D
12
8
4
0
0
5
10
15
20
25
30 iTunes
The Slope of the Budget Constraint
The slope of the budget constraint equals
I
the rate at which Alice can trade rentals for tickets
I
the opportunity cost of rentals in terms of tickets
I
the relative price of rental:
Price of rental
4
=
Price of ticket
5
Budget Constraint: Fall in Income
Now Alice can buy
I
$100/5 = 20 rentals
I
or $100/6.25 = 16
tickets
or any combination in
between.
Quality 16
A fall in income
shifts the budget
constraint down.
24
20
16
12
8
4
0
0
5
10
15
20
25
30 iTunes
Budget Constraint: Price Increase in Quality 16 tickets
Assume that the price of
Quality 16 tickets doubles.
Quality 16
An increase in the
price of Quality 16
tickets pivots the
budget constraint
inward.
24
I
Now Alice can still
buy 30 rentals.
I
But she can only buy
$150/$12.50 = 12
tickets
Notice: budget slope is
smaller, relative price of
rentals is now only
5
12.50 = 0.4 tickets.
20
16
12
8
4
0
0
5
10
15
20
25
30 iTunes
Preferences: What the Consumer Wants
Indifference curve:
shows consumption
bundles that give the
consumer the same level
of satisfaction.
Quality 16
24
20
16
A, B, and all other
bundles on I1 make Alice
equally happy – she is
indifferent between them.
B
12
8
A
I1
4
0
0
5
10
15
20
25
30 iTunes
Four Properties of Indifference Curves
1. Indifference curves
are downward-sloping.
Quality 16
One of Alices indifference curves.
24
20
If the quantity of rentals is
reduced, the quantity of
tickets must be increased
to keep Alice equally
happy.
16
B
12
8
A
I1
4
0
0
5
10
15
20
25
30 iTunes
Four Properties of Indifference Curves
2. Higher indifference
curves are preferred to
lower ones.
Quality 16
A few of Alices indifference curves.
24
20
Alice prefers every bundle
on I2 (like C) to every
bundle on I1 (like A).
16
D
12
C
8
She prefers every bundle
on I1 (like A) to every
bundle on I0 (like D).
A
I2
I1
4
0
I0
0
5
10
15
20
25
30 iTunes
Four Properties of Indifference Curves
3. Indifference curves
cannot cross.
Quality 16
24
Suppose they did.
20
Alice should prefer B to
C, since B has more of
both goods.
16
Yet, Alice is indifferent
between B and C: She
likes C as much as A
(both are on I4 ). She likes
A as much as B (both are
on I1 ).
B
12
C
8
A
I4
I1
4
0
0
5
10
15
20
25
30 iTunes
Four Properties of Indifference Curves
4. Indifference curves
are bowed inward.
Quality 16
24
B
20
Alice is willing to give up
more tickets for a rental if
she has few rentals (B)
than if she has many (A).
10
16
12
4
A
3
8
4
I1
4
0
0
5
10
15
20
25
30 iTunes
The Marginal Rate of Substitution
Marginal rate of
substitution (MRS): the
rate at which a consumer
is willing to trade one
good for another.
Quality 16
MRS = slope of indifference curve
24
B
20
Alice’s MRS is the amount
of tickets she would
substitute for another
rental.
16
MRS falls as you move
down along an indifference
curve.
4
10
12
MRS =
4
10
4
A
= 2.5
MRS =
3
8
3
4
4
0
I1
0
5
10
15
20
25
30 iTunes
One Extreme Case: Perfect Substitutes
Perfect substitutes: two
goods with straight-line
indifference curves,
constant MRS
Nickles
12
10
Example: nickels and
dimes
I
Consumer is always
willing to trade two
nickels for one dime.
8
6
4
2
0
I0
0
1
2
I1
3
4
I2
5
6
Dimes
Another Extreme Case: Perfect Complements
Perfect complements:
two goods with right-angle
indifference curves
Example: Left shoes, right
shoes
I
Right shoes
I1
6
I2
5
4
3
2 left shoes, 2 right shoes
is just as good as
3 left shoes, 2 right shoes
2
1
0
0
1
2
3
4
5
6 Left shoes
Less Extreme Cases: Close Substitutes and Close
Complements
Pepsi
Indifference curves
for close substitutes
are not very bowed.
Hot dog buns
Coke
Indifference curves
for close complements are very
bowed.
Hot dogs
Optimization: What the Consumer Chooses
A is the optimum: the
point on the budget
constraint that touches
the highest possible
indifference curve.
Alice prefers B to A, but
she cannot afford B.
Alice can afford C and D,
but A is on a higher
indifference curve.
Quality 16
The optimum is the
bundle Alice most
prefers out of all the
bundles he can afford.
24
B
12
A
9
C
D
0
0
12 15
30 iTunes
Optimization: What the Consumer Chooses
At the optimum, the slope
of the indifference curve
equals the slope of the
budget constraint:
MRS =
Quality 16
24
Ptickets
Prentals
12
marginal value
of ticket (in
terms of rental)
A
9
0
0
12 15
30 iTunes
Optimization: What the Consumer Chooses
At the optimum, the slope
of the indifference curve
equals the slope of the
budget constraint:
MRS =
Quality 16
24
Ptickets
Prentals
12
price of rental
(in terms of
tickets)
A
9
0
0
12 15
30 iTunes
The Effects of an Increase in Income
An increase in income
shifts the budget
constraint outward.
Quality 16
24
If both goods are
“normal,” Alice buys more
of each.
B
12
0
A
0
15
30 iTunes
Inferior vs. normal goods
An increase in income
increases the quantity
demanded of normal
goods and reduces the
quantity demanded of
inferior goods.
I
In this example,
rentals are normal
goods and tickets are
inferior.
Quality 16
24
12
A
B
0
0
15
30 iTunes
The Effects of a Price Change
Initially, one ticket costs
$6.25 and one rental costs
$5
I
Assume that the price
of one rental is halved
to $2.50.
I
budget constraint
rotates outward,
I
Alice buys more
rentals and fewer
tickets.
Quality 16
A (initial)
B (new bundle)
iTunes
The Income and Substitution Effects
A fall in the price of rentals has two effects on Alice’s optimal
consumption of both goods.
I
Income effect: A fall in Prentals boosts the purchasing
power of Alice’s income, allows her to buy more tickets and
more rentals.
I
Substitution effect: A fall in Prentals makes tickets more
expensive relative to rentals, causing Alice to buy
fewer tickets and more rentals.
Notice: The net effect on tickets is ambiguous.
The Income and Substitution Effects
I
Initial optimum at A.
I
Prentals falls.
I
Substitution effect:
from A to A’, Alice
buys more rentals and
fewer tickets.
I
Income effect: from
A’ to B, Alice buys
more of both goods.
Quality 16
In this example, the
net effect of a price
decrease on iTunes
rentals on Quality 16
tickets is negative.
A (initial)
B (new bundle)
A’
iTunes