Transcript Indifference Curves - Cornell University

Consumer Theory
1
What is Consumer Theory?
 Study
of how people use their limited means to
make purposeful choices.
 Assumes that consumers understand their
choices (possibilities) and the prices
(opportunity costs) associated with each
choice.
 Assumes that consumers consider the
alternatives and choose the one they like best.
2
Consumer Theory - Why?
 Two
important reasons:
– to understand the foundations of market
demand (bake the demand curve from
scratch)
– to address several interesting consumer
theory issues that are best understood
using this model rather than the aggregate
demand model
3
Two Components of
Consumer Demand
 Opportunities:
– What can the consumer afford?
– What are the consumption possibilities?
– Summarized by the budget constraint
 Preferences:
– What does the consumer like?
– How much does a consumer like a good?
– Summarized by the utility function
4
What is a Budget Constraint?
 A budget
constraint shows the
consumer’s purchase opportunities as
every combination of two goods that can
be bought at given prices using a given
amount of income.
 The budget constraint measures the
combinations of purchases that a person
can afford to make with a given amount
of monetary income.
5
Li’s Demand for Wheat and Rice
 Illustration
of consumer theory
 Li’s demand for wheat and rice depends
upon the prices for these goods, her
income, and her preferences.
 Suppose we look first at her budget
constraint:
– Wheat costs $4/lb.
– Rice costs $2/lb.
– Li has $40 of income.
6
Li’s Budget Constraint
 The
mathematical expression for Li’s
budget constraint is:
I = PW W + PR R
R = I/PR - (PW / PR)W
I
like to refer to the |slope| of the budget line
as the ERS=Economic Rate of Substitution
 In
this case it is PW / PR
 For
Li: PW=$4 PR=$2 I=$40 ERS=2
7
Graph of Li’s Budget
Constraint


The graph to the right
shows a picture of Li’s
budget constraint.
Each blue diamond is a
point from the table.
The slope is equal to -2,
as shown on the last
slide.
Li's Budget Constraint
20
15
Rice

10
5
0
0
5
10
15
20
Wheat
8
Budget Line gymnastics
An increase in income only.
 An increase in the price of wheat only.
 A decrease in the price of rice only.
 Income doubles as do the prices of wheat and
rice.


Note: Changes in the price of wheat relative to
the price of rice will change the ERS.
9
Preferences
 Let
R = “at least as good as”
– B0 R B1 means: B0 is at least as good as B1
 Let
IN = “indifferent to”
– B0 R B1 and B1 R B0 implies B0 IN B1
 Let
P = “strictly preferred to”
– B0 R B1 and not B1 R B0 implies B0 P B1
10
Preferences
 Basic
assumptions about an individual’s
preferences (R) over bundles (B)
– more is better: If B0 has more in it than B1 then
B0 R B1
– transitivity: If B0 R B1 and B1 R B2 then B0 R B2
– average bundles are at least as good as
extreme bundles: If B0 IN B1 and B2 is an
“average” of B0 and B1, then B2 R B0 and B1
11
Utility and Preferences
 Utility
is the way economists represent
preferences.
 Among two bundles, the one with the
higher utility is the preferred bundle.
 If two bundles have the same utility, we
say that the consumer is indifferent.
12
Indifference Curves
Preferences that satisfy the conditions I have
noted above can be represented by
indifference curves.
 The set of all indifference curves that describe
an individual’s preferences are referred to as
an indifference curve map.
 An indifference curve connects all of the
bundles that a consumer likes equally.
 We will assume only two goods when using
indifference curve analysis.

13
Indifference Curve Map Properties
 An
indifference curve should not slope
up.
 Indifference curves can not cross one
another.
 Better bundles are to the northeast.
 Indifference curves will not be “bowed
out.”
14
Li’s Preferences in
Indifference Curves



An indifference curve connects
all the bundles that have the
same utility.
Higher indifference curves
indicate more utility (IC2 is
preferred to IC1).
Lower indifference curves
indicate less utility (IC1 is
preferred to IC0).
The indifference curve map is
FULL of indifference curves.
Li's Indifference Curves
30
25
I2
I1
I0
20
Rice

15
10
5
0
0
10
20
Wheat
15
The Marginal Rate of
Substitution


The Marginal Rate of
Substitution(MRS) tells us
how much of one good Li
would willingly trade for an
incremental unit of the other
good and remain indifferent.
The MRS=|slope| of the
indifference curve at a
bundle.
Common to assume the MRS
declines as we move down
an indifference curve.
Li's Indifference Curves
30
25
I2
I1
I0
20
Rice

15
10
5
0
0
10
20
Wheat
16
How Much Wheat and Rice
 Li’s
optimal amount of wheat and rice to
consume is the amount that maximizes Li’s
utility subject to her budget constraint.
 In the graph...
– Get to the highest indifference curve possible
– Stay on the budget constraint (b/c more is
better)
17
How to Find Li’s Best
Combination




The black bundle is best.
The pink bundle is not the
best. Li has spent all her
income but is not on the
highest indifference curve
possible.
Bundles n/e of IC0 are
better and some are
affordable.
At (W*, R*) she is doing the
best she can subject to her
budget constraint.
Rice
20
R*
IC2
IC1
IC0
W*
10
Wheat
18
How to Find the Best
Combination
 Utility
is maximized when:
– the indifference curve is just tangent to the budget
line.
 Utility
is maximized when:
– you are on the budget line and
– the slope of the indifference curve equals the
slope of the budget line
 Utility
is maximized when:
– Income=PRR + PWW
– MRS=ERS
19
The “bang per buck” story

Let MUW = Li’s marginal utility of wheat
– it measures the change in utility as we change wheat
consumption by an incremental unit while holding rice
constant
 Let
MUR = Li’s marginal utility of rice
– it measures the change in utility as we change rice
consumption by an incremental unit while holding
wheat constant
 Common
to assume that marginal utilities decline
as we increase consumption - the law of
diminishing marginal utility
20
The “bang per buck” story
 The
MRS = MUW / MUR
 The ERS = PW / PR
 At an optimal bundle: MRS=ERS
 Rewritten we have:
– MUW / MUR = PW / PR
– MUW/PW = MUR/PR
– bang/buck in wheat = bang/buck in rice
 Get
same optimal bundle either way
21
Handling a change in PW

Li wants to achieve the
highest indifference curve
that the budget constraints
permit.
Li's Demand for Wheat
30


The points A, B, and C
represents the best that Li
can do at prices of $4, $2,
and $1 for wheat.
The equation MRS=ERS is
satisfied at each of the
points.
Rice
25
I2
I1
I0
4
2
1
20
C
15
B
10
A
5
0
0
5
10
15
20
Wheat
22
Li’s Demand for Wheat
 The
table shows the
amount of wheat
that Li demands at
each price.
 These
are the points
of tangency from the
previous slide.
Li's Demand for Wheat
Quantity
Price Point
6
4
A
10
2
B
16
1
C
23
Graph of Li’s Demand for
Wheat

When we connect the
points from the table in
the previous slide we
get Li’s demand for
wheat.
The points A, B, and C
correspond to the
tangencies of the
budget constraint and
the indifference curves.
Li's Demand for Wheat
A
4
3
Price

B
2
C
1
0
0
2
4
6
8 10 12 14 16 18 20
Quantity
24
Li’s Best Choice
Reconsidered






Consider the choice at PW=$2/lb.
The point B is optimal.
The point A is feasible but inferior to
all points on the red budget line
between E and F.
The point C is preferred to B but
cannot be purchased with Li’s $40
income at the given prices; it is
above the red budget line.
The point E is feasible but Li prefers
more wheat and less rice (B).
The point F is feasible but Li prefers
less wheat and more rice (B, again).
There is no combination that Li
prefers to B that she is able to buy.
Li's Best Choice of Wheat and Rice
30
25
20
I2
I1
I0
2
E
Rice

15
C
B
10
A
5
F
0
0
5
10
Wheat
15
20
25
Handling a change in PW

Li wants to achieve the
highest indifference curve
that the budget constraints
permit.
Li's Demand for Wheat
30


The points A, B, and C
represents the best that Li
can do at prices of $4, $2,
and $1 for wheat.
The equation MRS=ERS is
satisfied at each of the
points.
Rice
25
I2
I1
I0
4
2
1
20
C
15
B
10
A
5
0
0
5
10
15
20
Wheat
26
Li’s Demand for Wheat
 The
table shows the
amount of wheat
that Li demands at
each price.
 These
are the points
of tangency from the
previous slide.
Li's Demand for Wheat
Quantity
Price Point
6
4
A
10
2
B
16
1
C
27
Graph of Li’s Demand for
Wheat

When we connect the
points from the table in
the previous slide we
get Li’s demand for
wheat.
The points A, B, and C
correspond to the
tangencies of the
budget constraint and
the indifference curves.
Li's Demand for Wheat
A
4
3
Price

B
2
C
1
0
0
2
4
6
8 10 12 14 16 18 20
Quantity
28
From IC Map to Li’s Demand
for Wheat
Li's Demand for Wheat
Li's Demand for Wheat
4
30
I2
I1
I0
4
2
1
20
C
15
B
10
A
5
0
0
5
10
Wheat
15
20
3
Price
Rice
25
A
B
2
1
C
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quantity
29
Income and Substitution
Effects



Economists decompose the effect of a change in price
on the quantity demanded into an income and a
substitution effect.
Income effect: due to the increase in real income
associated with a fall in prices (you can buy more with
the same nominal income) or the loss of real income
associated with a rise in prices (you cannot buy as much
as you once did with the same nominal income).
Substitution effect: due to the change in the relative
price of the good, cheaper goods are substituted for
more expensive ones.
30
Income and Substitution Effects:
Price Decline, “X” normal



When the price of a good falls, the quantity
demanded rises for two reasons.
The income effect: real income is higher because the
same money income buys more at the lower prices.
For normal goods, then, the income effect of a price
fall is positive.
The substitution effect: consumers substitute the now
cheaper good for ones whose price has not fallen,
real income held constant. This increase in demand
is called the substitution effect of a price decline.
31
Li’s Income and Substitution
Effects: Price Fall, Rice normal


Graph shows the income and
substitution effects of the fall in
the price of wheat from $4/lb. (A)
to $1/lb. (C).
The movement from point A to
point D is the substitution effect: Li
buys less rice and more wheat,
and would do so even if she had
an income of only $20 (as the
black budget line shows).
The movement from point D to
point C is the income effect, the
price decline is like giving Li an
additional $20 of real income.
Li's Income and Substitution Effects
30
25
20
Rice

15
I2
I0
4
1
1
C
10
A
D
5
0
0
5
10
Wheat
15
20
32
Li’s Substitution Effect
 The
substitution effect is the amount by
which Li's wheat consumption increased
holding real income constant.
 Substitution effect is the difference
between Li's consumption of wheat at the
new and old prices holding her real
income constant, that is, staying on the
same indifference curve (compare points
A and D).
33
Li’s Income Effect



When the price falls from $4/lb. of wheat to $1/lb. per
wheat, Li is able to buy both more wheat and more
rice.
The income effect is the difference between what she
would have bought on the old indifference curve at
the lower wheat price (point D) and what she actually
did buy with her nominal income ($40) at the lower
price (point C).
Li increases her consumption of wheat and rice
because of the increase in her real income from the
price decline.
34
General effect of a price fall
PX falls
Income effect - you feel richer
“X” normal
Quantity demanded increases
Substitution Effect
X now looks relatively cheaper
“X” inferior
Quantity demanded decreases
Quantity demanded increases
Total effect is the substitution effect AND the income effect
working at the same time.
35
From Individual to Market
Demand
 Market
demand is the sum of all
individual demands in the economy.
 In the following example there are two
consumers of wheat: Li and Juanita.
 The market demand, then, is the sum of
the quantities demand by Li and
Juanita.
36
Juanita’s Demand for Wheat



Juanita’s income is also
$40.
Juanita faces the same
price for rice as Li: $2/lb.
Her preferences are
different from Li’s.
Her demand for wheat is
derived in the figure at
the left.
Juanita's Demand for Wheat
30
25
I2
I1
I0
4
2
1
20
Rice

15
C
B
10
A
5
0
0
5
10
15
20
Wheat
37
Graph of Juanita’s Demand
for Wheat
 The
Juanita's Demand for Wheat
A
4
3
Price
points A, B and
C correspond to
Juanita’s best
choices given her
income and the
three prices of
wheat illustrated.
 This is her demand
curve for wheat.
2
B
1
C
0
0
2
4
6
8 10 12 14 16 18 20
Quantity
38
Market Demand



The market demand (green)
is the sum of Li’s (blue) and
Juanita’s (red) demand for
wheat at each price.
At PW=4, Li demands 6 lbs.,
Juanita demands 5 lbs. and
the market demand is 11
lbs.
At PW=2, Li and Juanita
demand 10 lbs. and the
market demand is 20 lbs.
At PW=1, Li demands 16
lbs., Juanita demands 18
lbs. and the market demand
is 34 lbs.
Market for Wheat
4
Price of Wheat

3
Li's Demand
Juanita's Demand
2
Market Demand
1
0
0
20
40
Quantity of Wheat
39
Application: Effect of a Tax &
Transfer Program

Suppose I have the
preferences illustrated
at the right.
Question A:
If Income = $16
If Price of food = $1
If Price of shelter = $1
Food = ?
Shelter = ?
Indifference curve = ?
Preferences
Shelter

16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
I6
I5
I4
I3
I2
I1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
Food
40
Answer A
Initial Point
Point A:
If Income = $16
If Price of food = $1
If Price of shelter = $1
Food = 7
Shelter = 9
Indifference curve = I4
Shelter

16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
A
I6
I5
I4
I3
I2
I1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
Food
41
Effect of a Tax and Transfer
Program: Addition of Tax
Question B:
If Income = $16
If Price of food = $1
If Price of shelter = $1
and Tax on shelter =
100%
Tax-inclusive price of
shelter = ?
Food = ?
Shelter = ?
Indifference curve = ?
Initial Point
Shelter

16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
A
I6
I5
I4
I3
I2
I1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
Food
42
Answer B
Point B
If Income = $16
If Price of food = $1
If Price of shelter = $1
and Tax on shelter =
100%
Tax-inclusive price of
shelter = 2
Food = 9
Shelter = 3.5
Indifference curve = I2
Tax Only
Shelter

16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
A
I6
I5
I4
B
I3
I2
I1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
Food
43
Effect of a Tax and Transfer
Program: Tax & Transfer
Question C:
If Income = $16
If Price of food = $1
If Price of shelter = $1
and Tax on shelter =
100% and
Transfer payment = $8
Food = ?
Shelter = ?
Indifference curve = ?
Tax Only
Shelter

16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
A
I6
I5
I4
B
I3
I2
I1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
Food
44
Answer C
Point C
If Income = $16
If Price of food = $1
If Price of shelter = $1
and Tax on shelter =
100% and
Transfer payment = $8
Food = 10
Shelter = 7
Indifference curve = I4
Tax and Transfer
Shelter

16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
A
I6
C
I5
I4
B
I3
I2
I1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
Food
45
Tax and Transfer Systems
Give Pure Substitution Effects




Notice in the example that the consumer ends up on the same
indifference curve after the tax and transfer program as in the
initial choice (I4).
In public finance (the study of tax and transfer systems) this
result usually occurs when the tax and transfer system is
combined with a balanced budget.
In our example, tax receipts are $7 per person (= 7 units of
shelter x $1 tax), while the transfer is $8 per person. This is as
close to “balanced” as we can get and still be able to graph the
consumer’s choice legibly.
Knowledge of the substitution effect of the price change induced
by the shelter tax is sufficient to predict the effect of the
complete tax and transfer system.
46
Food Stamps vs. $$$$$
 Suppose
–
–
–
–
the following for the Parker family:
u(F, $aog) where $aog=$all other goods
I=$200
PF = $2/unit
Paog = $1
 Consider
three alternative government
policies
– no support
– $200 in food stamps
– $200 in cash
47
Food Stamps vs. $$$$$

$aog
Notes:
– the budget line under the
food stamp program is
the thick black segment
and the purple segment
– The budget line with
cash is the red and
purple segments
– the Parkers are
indifferent between food
stamps and cash
200
IC1
IC0
BL0
100
200
Food
48
Food Stamps vs. $$$$$

$aog
IC$$
ICFS
IC0
Notes:
– the budget line under the
food stamp program is
the thick black segment
and the purple segment
– The budget line with
cash is the red and
purple segments
– if this is the case then the
Parkers prefer cash to
food stamps
BL0
Food
49