1
The Indifference Curves
Ch. 7
Appendix Chapter 7
THE INDIFFERENCE CURVES
1. WHAT IS AN INDIFFERENCE CURVE?
2. PROPERTIES OF INDIFFERENCE CURVES
3. SETS OF INDIFFERENCE CURVES
4. THE BUDGET CONSTRAINT LINE
5. CONSUMER OPTIMUM
6. INCOME EFFECT (THE INCOME-CONSUMPTION CURVE)
7. PRICE-EFFECT (PRICE-CONSUMPTION CURVE)
8. THE SUBSTITUTION EFFECT
9. DIFFERENTIATING SUBSTITUTION AND INCOME EFFECT
10. DIFFERENT RATES OF MARGINAL RATES OF SUBSTITUTION (MRS)
11. THE INDIFFERENCE CURVE AND THE DEMAND CURVE
1. WHAT IS AN INDIFFERENCE CURVE?
An Indifference Curve is a curve that shows goods in different combinations, with the assumption
that each good gives the consumer the same total satisfaction as every other. This concept of indifference
curves was first developed by Francis Ysidro Edgeworth (Ireland, 1845-1926), Vilfredo Pareto (Italy,
1848-1923), and Eugen Slutsky (Russia, 1880-1948). It was made popular by J. R. Hicks (England, 19041965) and Roy G.D. Allen (England, 1906-1983) in 1934, in an article entitled, “A Reconsideration of the
Theory of Value.”
Given a choice between two products of (e.g. soda and cookies) a consumer may state that s/he gets
the same total satisfaction (e.g. 70 utils) from any combination of these two products. Here we assume
that one can of soda is of the same quality as the second can, and we say that the cans are homogeneous.
And that is also true for the cookies that they are homogeneous. In other words, whether the consumer
chooses combination A, B, C, D or E is a matter of indifference. (See Table 1 and Figure 1). If the
consumer decides to consume the second can of soda, then s/he is willing to forgo four cookies while still
having the same satisfaction (70 utils) as before. This is called the marginal rate of substitution (MRS),
the rate at which a consumer is willing to consume less of one product in order to consume more of
another and still remain on the same indifference curve.
Table 1
4=(∆ in Col.3)/( ∆ in Col. 2)
2-Given
3-Given
Combination
Sodas
/Hr.
Cookies
/Hr.
A
1
>
2
>
3
>
4
>
5
B
C
D
E
Fig. 1
For Students
Calculate MRS
Calculating Marginal rate of Substitution (MRS)
1-Given
MRS for each Can of Soda
MRS
(8.5 - 4.5) / (2-1) = 4/1 =4.0
1:4
8.5
>
>
(4.5 - 3) / (3-2) = 1.5/1 = 1.5
1 :1.5
3
>
(3 - 2) / (4-3) = 1/1 = 1.0
1:1
2
>
(2-1.7)/(5-4) = 0.3/1 =0.3
1: 0.3
1.7
Y/wk.
MRS/ each
unit of X.
18
>
11
>
6
>
3
>
1
For Students: Indifference Curve and MRS
Y/ Hr.
IC1-70 utils
A
8
1
>
2
>
3
>
4
>
5
4.5
Indifference Curve and MRS
Cookies/ 10
Hr.
X/wk.
20
16
12
6
B
8
C
4
2
4
E
0
1
2
3
4
Soda cans/Hr.
5
0
1
2
3
X/Hr.
4
5
2
The Indifference Curves
Ch. 7
2. PROPERTIES OF INDIFFERENCE CURVES (IC)
Indifference curves share the following four properties:
a) Indifference curves are always downward (negative) sloping from left to right
Although different combinations of goods of the same quality may give the consumer
the same amount of satisfaction in one hour, fewer units of any second good (say,
cookies) are needed by the consumer for each extra unit of the first good (say, cans of
soda), to have the same amount of satisfaction. We can see this from Table 1 and Figure
1. This can also be explained by the law of decreasing marginal utility, explained earlier
in this chapter.
b) Indifference curves cannot take the form of a straight line (Table 2 and Fig. 2).
A straight line would suggest that the consumer would give the same value to the first
can of soda as to the third cookie in that hour, which is not the case, since each additional
cookie gives less and less satisfaction to the consumer (diminishing marginal utility).
Obviously, after the third can of soda, the consumer will say, I would rather have a
cookie. (Table 2, and Figure 2.)
Table 2. Straight Line Indifference Curve.
1-Given
2-Given
Sodas/
Q
A
0
>
1
>
2
>
3
B
C
D
3-Given
Cookies/
Q
3
>
2
>
1
>
0
Fig. 2. Straight Line IC
3=(∆ in 3)/(∆ in 2)
Marginal Rate of
Substitution (MRS)
(3-2)/(1-0)=1
1:1
(2-1)/(2-1)=1
1:1
(1-0)/(3-2)=1
1:1
Cookies/
Hr.
D
3
C
2
B
1
A
0
1
2
3 Sodas/
Hr.
c) Indifference Curves cannot be upward sloping (Table 3 and Fig. 3).
Looking at Figure 1, consumers, when picking combination B, will have 2 cans of
soda and 4.5 cookies. Combination C means giving up 1.5 [4.5-3=] units of cookies in
favor of 1[3-2=] can of soda. If indifference curves were to be upward sloping,
consumers would always choose combination E, meaning they wish to consume more of
both cookies and soda. (See Table 3 and Fig. 3), a situation which is implausible.
Table 3: The consumer would always choose combination E if
Indifference Curve were to be upward sloping, which is not possible.
1-Given 2-Given 3-Given 4-Given
5-Given
Combination
A
B
C
D
E
Soda cans/Hr.
1
2
3
4
5
Cookies/Hr.
1.75
2
3
4.5
8.5
Fig. 3. Indifference Curve is Never Upward Sloping (Positively Slope).
Cookies/Hr.
10
E
8
D
6
C
4
A
2
0
B
1
2
3
4
5 Soda cans/Hr.
Ch. 7
3
The Indifference Curves
d) Indifference curves never intersect each other (Figure 4)
In Figure 4, A, B, and C are combinations of sodas and cookies. If the two
indifference curves, IC1 and IC2, represent different amounts of satisfaction, then, on
curve IC1 (65 utils), the satisfaction one gets with combination A will be equal to that
with combination B, 3 sodas and 5 cookies. So, A=B (65 utils).
On curve IC2 (95 utils), combination A gives the same satisfaction as point C, 3
sodas and 2.5 cookies. Hence, A=C (95 utils).
At B the consumer’s choice will be 3 sodas and 5 cookies; at C the consumer’s
choice will be 3 sodas and 2.5 cookies, giving the consumer the same amount of
satisfaction, which is not possible.
Thus, B=C is not possible; therefore, two indifference curves cannot intersect each
other. (Figure 4).
Fig. 4
Indifference Curves Will Never Intersect Each Other.
10
IC1
IC2
Cookies/Unit
8
A
IC1 (65 utils)
5
IC2 (95 utils)
2.5
0
1
2
3
4
Soda cans/Hr.
3. SETS OF INDIFFERENCE CURVES (Figure 5)
Consumers may have many sets of indifference curves (also called indifference
maps). Let us assume that the consumer is able to purchase more sodas and cookies in an
hour than before, whether because of an increased budget or because of a decline in
prices of soda and cookies. The consumer will now have sets of indifference curves,
showing a greater or lesser combination of the goods than before. These sets show
different levels of satisfaction from different combinations of these two goods. In Figure
5, indifference curves giving greater satisfaction are to the right. (Figure 5).
Figure 5. Sets of Indifference Curves (Indifference Map)
Cookies/Hr.
IC1
10
IC2
IC3
8
6
4
(140 utils)
2
0
1
2
3
4
(100 utils)
(75 utils)
5 Soda cans/Hr.
4
The Indifference Curves
Ch. 7
4. THE BUDGET CONSTRAINT LINE (BCL)
A) Calculating the Budget Constraint Line (BCL):
Once we know the consumer’s indifference curves, as well as his budget and the price of each
good, we can determine which combination of goods will maximize his satisfaction. Let us
assume that the consumer has $12 to spend, and that he is thinking of consuming two
products: X, priced at $3.00 per unit; and Y, priced at $1.00 per unit.
There are three choices:
i) Spend all the budget on X, in which case the money will buy 4 units [12/3=] of X and
nothing of Y.
ii) Spend all the budget on Y, in which case the money will buy 12 units [12/1=] of Y and
nothing of X.
iii) Spend some of the budget on X and some on Y, to the limit of $12 total.
The number of units of sodas and cookies purchased is constrained by the budget of $12, on the
one hand, and by the given price of the goods, on the other.
The Budget Constraint Line represents these limits on purchasing power at any point in time.
To obtain the budget constraint line, calculate as follows:
Budget
$12
=
= 4 units of X. This calculation will give you point A on X-axis in Fig. 6-A.
Price of X
$3
Budget
Price of Y
$12
= 12 units of Y. This calculation will give you point E on Y-axis in Fig. 6-A.
$1
In other words, dividing the budget by the price of a product will give us the maximum
number of units of a product obtainable if the entire budget is spent only on that product.
=
Table 4-A: Obtaining the Budget Constraint Line
1-Given 2-Given
5=(3 x Px) + (4 x Py)
3=1/Px 4=1/Py
4-B. For Students:
Budget
Budget =
$16
Combination
A
B
C
D
E
$12
$12
$12
$12
$12
No. of
X/hr.=
No. of
Y/hr.=
Check: that Total
Budget of $12 is spent.
12/3 = 4
9/3 = 3
6/3 = 2
3/3 = 1
0/3 = 0
0/1 = 0
3/1 = 3
6/1 = 6
9/1 = 9
12/1 = 12
(4 x $3) + (0 x $1) = $12
(3 x $3) + (3 x $1) = $12
(2 x $3) + (6 x $1) = $12
(1 x $3) + (9 x $1) = $12
(0 x $3)+(12 x $1) = $12
$16
$16
$16
$16
$16
X=$4
Y=$1
X/hr.
Y/hr.
4
3
2
1
0
As we can see from Table 4-A, and Figure 6-A, any combination that the consumer
chooses on the budget constraint line (A, B, C, D or E) will have the same price, exactly
$12.00. The consumer cannot buy a combination of 3 units of X and 6 units of Y at “U,”
because $15 [(3x$3)+(6x$1) =9+6=], is beyond the original budget of $12. On the other hand,
the consumer will not choose combination R because at that point s/he will not maximize
satisfaction. At R the consumer will only be spending $9 [(1x$3)+(6x$1)=] of the $12 budget.
In such cases, the consumer cannot maximize satisfaction since the complete budget has not
been spent.
Fig. 6-A. Budget Constrain Line (BCL).
Fig. 6-B. For students: Draw BCL.(Table 4-B)
Y
Y
E
12
Units
D
9
12
R
6
C
U
8
4
B
3
0
1
16
Units
2
3
A
4 X units
0
1
2
3
4 X units
5
The Indifference Curves
Ch. 7
B) Factors that Shift the Budget Constraint Line
There are two factors that can shift the budget constraint line:
a) Change (increase or decrease) in budget, and/or
b) Change in price of the goods.
a) Change (increase or decrease) in budget: (Table 5 and Fig. 7-A)
Let us assume that consumer’s budget increases from $12 to $18, but the price of X and Y
remains the same. The first step is to calculate the budget constraint line by dividing the new
budget by the price of X ($18/3); this will give us the value on the X-axis. Next, divide the new
budget by the price of Y ($18/1) and this will give us the value on the Y-axis. (These
calculations are shown in Table 5). When these new values are drawn in Figure 7-A, we see
that the new budget constraint line shifts to the right. Hence, whenever budget increases and
the price of two goods remains the same, the budget constraint line will shift to the right. Of
course, the budget line would shift to the left if the budget were to decrease from the original
$12. Table 5 shows how the new budget line is calculated.
Table 5 New Budget Line With Increase in Budget While Price of X and Y remain the same.(For Fig.7-A.)
1-Given
2-Given 3=1/2
4=1=2x3
5-Given 6=1/5
7=1=6=(5x6)
Price
Quantity
Total
Price
Quantity
Bought of Budget Spent
Total
Bought of
Total Budget
X
Y
Budget ($)
Spent ($)
Budget Line
($)
($)
($)
X
Y
Old (Gray Line)
12/$3= 4
12/$1=12
12
3
4 x $3 =12
1
(12 x $1) =12
New (Dotted Line)
18/$3= 6
18/$1=18
18
3
6 x $3 =18
1
(18 x $1) =18
b) Change In Price Of The Goods
i) Change in price of the goods in the same proportion. (Table 6 and Fig. 7-B)
Table 6 and Figure 7-B also show what happens when the price of X decreases from
$3/unit to $1.5/unit and the price of Y decreases from $1 to $0.50. Because the decline in
prices is in the same ratio (50%), the consumer can buy more units of both goods, which
will shift the budget constraint line parallel to the right.
Table 6 For Students: Calculate the New Budget Constraint Line with Decrease in price of X to $1.5/unit
and of Y to $0.5, with budget staying the same. (For Fig.7-B.)
1-Given 2-Given 3=1/2 4=1=2x3 5-Given
6=1/5
7=1=4=(5x6)
Total
Price Quantity Total
Quantity
Total Budget
Bought Budget Price Y Bought of
Budget
X
Budget Line
($)
Spent ($)
of X Spent ($)
($)
($)
Y
Old (Gray Line)
12
3
1.0
New (Dotted Line)
12
1.5
0.5
Figure 7 Shifts in the Budget Constraint Line.
Fig. 7A Shift in Budget Constraint Line because
of change in budget, with prices of X and Y
staying the same.
Fig. 7-B Shift in Budget Constraint Line because
of change in price of goods: (X=$1.50,Y=$0.50)
with budget staying the same.
18/1= 18
12/0.5=24
New Budget Line With
$18.00
Y/units
12/1= 12
Old budget line
With $ 12.00
0
4
12/3=4
6
X/units
18/3=6
New Budget Line With
Lower Prices
Y/units
12/1=12
Old budget line with
Higher Prices
0
4
12/3=4
8
X/units
12/1.5=8
6
The Indifference Curves
Ch. 7
ii) Changes in price of the goods in different proportions. (Table 7 and Figs. 8-A
and 8-B)
If the price of products increases or decreases in different proportions, and the budget
stays the same, the shape of the budget line will change. Let us assume that the price of X
stays at $3/unit, while that of Y decreases from $1.00 to $0.50/unit. This change will shift
the budget constraint line point upwards for the Y-axis, while for the X-axis the point will
remain the same. (Fig. 8-A.)
On the other hand, if the budget is still $12, but the price of X decreases from $3.00
to $1.5 /unit, and the price of Y stays at $1.00/unit, the budget constraint line will shift
outwards for X-axis, while for Y-axis the line will remain the same. (Fig. 8-B.)
Table 7 : New Budget Line with Decrease in price of X and Y, with budget staying the same.(For Fig. 8-A.)
1-Given 2-Given 3=1/2
4=1=2x3
5-Given
6=1/5
7=1=4=(5x6)
Total
Price
Quantity
Quantity
Total Budget
Budget
Bought of Total Budget
Bought of
X
Spent
Spent
Price Y ($)
($)
($)
Budget Line
X
Y
Old(Gray Line)
12/3=
4
12/1=12
12
3
4 x $3=12
1
(12 x $1) = 12
New (Dotted Line)
12
12/1.5= 8 8 x $1.5=12
1.5
Fig. 8-B. Budget stays at $12, but budget line
shifts because price of X decreases from $3 to
$1.50/unit, but price of Y stays at $1/unit.
12/0.5=24
Fig. 8-A. Budget stays at $12, but budget constraint
line shifts because price of Y decreases from $1 to
$0.50/unit, but price of X stays at $3/unit.
Y/units
New Budget Line
New Budget Line
12/1=12
Old Budget Line
Old Budget Line
0
4
(12/$3)=4
(24 x $0.5) =12
24/0.5=24
(12/1)=12 units of Y
Y/units
12
0.5
8
X/units
(12/$1.5)=8
0
4
(12/3)=4
X/units
7
The Indifference Curves
Ch. 7
5. CONSUMER OPTIMUM (Figure 9-A)
Earlier in the chapter we saw that a consumer maximizes his/her satisfaction when
the following equation [(MUx/Px)=(MUy/Py)] is true. In other words, the consumer
maximizes his/her satisfaction when the marginal utility the consumer gets from the last
dollar spent on various goods and services has the same value. Now, we can determine
consumer satisfaction by using the same concept used above, but this time we will bring
the indifference curve and the budget constraint line together. The consumer will
maximize satisfaction when the budget line is tangential to an indifference curve.
Let us assume we have the following information: a consumer’s budget is $10,
Px=$2/unit, Py=$1/unit, and the indifference curves are IC1, IC2 and IC3. (See Figure 9A). Naturally, the consumer wants to get the highest satisfaction for the money spent. So
let us look at different combinations of goods the consumer can buy with the $10 budget.
Combination P, on indifference curve IC1, can be obtained with the given budget line of
$10.00, but it will give only 75 utils of satisfaction. This is also true for combination R on
IC1. Thus, combinations at points P or R on the budget line will not be acceptable. As
for indifference curve IC3, it is outside of the budget line of $10.00 and therefore must be
rejected also. Only combination Q ( 3 units of X and 4 units of Y) gives the highest
satisfaction, or consumer optimum, of 100 utils, within the budget of $10.00
[(3x$2)+(4x$1)=].
Fig.9-B For Students: Use results from Table 4-B
Y 20 IC1 IC2 IC3
Figure 9-A. Consumer Optimum
Y
10
IC1 IC2 IC3
Units16
P
Units 8
6
Q
4
0
1
2
3
4
140 unitls
100 utils
75 utils
5 X units.
12
210 utils
8
95 utils
4
60 utils
0
1
2
3
4
5 X units.
8
The Indifference Curves
Ch. 7
6. INCOME EFFECT (THE INCOME-CONSUMPTION CURVE) (Tables 8, Fig.10)
When a consumer's income increases and the price of goods remains the same, the
consumer can buy more goods. Let us assume that we are given the following pieces of
information: Budget=$3, Px=$2, Py=$1, and the indifference curves are IC1, IC2 and IC3. To
determine how many units of X and Y the consumer will buy of each product we have to follow
these steps: First, calculate the budget constraint line by dividing the budget by the price of X
and then by the price of Y. This will give us the points where the budget constraint line will cut
the X-axis and Y axis. From Table 8 and Figure 10, we can see that when the budget is $3, the
budget constraint line will touch the X-axis at 1.5 and Y at 3. From Figure 10, we can see that
the budget constraint line is tangential to the indifference curve (IC1) at P. Thus, from Figure
10, we can see (at P) that the consumer will purchase 1 unit of X and 1 unit of Y, spending the
total budget of $3 [($2 x 1)+($1 x 1) =].
The calculation of budget constraint lines for different budgets-- $3, $7.5 and $10 -- is
shown in Table 8. The same information is represented in Figure 10.
Table 8
Calculating the Budget Constraint Lines for Different Budgets.
1-Given 2-Given
3=1/2
4-Given
Price
Quantity
Price
Total
At X-axis
Y($)
Budget ($) X ($)
For Students
5=1/4
Quantity
at Y-axis
3
2
3/2=1.5
1
3/1=3
7.5
2
7.5/2=3.75
1
7.5/1=7.5
10
2
1
From Figure 10, we can see that the budget constraint line for the budget of $7.5 is
tangential to the indifference curve (IC2) at Q, and the budget constraint line for the budget of
$10 is tangential to the indifference curve (IC3) at R. We can also see, from Figure 10, that at
Q, the consumer will purchase 2.5 units of X and 2.5 units of Y. At R, the consumer will
purchase 3 units of X and 4 units of Y.
So, we can see that the consumer will move from combination P to Q to R as his/her
income increases. This movement gives us the income-consumption curve. Table 9 shows
that the consumer spends all of his budget at points P, Q, or R--no more and no less.
So, the Income-Consumption Curve is a set of optimum consumption points that show
how consumption changes when the consumer’s income varies, with the price of goods
staying the same.
Table 9
Calculations Showing the Total Budget Spent at Different Points on the IncomeConsumption Curve for Points P,Q and R from Fig. 10.
1-Given 2-Given 3-Read from IC 4-Given 5-Read from IC 7=(2x3)+ (4x5)=1
6-Given 7-Given
Total
Price
Quantity
Price
Quantity
Indifference
Point Budget ($) X ($)
Curve
Utils
Bought of X
Y($)
Bought of Y Total Budget Spent
P
IC1
3
2
1
1
1
(2x1) + (1x1) =3
75
Q
IC2
7.5
2
2.5
1
2.5
(2x2.5)+(1x2.5)=7.5
100
R
IC3
10
2
3
1
4
(2x3) + (1x4)=10
140
Figure 10. Income-Consumption Curve
Y units 10
Income-Consumption Curve
IC3
7.5
IC2
R
4
3
2.5
140 utils
Q
1
100 utils
IC1 75utils
0
1
1.5
2.5
3
3.75
5 X units.
9
The Indifference Curves
Ch. 7
Income Effect for Normal Goods and Inferior Goods
In Figure 10, we noticed that the consumer bought more of both X and Y as his/her
income increased. As we saw in Chapter 3, goods for which demand increases as income
increases, such as cars or computers, are called normal goods. On the other hand, goods
for which demand decreases as income increases, such as rice and lentils (traditionally
eaten by the poor but often abandoned as daily food when the poor are no longer poor
and can afford alternative foods) are called inferior goods. We can use the concept of
indifference curves to determine which goods are normal or inferior. This is shown in
Figure 11-A and 11- B below.
In Figure 11-A, as the income increases, the consumer buys more of Y but less of X.
Hence, in this case, Y is a normal good and X is an inferior good. In Figure 11-B, as
income increases, the consumer buys more of X and less of Y. In this instance, X is a
normal good and Y is an inferior good.
Fig. 11-A: The Income-Consumption Curve: X
is an inferior good, because less of X is bought;
whereas Y is a normal good, because more Y is
bought as income increases.
Fig. 11-B: The Income-Consumption Curve: X
is a normal good, because more of X is bought;
whereas Y is an inferior good, because less Y
is bought as income increases.
Y units/
Hr.
Y units/
Hr.
Income Consumption Curve
Y3
New Budget Constraint Line
New Budget Constraint Line
Y1
Y2
Y3
Y2
U
Y1
Income
U Consumption
Curve
0 X1
0
X3 X2 X1
X units/hr.
RX2
X3
X units/hr.
To generalize, the slope of the income consumption curve tells us whether the good is
a normal or an inferior good. If the income consumption curve is positive (upward
sloping), then both the goods are normal goods since consumption increases with income
in both cases. However, if the income consumption is negative (downward sloping), then
one good must be an inferior good. As in Figure 11-A, if the slope is more negative
(steeper), then Y would be a normal good and X would be an inferior good. Conversely,
in Figure 11-B, if the slope is less negative (flatter), then X would be a normal good and
Y would be an inferior good.
10
The Indifference Curves
Ch. 7
7. PRICE EFFECT (PRICE-CONSUMPTION CURVE) (Table 10 and Fig. 12)
So far we have seen how a consumer’s behavior changes with change in income.
Now we see how a consumer’s behavior alters when the price of goods changes, with
income staying the same. The first step is to calculate the budget constraint line by
dividing the given budget with the new price of X (See Table 10, column 2). Note that
values in columns 4 and 7 will always be equal to the given budget--in this case, $10.
When the price of X declines and the price of Y stays the same, and the budget is
unchanged, as we saw in Figure 8-B, the new budget line shifts to the right. The next step
is to see where each budget line is tangential to the indifference curves. We can see that
the consumer will consume more of X than before. The consumer's purchase of X will
move from Q1 (where Px=$10) to Q2 (where Px=$4) and to Q3 (where Px=$2), as shown in
Figure 12. When we join the points P, Q, and R, we get the price-consumption curve.
So, the Price-Consumption Curve is a set of optimum consumption points that show
how consumption changes when the price of a product varies, with the consumer’s
budget staying the same.
Table 10 Price-Consumption Curve
1-Given
Point
P=Q1
Q=Q2
R=Q3
3=1/2
Quantity
Bought of
X
4=2x3
Total
Budget
Spent
5-Given
Price
Y
($)
6=1/5
Quantity
Bought of
Y
7=(5x6)=1 or 4
Total
Budget ($)
2-Given
Price
X
($)
10
10
10/10=1
10 x 1 = 10
1
10
(10 x 1) = 10
10
4
10/4=2.5
4 x 2.5 = 10
1
10
(10 x 1) = 10
10
2
10/2=5
2 x 5 = 10
1
10
(10 x 1) =10
Total Budget
Spent
Figure 12 Price-Consumption Curve
Y
10
Units/hr.
8
IC3
IC1
Price-Consumption Curve
IC2
6
P
Q
R
4
2
0
0.5
1
1.5
Px=$10
Q1=10/10=1
2.5
Px=$4
Q2=10/4=2.5
3
4
5 X units/hr.
Px=$2
Q3=10/2=5
11
The Indifference Curves
Ch. 7
8. THE SUBSTITUTION EFFECT (Table 11-A, Figure 13)
Substitution effect: When a consumer buys more units of a cheaper product and
fewer of an expensive one, in such a way that his satisfaction remains unchanged (that is,
he stays on the same indifference curve), we have what is called a substitution effect. In
discussing the substitution effect, we assume that:
i) the consumer’s income remains the same;
ii) the relative prices of the two goods have changed, making one cheaper than the
other;
iii) the increase in price of one good and decrease in price of the second good is such
that the consumer’s choice remains on the same indifference curve.
Bearing the above three points, let us assume that the consumer’s budget is $15,
Px=$7.5, and Py=$1. The first step is to calculate the budget constraint line by dividing
the budget with the Px and Py. The value of Qx we get is 2 [15/7.5], and the value of Qy
is 15 [15/1], as shown in Table 11-A and Figure 13. This budget constraint line is
tangential to the indifference curve at point A, in Figure 13. At that point the consumer
purchases 0.8 units of X and 9 units of Y, spending the total budget of $15 [($7.5 x
0.8)+($1x9)]. These calculations are also shown in Table 11- B.
Now let us assume that the consumer’s budget stays the same at $15, but the price of
X decreases to $3 and the price of Y increases to $2.5. Again, the first step is to calculate
the budget constraint line by dividing the consumer’s budget with the new Px and Py.
From Table 11-A, we can see that the new budget constraint line (gray line) has a value
of Qx=5 [15/3] and Qy=6 [15/2.5]. From Figure 13, we can see that the consumer will
choose combination B on the same indifference curve, purchasing 2.5 units of X and 3
units of Y. Also at B, as at point A, the consumer will spend all his income of $15 [(2.5 x
$3)+(3x$2.5)].
An increase in the purchase of X and a decrease in the purchase of Y, due to change
in relative prices of X and Y, constitutes the substitution effect.
Table 11-A Substitution Effect
Table 11-B
Table 11- A: Calculating the Budget Constraint Points for Table 11-B. Values of Qx and Qy are Read from
the X and Y axes.
the Indifference Curve (IC) from Fig.13.
126-Read
7-From 8-From
Given Given 3=1/2 4-Given 5=1/4
from IC
Point-A Point-B 9=(2x7)+(4x8)
Budget Px($) Qx
Py($)
Total Spent
Qy Read from IC Qx
Qy
Old Budget Line
(Dark Line)
New Budget
Line (Gray Line)
15
7.5
15
3
15/7.5=
2
15/3=
5
1
2.5
15/1=1 Read from A
5
15/2.5
Read from B
=6
0.8
9
15
2.5
3
15
Fig. 13 Substitution Effect: Movement along the same IC with same budget.
Y units
15
12
A
9
6
B
IC1 60 utils
3
0
0.8
2
2.5
4
5 X units.
12
The Indifference Curves
Ch. 7
9. DIFFERENTIATING SUBSTITUTION AND INCOME EFFECT (Figure 14-A)
In reality, the above three assumptions, in section 8 of this chapter, are rarely met.
Prices may change in such a way that the new budget line may not be tangential to the
same indifference curve. So now we are going to look at what happens when the price of
one product decreases and is tangential to a new indifference curve, and then determine
how much more the consumer bought because of the substitution effect and how much
more he or she bought because of real income effect. So, when the price of one product
decreases, the consumer will buy more of that product for two reasons: i) the substitution
effect, and ii) the real income effect.
i) The substitution effect: (Fig 14-A, read from IC1). We have the substitution effect
when the consumer purchases more of the cheaper good than the more expensive one,
while still staying on the same indifference curve (IC1), between A and C (see Figure 14A). In this case the consumer purchases 1.1 more units of X (1.9 - 0.8) because of the
substitution effect.
ii) The real income effect: (Fig. 14-A, read from IC2). With the relative lowering of
the price of a good, the purchasing power of the consumer increases, enabling him to buy
even more of that good. But with income effect, the budget constraint line shifts to a
higher indifference curve (IC2) –see Figure 14-A. Between C and B the consumer will
purchase 0.6 more units of X (2.5-1.9) because of the real income effect.
When the real income effect is subtracted from the total increase in demand, we
have the substitution effect. In other words, price effect is equal to substitution effect plus
real income effect.
PRICE EFFECT = SUBSTITUTION EFFECT + REAL INCOME EFFECT
Fig. 14-A. Substitution and Income Effect
Y 15
Fig. 14-B. Substitution and Income Effect
Step 3 Y 15
Step1
Step 2
A
B
12
10
A
10
B
C
6
C
6
IC2
3
IC1
0
0.8
1.9
2.5 3.3
Substitution Income
Effect
Effect
IC2
IC1
3
5 X
0
0.8
1.9
2.5 3.3
5 X
Substitution Income (Step 4)
Effect
Effect
We can use the following steps to determine the substitution and income effect when
there is a decrease in price of one product--for example X in this case. (See Figure 14-B).
Step 1) Determine the original quantity purchased (Fig. 14-B): Where the first budget
constraint line cuts the IC1, we find the original quantity bought of X. In this case, it is
point A, and the consumer will purchase a total of 0.8 units of X.
Step 2) Determine the total increase in quantity purchased (Fig. 14-B): Draw a new
budget constraint line with the reduced price of X which, in this case, decreased from
$7.5 to $3 per unit. See where this new budget constraint line (gray line) is tangential to
the new indifference curve, (IC2). (The second budget constraint line should already be
given on the graph). This gives us point B. This means the consumer will now purchase a
total of 2.5 units of X, or 1.7 more units (2.5 - 0.8) of X than before.
13
The Indifference Curves
Ch. 7
Step 3): Determine the substitution effect (Fig. 14-B): Draw a parallel (imagined
reduction in the consumer budget) line to the left of the new budget line drawn earlier,
until it just touches the first IC1. In other words, we are reducing the consumer’s budget.
In this case, the consumer’s budget was reduced from $15 to $10, or by 33.33%. We can
determine that the budget was reduced to $10 by seeing where the parallel line drawn
cuts the X-axis. We see that it cuts the X-axis at 3.3 units. So, 3.3 units of X, multiplied
by $3/unit (new price of X), equals $10 (except for the rounding error). We could have
also determined the reduced budget by seeing where the new parallel line cuts the Y-axis.
Since the reduced budget constraint line meets the Y-axis at 10, and since the price of Y is
$1/unit, we see that the reduced budget is 10 x $1= $10. So either way, using information
from the X or Y-axis, we arrive at the same answer of $10 for the reduced budget.
The new parallel line cuts the old IC1 at C. Remember that when the new budget
line is tangential to the same indifference curve, the difference in quantities of the
product we buy is due to the substitution effect. So in this case, the additional amount
purchased due to the substitution effect, is 1.1 units (1.9- 0.8) of X.
SUBSTITUTION EFFECT = PRICE EFFECT – REAL INCOME EFFECT
Step 4) Determine the real income effect (Fig. 14-B): the income effect is determined
by subtracting the substitution effect from the total additional amount. In this case it is B
minus C or 0.6 units (2.5-1.9) of X.
REAL INCOME EFFECT = PRICE EFFECT – SUBSTITUTION EFFECT
10. DIFFERENT RATES OF MARGINAL RATES OF SUBSTITUTION (MRS)
The consumer will buy more units of a cheaper product and fewer of an expensive
one. We can classify the Indifference Curves into four types:
a) constant marginal rate of substitution (also called perfect substitutes),
b) zero marginal rate of substitution (also called perfect complements),
c) decreasing marginal rate of substitution, and
d) increasing marginal rate of substitution.
a)
Constant Marginal Rate Of Substitution: (Perfect Substitutes) (Table 12 and
Fig. 15)
If two goods--say a CD made by Sony (S) and a CD made by Memorex (M)—are
perfect substitutes, this means that a consumer would choose one just as readily as the
other. The choice of the consumer is shown in Table 12. From column 3 in Table 12, we
can see that when two goods are perfect substitutes, the marginal rate of substitution
(MRS) between those goods must be constant. (See Figure 15.) In this example, the MRS
(marginal rate of substitution) is 1. The marginal rate of substitution need not always be
one; for example, if one piece of cake is three times the size of the other, but they are the
same type of cake, the MRS will be three. The important point is that, for perfect
substitutes, the MRS is constant.
Fig. 15. Perfect Substitutes.
Table 12. Perfect Substitutes
1-Given
2-Given
Sony
CD’s/Q
3-Given
Memorex
CD’s/Q
A
0
>
1
>
2
>
3
3
>
2
>
1
>
0
B
C
D
3=(∆ in 3)/(∆ in 2)
Marginal Rate of
Substitution
(3-2)/(1-0)=1
S CD’s/ 3
Units
D
C
2
B
1
A
(2-1)/(2-1)=1
(1-0)/(3-2)=1
0
1
2
3 M CD’s/
units
14
The Indifference Curves
Ch. 7
b) Zero Marginal Rate Of Substitution: (Perfect Complements) (Table 13 and Fig.
16)
Some goods go hand in hand, so they must be used in a certain combination (ratio)
for them to give any satisfaction. Examples include a second chopstick to use with the
first, a flashlight and a bulb, a pair of gloves, and so on.
For two goods to be perfect complements, the MRS for both must be zero, as is the
case for flashlights (MRSLB) and bulbs (MRS BL) in Table 13-A and 13-B. For example, if
a man has one flashlight, then he needs only one bulb. This pair of flashlight and bulb
will give him a certain amount of satisfaction; say point A, of 65 utils (Figure 16). But if
he has one flashlight and 2 (Point B) or 3 bulbs (Point C), he will have no more
satisfaction than if he had one of each. The man is completely content with only one
bulb, so long as he also has a flashlight; he does not desire any more bulbs for the
moment. Of course, he would have the same satisfaction of 65 utils if he had only 1 bulb
and 2 flashlights (Point D). But on the other hand, if he had 2 flashlights and 2 bulbs, he
would have a higher satisfaction of 95 utils on IC2, Point E on IC2. Similarly, a man
having 2 flashlights and 3 bulbs (Point F) gets no more satisfaction than if he had 2
bulbs, as he would still be on IC2.
Table 13-A. Perfect Complements: MRS of
Flashlight and Bulb.
1Given
A
B
C
2-Given
Flashlig
ht/Q
1
>
2
>
3
3-Given
3=(∆ in 3)/(∆ in 2)
Bulb/Q
Marginal Rate of
Substitution
(MRSLB)
1
>
1
>
1
Figure 16. Perfect Complements
Bulbs 5
Units 4
IC1 IC2
3
C
F
2
B
E
A
(1-1)/(2-1)=0/1=0
1:0
1
(1-1)/(3-2)=0/1=0
1:0
0
1
2
IC2(95 utils)
IC1 (65 utils)
D
3 flashlights/units
Table 13-B. Perfect Complements: MRS of Bulb
to Flashlight
1Given
2Given
Bulb/Q
A
B
C
1
>
2
>
3
3Given
Flashlig
ht/Q
1
>
1
>
1
3=(∆ in 3)/(∆ in 2)
Marginal Rate of
Substitution (MRS BL)
(1-1)/(2-1)=0/1=0
1:0
(1-1)/(3-2)=0/1=0
1:0
c) Decreasing Marginal Rate of Substitution (Figure 17)
The marginal rate of substitution is equal to the absolute slope of the budget
constraint line when the budget constraint line is tangential to the indifference curve. In
Figure 17, at point A, MRS is 7.5 [15/2], which means that for each additional unit of X,
a person is willing to give up 7.5 units of Y. At Point B, MRS is 1.2 [6/5], which means
that a person is willing to give up only 1.2 units of X for one unit of Y. A diminishing
marginal rate of substitution takes place with most goods, as shown in Figure 17.
15
The Indifference Curves
Ch. 7
Fig. 17 Diminishing Marginal Rate of Substitution (MRS).
Y units 15
IC1 60 utils
12
9
7.5
6
A: MRS=7.5/ 1=7.5
B: MRS=6/5=1.2
3
0
1
2
2.5
5 X units.
4
d) Increasing marginal rate of substitution (Table 17, Fig. 18)
This is a condition that can never occur. In Figure 18, there are two indifference
curves, IC1 (75 utils) and IC2 (100 utils). Combination C, on IC1 and the budget
constraint line, yields only 75 utils of satisfaction. The consumer would maximize
satisfaction on the indifference curve IC2 with 100 utils, but would consume only the
good X and none of Y. No consumer uses only one product; so, an increasing marginal
rate of substitution never takes place.
Let us look at Figure 18. The budget constraint line is given by line BC. The budget
constraint line BC is tangential to IC1 at A, which gives less satisfaction than IC2, where
the line BC touches either X at 3 and Y is zero, or at B where Y is 16 and X is zero. With
the given budget, satisfaction is maximized by either consuming only 3 units of X and
none of Y, or 16 units of Y and none of X. This we know cannot be true. It’s as if one
were to spend all $10 on coffee and nothing on cake. We also call this (the increasing
marginal rate) the corner solution, because the choice the consumer makes is just to one
corner. We can look at Table 17, where we see that the marginal rate of substitution
increases. That is, for each additional unit of X, a consumer is willing to give up more
and more of Y, which, as we saw at the start of this section, is not possible.
Table 17: Increasing Marginal Rate of Substitution
1Given
A
B
C
D
2Given
3Given
Q of X
Q of Y
0
>
1
>
2
16
>
14
>
11
3
0
3=(∆ in 3)/(∆ in 2)
Marginal Rate of Substitution
(MRS XY)
Fig. 18. Increasing Marginal Rate of
Substitution
Y 16
IC2 (100 utils)
12
(16-14)/(1-0)=2/1=6
1:2
8
(14-11)/(2-1)=13/1=3
1:3
4
(11-0)/(3-2)= 11/1=11
1:11
A
(75 utils) IC1
C
0
1
2
3
4 X
16
The Indifference Curves
Ch. 7
11. THE INDIFFERENCE CURVE AND THE DEMAND CURVE
Indifference curves can also be used to derive the demand curve for a product. In
section 7 of this appendix, we saw how the budget constraint shifts to the right when the
price of X decreased, and because of this the consumer purchased more of X with the
decline in price. When the Px=$10/ unit, the consumer purchased 0.5 units. When Px=$4,
the quantity purchased was 1.5 units, and when Px=$2, the quantity was 3 units.
We can chart this increase in number of units purchased, along with the decrease in
the price of X, on a graph, which will give us the demand curve for X, as shown in
Figure 19-B.
Figure 19-A. Using Indifference Curves to Derive the Demand Curve
Y
10
IC3
8
.
IC1
Price-Consumption
Curve
IC2
P
Q
R
4
2
0
0.5
1.5
3
Fig. 19-B
Price 10
/X
4
5 X units/hr.
Fig. 19-B. The Demand Curve
P
8
6
4
Demand Curve
2
0
0.5
1
1.5
2
3
4
5 QX
Hence this way we get the demand curve from the indifference curves.