Introduction to Industrial Organization,2nd Ed
Solutions to End-of-Chapter Exercises
Lu´ıs Cabral
This draft: March 2017
1 Introduction
1.1. Competition and performance.Empirical evidence from a sample of more
than 600 UK firms indicates that, controlling for the quantity of inputs (that is, taking
into account the quantity of inputs), firm output is increasing in the number of
competitors and decreasing in market share and industry concentration.1 How do
these results relate to the ideas presented in this chapter?
Answer: In Section 1.2, I argued that one of the implications of market power
is the decline of productive efficiency. Controlling for input levels, the level of
output is a measure of productive efficiency. The number of competitors and
the degree of concentration are measures of the degree of competition
(concentration is an inverse indicator). The empirical evidence from UK firms is
therefore consistent with the view presented in the text.
,2 Consumers
2.1. Fruit salad. Adam and Barbara are big fruit salad fans (and both agree
that the more the better). However, their tastes differ regarding the way the
salad is made. For Adam, for each apple you throw in, there should be one and
only one banana (if you give him more than one banana, he will throw it way).
For Barbara, as long at it’s fruit, it doesn’t matter; in other words, all that counts
is the number of pieces of fruit.
(a) Show what Adam’s and Barbara’s indifference curves look like.
Answer: Figure 2.1 depicts Adam’s and Barbara’s indifference curves (left
and right panels, respectively).
(b) Are apples and bananas substitutes or complements?
Answer: For Adam, apples and bananas are perfect complements; for Barbara, perfect
substitutes.
2.2. Village microbrew. Village microbrew raised its price from $10 to $12 a
case (wholesale). As a result, sales dropped from 10,500 to 8,100 (in units). Based
on your estimate of the demand elasticity, what percent change in sales would
you predict if price were cut from $10 to $9? What demand level would this
correspond to?
Figure 2.1
Indifference curves: Adam and
Barbara
bananas bananas
U =1 U =2
3 3
...... ...... ...... ...... ...... ...... ...... ...... ..... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ..
.
....
. 3 U =3
..
.. .
...
...
....
....
...
....
...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... .... ... ..
.. ..
.
... .
..... ...
. .
...
. ...
.
.
... ...
.
..... ..
,2 2
1 1
appl apples
es
1 2 1 2
3 3
4
, Answer: We can approximate it by the “change formula,”
∆q p 10, 500 − 8, 100 12
ϵ≈ = = −1.77
∆p q 10 − 8, 100
12
This is approximate, since we’re using discrete changes. If we assume that the
elasticity of demand is constant then we could get an exact solution by using the
log formula:
∆ log q log 10500 − log 8100
ϵ= = = −1.42
∆ log p log 10 − log 12
Did revenue rise or fall? Since ϵ < −1, the increase in prices led to an overall fall in
revenue. (If you want to make sure, then calculate the revenues before and after
the price change.) If the elasticity is constant, what is the demand at $9? If the
elasticity is constant then the log formula calculates the elasticity exactly and in
addition we know that:
log 10500 − log q9
=−
1.4
log 10 − log 9
2
where q9 is the demand when the price is $9 per case, so (after a little bit of
algebraic manipulation)
10
q 9= exp log 10500 + 1.42 log = 12195
9
With constant demand elasticity, the percent variation method only gives an
approximation of the value of demand elasticity. Moreover, estimating
demand for a different price level will give a different value than the log
formula. Specifically, the demand estimate when price is $9 is given by
q9 = 10500 1 + (−1.77) × (−10%) = 12358
since the drop in price from 10 to 9 corresponds to a −10% variation
2.3. Demand elasticity. Based on the values in Table 3.2, provide an
estimate of the impact on sales revenues of a 10% increase in each product’s
price.
Answer: Revenue is given by R = p × q. Differentiating, we get
dR = dp q + p dq
Dividing by dR q p
R, = dp +
R d
qR
R
Since R = p q and ϵ = dq/dp p/q, we have R
dR q
= dp
R
5
Solutions to End-of-Chapter Exercises
Lu´ıs Cabral
This draft: March 2017
1 Introduction
1.1. Competition and performance.Empirical evidence from a sample of more
than 600 UK firms indicates that, controlling for the quantity of inputs (that is, taking
into account the quantity of inputs), firm output is increasing in the number of
competitors and decreasing in market share and industry concentration.1 How do
these results relate to the ideas presented in this chapter?
Answer: In Section 1.2, I argued that one of the implications of market power
is the decline of productive efficiency. Controlling for input levels, the level of
output is a measure of productive efficiency. The number of competitors and
the degree of concentration are measures of the degree of competition
(concentration is an inverse indicator). The empirical evidence from UK firms is
therefore consistent with the view presented in the text.
,2 Consumers
2.1. Fruit salad. Adam and Barbara are big fruit salad fans (and both agree
that the more the better). However, their tastes differ regarding the way the
salad is made. For Adam, for each apple you throw in, there should be one and
only one banana (if you give him more than one banana, he will throw it way).
For Barbara, as long at it’s fruit, it doesn’t matter; in other words, all that counts
is the number of pieces of fruit.
(a) Show what Adam’s and Barbara’s indifference curves look like.
Answer: Figure 2.1 depicts Adam’s and Barbara’s indifference curves (left
and right panels, respectively).
(b) Are apples and bananas substitutes or complements?
Answer: For Adam, apples and bananas are perfect complements; for Barbara, perfect
substitutes.
2.2. Village microbrew. Village microbrew raised its price from $10 to $12 a
case (wholesale). As a result, sales dropped from 10,500 to 8,100 (in units). Based
on your estimate of the demand elasticity, what percent change in sales would
you predict if price were cut from $10 to $9? What demand level would this
correspond to?
Figure 2.1
Indifference curves: Adam and
Barbara
bananas bananas
U =1 U =2
3 3
...... ...... ...... ...... ...... ...... ...... ...... ..... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ..
.
....
. 3 U =3
..
.. .
...
...
....
....
...
....
...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... .... ... ..
.. ..
.
... .
..... ...
. .
...
. ...
.
.
... ...
.
..... ..
,2 2
1 1
appl apples
es
1 2 1 2
3 3
4
, Answer: We can approximate it by the “change formula,”
∆q p 10, 500 − 8, 100 12
ϵ≈ = = −1.77
∆p q 10 − 8, 100
12
This is approximate, since we’re using discrete changes. If we assume that the
elasticity of demand is constant then we could get an exact solution by using the
log formula:
∆ log q log 10500 − log 8100
ϵ= = = −1.42
∆ log p log 10 − log 12
Did revenue rise or fall? Since ϵ < −1, the increase in prices led to an overall fall in
revenue. (If you want to make sure, then calculate the revenues before and after
the price change.) If the elasticity is constant, what is the demand at $9? If the
elasticity is constant then the log formula calculates the elasticity exactly and in
addition we know that:
log 10500 − log q9
=−
1.4
log 10 − log 9
2
where q9 is the demand when the price is $9 per case, so (after a little bit of
algebraic manipulation)
10
q 9= exp log 10500 + 1.42 log = 12195
9
With constant demand elasticity, the percent variation method only gives an
approximation of the value of demand elasticity. Moreover, estimating
demand for a different price level will give a different value than the log
formula. Specifically, the demand estimate when price is $9 is given by
q9 = 10500 1 + (−1.77) × (−10%) = 12358
since the drop in price from 10 to 9 corresponds to a −10% variation
2.3. Demand elasticity. Based on the values in Table 3.2, provide an
estimate of the impact on sales revenues of a 10% increase in each product’s
price.
Answer: Revenue is given by R = p × q. Differentiating, we get
dR = dp q + p dq
Dividing by dR q p
R, = dp +
R d
qR
R
Since R = p q and ϵ = dq/dp p/q, we have R
dR q
= dp
R
5
