Exercises Lecture 5: Economies of Scale, Trade and Imperfect Competition
(From Textbook, Chapter 7 )
1. Evaluate the relative importance of economies of scale and comparative advantage
in causing the following:
(a) Most of the world’s aluminum is smelted in Norway or Canada.
(b) Half of the world’s large jet aircraft are assembled in Seattle.
(c) Most semiconductors are manufactured in either the United States or Japan.
(d) Most Scotch whiskey comes from Scotland.
(e) Much of the world’s best wine comes from France.
2. Consider a situation similar to that in Figure 7-3 in the textbook (or slide number
30 in the lecture of October 9th), where two countries that produce a good (buttons)
are subject to forward-falling supply curves.
In this case assume that the two countries have the same costs, so their supply curves
are identical.
(a) Describe the pattern of international specialization and trade. What would
determine who produces the good?
(b) Describe the benefits of international trade in this case. Do they accrue only to
the country that gets the industry?
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SOLUTIONS
1. (a) The fact that there are relatively few locations for this kind of production
suggests that it is characterized by the presence of external economies of scale.
If these operations are large, there may also be large internal economies of scale
in production.
(b) Since economies of scale are significant in airplane production, it tends to be
done by a small number of (imperfectly competitive) firms in a limited number
of locations. One of these location is exactly Seattle, where Boeing produces.
(c) The same reasoning as answer (b) applies: external economies of scale are
significant in semiconductor production, thus semiconductor industries tend to
be concentrated in certain geographic locations.
Moreover, if, for some historical reason, a semiconductor is established in
a specific location, the export of semiconductors by that country is due to
economies of scale and not comparative advantage.
(d) Scotch whiskey can only come from Scotland because the production requires
a particular technique known to skilled distillers who are concentrated in the
region.
In addition, soil and climactic conditions are favorable for grains used in local
scotch production. These arguments reflect comparative advantage rather than
the presence of external economies.
(e) Similarly to the previous answer, France has a particular blend of climatic
conditions and land that is difficult to reproduce elsewhere. This generates its
comparative advantage in wine production.
2. To make things simpler, we can assume that the two countries are identical, so they
have completely identical curves.
(a) If one country starts out as a producer of a good because, say, it has a head
start as a consequence of an historical accident, then all production will occur
in that country and it will export to the rest of the world.
(b) Consumers in both countries will pay a lower price for the good when all
production is located in a single country so as to maximize external economies.
The second part of the answer is driven by the same (standard) argument
explained during the lecture: increased production as a result of trade leads to
a price of the good that is lower than the price before trade in either country.
The benefits of international trade will therefore not be limited to the country
that gets the industry because the consumers in both countries can profit from
such lower price.
2
Numerical Example (from KOM, Chapter 8) & Exercise
Recall the following equations:
– Demand that each firm faces (I eliminate the i for notational purposes):
Q=S
h1
n
i
− b(p − p̄)
(1)
– AC Curve:
AC =
F
nF
+c=
+c
Q
S
as Q = S/n
(2)
– PP Curve:
P =c+
1
bn
(3)
By assuming that b = 1/30, F = 750 and c = 5, we have to find the equilibrium of the
model.
From eq. (1), we obtain:
Q=S
h1
n
−
i
1
(p − p̄)
30
and from eq. (2):
AC =
750
750
n
+5=
= 750
Q
(S/n)
S
as Q = S/n,
while from eq. (3):
P =5+
30
n
The solution can be computed both algebraically and graphically.
Algebraically, from P = AC (the intersection of CC and P P ), obtain:
AC = 750
n
30
+5=5+
=P
S
n
Hence:
3
750
n
30
+ 5 = 5 +
=P
S
n
⇒
⇒
750
r
30
S
n =
750
2
⇒
n=
n
30
=
S
n
30
S
750
which is the expression that gives us the number of firms.
Assume now that there are 2 countries, H and F , which are identical in everything, except
for the size S of their markets.
Sizes are given, respectively, by: SH = 900 and SF = 1600.
This implies that, for H:
n2H =
30
900 = 36
750
⇒
nH = 6
and
PH = ACH = 5 +
30
= 10
6
while for F :
n2F =
30
1600 = 64
750
⇒
nF = 8
and
PF = ACF = 5 +
30
= 8.75
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Graphically, the mkt equilibrium in the absence of trade is shown in Fig. 1
4
CHAPTER 8 Firms in the Global Economy
Price per auto,
in thousands of dollars
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
1 2 3 4 5
Price per auto,
in thousands of dollars
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
1 2 3 4 5
CC
PP
6
7
8
9
10 11 12
Number
of firms, n
(a) Home
5
Equilibrium in the Automobile Market
PP
6
CC
PP
8
(c) Integrated
Figure 8-5
CC
7
8
(b) Foreign
Price per auto,
Figure 1
in thousands of dollars
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
1 2 3 4 5 6 7
9
167
10 11 12
Number
of firms, n
9
10 11 12
Number
of firms, n
Suppose now that the two countries decide to integrate and to create a free-trade zone.
We want to determine how the previous equilibrium modifies and how it would be under
this hypothesis.
If there is an integrated market, then total market size S is given by:
S = SH + SF = 900 + 1600 = 2500 ,
thus the new equilibrium will be simply given by:
n2 =
30
2500 = 100
750
⇒
n = 10
and
P = AC = 5 +
which graphically is shown in Fig. 2.
6
30
=8
10
20
18
16
14
12
10
8
6
4
CC
PP
2
3
4
5
6
7
8
9
10 11 12
Number
of firms, n
1
2
3
4
5
(a) Home
7
8
9
1
(b) Foreign
Price per auto,
in thousands of dollars
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
1 2 3 4 5
8-5
6
CC
PP
6
7
8
9
10 11 12
Number
of firms, n
(c) Integrated
Figure 2
um in the Automobile Market
Home market: With a market size of 900,000 automobiles, Home’s equilibrium, determined by t
ion of the PP and CC curves, occurs with six firms and an industry price of $10,000 per auto. (b
market: With a market size of 1.6 million automobiles, Foreign’s equilibrium occurs with eight fi
try price of $8,750 per auto. (c) The combined market: Integrating the two markets creates a ma
on autos. This market supports ten firms, and the price of an auto is only $8,000.
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Exercise
Suppose the two countries previously considered were to integrate their market with a
third country Z which has a market size SZ given by SZ = 3125.
Find the number of firms, the output per firm and the price in the new integrated market
after trade.
Solution
To find the new equilibrium, it suffice to calculate the market size of the integrated market.
In this case, we have:
S = SH + SF + SZ = 900 + 1600 + 3125 = 5625 ,
thus the number of firms is given by:
n2 =
30
5625 = 225
750
⇒
n = 15
Using the price equation and the fact that b = 1/30, c = 5, you can easily find that
P =
1
30
+c=
+5=7
bn
15
Finally, output per firm can be computed using Q = S/n:
Q=
5625
S
=
= 375.
n
15
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Graphing Problem
C, P
6
A
A
A
A
A
10
@
@
@
@
@
@
A
A
A
A
@
@
@
A
A
A
8
@
@
@
A
A
A
@
@
@
A
A
A
MC
@
@
@
A
A
A
5
@
@
@
@
@
A
A
A
@
@
A
A
A
@
@
@
@
@
@
A
A
A
A
A
A
A
A
A
A
A MR
A
A
D ∗ = M R∗
@
@
@
@
@
@
@D
@
@
-
4
5
10
Q
Figure 3
1. Consider Fig. 3, which represents the demand and cost functions of a monopolist
firm.
If it was unable to export and constrained by its domestic market, what quantity
would it sell at what price?
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2. Assume that the monopolist discovers that it can export as much as it likes of
its product at the world price P ∗ = 5. How much product will the monopolist
produce/sell? At what price?
3. Given the opportunity to sell at world prices, what is the marginal (opportunity)
cost of selling one unit of product domestically?
4. While selling exports it would also maximize its domestic sales. Hence, how much
product would the firm sell domestically? At what price?
Answers
1. Given the intersection of the MC with the MR, the monopolist will sell 5 units of
product at the price P = 8.
2. In this case you have to consider that the optimal strategy for the firm is to equate
MC and MR on both markets, that is: M R∗ = P ∗ = M C , where ∗ stands for
international/foreign.
From this condition, you easily obtain that total production is Q = 10, which is sold
at the world price P ∗ = 5.
3. The marginal (opportunity) cost is 5.
4. To determine production at Home of the monopolist, you just have to apply the
condition M R∗ = M R.
From this, it follows that production at Home is Q = 4, which is sold at the price
P = 10.
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