1. No category

Monopolistic Competition and Trade∗
Luc Hens
April 1, 2015
Krugman et al. (2015, pp. 200–210) introduce a model of monopolistic competition and trade. This handout gives some details on the numerical example
as we developed it in class.
Each firm has the same total cost function:
C =F +c×Q
The linear total cost function implies that the average cost falls as the firm’s
output increases:
F
+c
AC =
Q
That is, each firm has internal economies of scale. Also assume that each firm
has the same demand schedule:
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Q=S×
− b × (P − P )
n
The demand schedule implies that, when all firms charge the same price (P =
P ), they each sell 1/n of the market size:
Q=
S
n
This implies that the average cost as a function of the number of firms (CC
curve) is given by the equation
AC =
F
×n+c
S
Prices are set as variable cost plus a mark-up, and the markup gets smaller
when there is more competition (price-setting curve PP ):
P =c+
1
b×n
In the numerical example, the fixed cost (F ) is € 750 000 000, the price sensitivity (b) is 1/€ 30 000, and the marginal cost (c) is € 5 000. Home (France) has a
market size (S) of 900 000 cars per year, and Foreign (Germany) has a market
size of 1 600 000 cars per year. The integrated market of France and Germany
∗ Handout
for Chapter 8 in Krugman et al. (2015).
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combined (EU-2) has a market size of 900 000 + 1 600 000 = 2 500 000 cars per
year. Using this information, the average cost curves become:
AC (France)
=
AC (Germany)
=
AC (EU-2)
=
750 000 000
× n + 5 000 ≈ 833n + 5 000
900 000
750 000 000
× n + 5 000 ≈ 469n + 5 000
1 600 000
750 000 000
× n + 5 000 = 300n + 5 000
2 500 000
All three markets have the same price-setting curve:
P =c+
30 000
1
= 5000 +
b×n
n
Table 1 shows price and average cost for different values of n (the number of
firms in each market). Use a calculator or a spreadsheet program to verify the
values in the table. Figure 1 shows the curves and the corresponding equilibria
(cf. figure 8-5 in Krugman et al. (2015, p. 208)). You should be able to plot the
curves on scale on squared paper. The document with R scripts on the course
web site has a script to generate table 1 and figure 1.
Table 1: The automobile market in Home, Foreign, and the integrated market
n
1
2
3
4
5
6
7
8
9
10
11
12
P
€35 000
20 000
15 000
12 500
11 000
10 000
9 286
8 750
8 333
8 000
7 727
7 500
AC (France)
€5 833
6 667
7 500
8 333
9 167
10 000
10 833
11 667
12 500
13 333
14 167
15 000
AC (Germany)
€5 469
5 938
6 406
6 875
7 344
7 813
8 281
8 750
9 218
9 688
10 156
10 625
AC (EU-2)
€5 300
5 600
5 900
6 200
6 500
6 800
7 100
7 400
7 700
8 000
8 300
8 600
References
Krugman, P. R., Obstfeld, M., and Melitz, M. J. (2015). International Economics: Theory and Policy. Pearson Education, Harlow, 10th edition.
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Figure 1: The automobile market in Home, Foreign, and the integrated market
Price
14000
Average cost (France)
Average cost (Germany)
12000
Price, Average cost (euro)
10000
Average cost (EU-2)
8000
6000
4000
2000
0
0
2
4
6
8
Number of firms
3
10
12
14