M.Phil. in Economics: International Trade 2009-10
Problem Set II, Hilary Term 2010
1. Consider the model of homogeneous-…rm monopolistic competition from
Krugman (1979) as discussed in class. Explore the e¤ects of a uniform increase
in the labour supply in each country on: …rm scale, real wages, variety, trade,
and welfare.
2. Consider the model of heterogeneous-…rm monopolistic competition from
Melitz (2003) as discussed in class. Show that the ZCP (Zero Cuto¤ Pro…t) locus
is horizontal when the distribution of …rms’ productivities is Pareto: G (') =
k
b
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. Explore the implications for the e¤ects of moving from autarky to
'
free trade on the equilibrium distributions of home and export sales across …rms
3. Consider a two-country world in which n home …rms, each with unit cost
c, and n foreign …rms, each with unit cost c , engage in Cournot competition,
with national markets segmented from each other (so the same prices need not
prevail at home and abroad). All …rms (both home and foreign) face a tari¤ t on
their export sales. Solve for equilibrium sales in the home and foreign markets.
When will reciprocal dumping occur? How are home pro…ts a¤ected as t falls
from the prohibitive level towards zero?
4. (M.Phil. 2008) Consider a two-country world with a continuum of sectors
in each of which n home …rms, each with unit cost c, and n foreign …rms,
each with unit cost c , engage in Cournot competition on an integrated world
market.
(a) By calculating the oligopoly equilibrium in a typical sector, illustrate
the combinations of c and c that are consistent with …rms in each country
producing positive outputs.
(b) Let (n; n ; c; c ) and (n; n ; c; c ) denote the pro…ts of a home and
foreign …rm respectively, as functions of the number of active …rms at home and
abroad and of their unit costs. Suppose that a cross-border merger, in which
a foreign …rm acquires a home …rm, will occur if the resulting change in the
foreign …rm’s pro…ts exceeds the initial pro…ts of the home …rm; i.e., if:
GF H (n; n ; c; c )
(n; n ; c; c )
(n; n ; c; c ) > 0
where:
(n; n ; c; c )
(n 1; n ; c; c )
(n; n ; c; c ):
Show that such mergers are pro…table for a subset of the values of c and
c consistent with positive output in both countries in the absence of mergers.
What does this imply about the correlation between the patterns of international
trade and foreign direct investment?
(c) What central features of real-world mergers are absent from this model
and how might you amend it to take them into account?
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