ECO 364: International Trade
Problem Set 4
Due date: 5:00 PM, 22 November 2018
Trade and the Gains from Variety
Consider the monopolistic competition model of trade studied in class. Suppose that
there are M ≥ 2 countries, and all countries are identical. In each country, demand for each �rm’s product is given by:
Q = S
[ 1
N − r
( P − P̄
)] where S denotes the size of the market in each country, N denotes the number of �rms
producing, and P̄ denotes the average price charged by �rms in the market. All �rms
produce with the same technology, which features a constant marginal cost c and a �xed
cost of production f , such that the total cost for a �rm producing Q units of output is:
TC = cQ+ f
In what follows, assume that the parameter values are:
S = 10
r = 0.01
c = 1
f = 0.1
First, suppose that each country is in autarky, and take the number of �rms N as given.
(a) Write down the pro�t-maximization problem for each �rm (assume that �rms choose
output Q).
(b) What output level does each �rm choose? What is the corresponding price?
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(c) What are operating pro�ts π (revenue net of total costs) for each �rm?
Now suppose that there is free entry, so that in equilibrium, all �rms earn zero operating
pro�ts.
(d) What must the number of �rms N be given free entry?
Now suppose that the M countries sign a trade agreement that allows each country to trade
freely with all the other countries. The size of the market for �rms in any one country is
hence MS instead of S.
(e) What must the total number of �rms N be given free entry under trade?
(f) How does the total number of �rms N vary with the number of countries M? Explain
why N varies with M in this way.
(g) How do prices P and output per �rm Q vary with the number of countriesM? Explain
why P and Q vary with M in this way.
(h) How does the number of �rms per country N/M vary with the number of counrtries
M? Explain why N/M varies with M in this way.
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O�shoring
Consider the model of o�shoring studied in class. There is a single �nal good that is
produced by assembling a continuum of intermediate inputs indexed by a ∈ [0, 1]. The total cost of producing the �nal good is:
logP =
∫ 1 0
log p (a) da
where p (a) is the cost of producing intermediate good a. Each intermediate can either be
produced domestically in Home or o�shored to Foreign.
If intermediate a is produced in Home, its cost of production is:
pH (a) = ( wH )1−a (
rH )a
where wH and rH are the unskilled and skilled wage in Home respectively. (Note that the
index of the good is equal to its skill intensity, a.) Alternatively, if intermediate a is o�shored
to Foreign, its cost of production is:
pF (a) = t ( wF )1−a (
rF )a
where wF and rF are the unskilled and skilled wage in Foreign respectively, and t is the cost
of o�shoring. In equilibrium, intermediate a is produced in the lowest-cost location, and
hence:
p (a) = min { pH (a) , pF (a)
} In what follows, assume that wages are �xed, and that the parameter values are:
logwH = 6
log rH = 10
logwF = 1
log rF = 9
log t = 4
(a) Which intermediates are o�shored to Foreign and which are produced in Home? (Hint:
solve for the intermediate a∗ such that pH (a∗) = pF (a∗) .)
(b) What is the cost of producing the �nal good, logP?
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Now suppose that the cost of o�shoring falls, such that:
log t = 3
(c) Which intermediates are now o�shored to Foreign and which are produced in Home?
(d) What is the cost of producing the �nal good, logP? How does this compare to your
answer to part (b)?
Now suppose that wages can change in response to the fall in the cost of o�shoring.
(e) How would you expect the relative wage of skilled vs. unskilled workers to change in
Home and Foreign? Explain your answer.
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