How w’d you expect the relative wage of skilled vs. unskilled workers to change

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?

1

(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.

2

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?

3

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.

4

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