Foreign Direct Investment and the Single Market

Assume specifically that the fixed costs of locating a plant differ between union
countries. Let f(i,φ) be the fixed cost of locating in country i, where φ is a shift parameter.
By convention, and without loss of generality, assume that f is increasing both in i (so the
countries are ordered by fixed cost) and in φ. The form of f is otherwise completely general,
but a simple specification which is helpful to fix ideas is: f(i,φ)=w_iφ, where φ is the level of
labour input needed to operate a plant wherever it is located, and w_i, increasing in i, is the
wage in country i.

Consider first the case where internal and external barriers are equal. Suppose the
multinational has already established plants in m-1 union countries (where m may equal
anything between 1 and n). The gain in profits from establishing one additional plant may
then be written as follows:

_π⅛ ₌ ∏⅛-l₊γ[t∕(_m,φ)] _w = l₅n               ⁽³⁶⁾

Here γ(t,f), the gain from tariff-jumping into an individual union country, is as defined in (3).
However, unlike in earlier sections, it varies with the country under consideration. Setting
it equal to zero, we can solve for the threshold value of the shift parameter in fixed costs at
which it is just profitable to set up a plant in country m:

γ[r,∕(zn,φ)]=O     (3 φ = φ(r,m),     w=l,..n             (37)

+ -

The threshold value of φ is increasing in t, since a higher external tariff increases the gains
from tariff-jumping, requiring a compensating rise in φ to leave the multinational indifferent
about locating in country m. It is also decreasing in m, since locating in a country with a
higher fixed cost clearly reduces profits, and a uniform reduction in fixed costs is needed if
that country is to remain marginal for the multinational. These relationships are indicated by

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