Foreign Direct Investment and the Single Market

markets. So, in Figure 3, the F1 region expands to its maximum extent relative to the X and
O regions. Moreover, there are now no gains to jumping internal tariffs: γ(0,f ) is non-positive
even if f is zero.⁵ Hence it is never profitable to have more than one union plant: the Fn
region vanishes.

2.4 A Linear Example

An advantage of the diagrams in {f,t} space is that all the loci can be written as
explicit functions of t and τ. However, for comparison with later models, it is useful to
illustrate the results for a concrete example. Assume therefore that the inverse demand
function in each member country is linear, given by:

(1 = 1-х                                (11)

It is convenient to normalise the intercept and slope to equal unity. We also simplify, without
loss of generality, by setting the constant marginal cost of production equal to zero.⁶

Under these assumptions, the multinational’s sales in any market facing a tariff t equal
(1-t)/2, and so its operating profits are:

⁵ Strictly speaking, when fixed costs are zero, the firm’s profits are the same irrespective of
the number of plants it builds. To avoid more tedious qualifications of this kind, I assume
throughout that, when the profits in two regimes are identical, the firm chooses the option
with the least possible number of plants.

⁶ Because of these normalisations, the tariff levels should be interpreted as measured with
respect to the size of the market. Suppose instead that the demand function (11) were written
as p=a-bx and the marginal cost of production as c. Then each expression for output must
be multiplied by (a-c)/b; each expression for profits must be multiplied by (a-c)²/b; and both
tariffs t and τ, must be deflated by a-c. The term (a-c)/b is the maximum level of sales
consistent with breaking even, and can be interpreted as a measure of market size. See
Rowthorn (1992) for further discussion.

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