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.