Figure 1 illustrates the possible regimes in {f,t} space. Exporting is profitable only
for tariffs below a threshold level t, which is defined implicitly, from (1), by: π(t)=0. FDI
is profitable only for fixed costs below a threshold level which, from (6), equals π(0). If both
of these thresholds are breached, in the region labelled "O", the potential multinational will
not supply any of the union countries. Otherwise, the union will be supplied either from
exports or from n domestic plants, for parameters in the regions labelled "X" and "Fn"
respectively. Finally, the boundary separating the X and Fn regions is, from (3), defined by
γ(t,f )=0, and must be concave as shown.3
2.2 A Reduction in Internal Tariffs
Suppose now that internal barriers between union partner countries are reduced from
t to τ, while the common external tariff remains at t.Ifτ is above the prohibitive level tt,
nothing in the previous sub-section is affected. So, suppose instead that τ is set below tt. The
returns from exporting only are still given by (1). However, the profits from establishing a
single plant within the union, ΠF1, now equal:
Πf7 = π(0)-∕+(n-l)π(τ) (7)
Compare this with the profits from exporting:
3 This holds irrespective of the functional form of the demand function. The profit function
π(t) is the outcome of maximising operating profits in country i by choice of sales x: π(t) ≡
Maxx [p(x)-c-t]x, where p(x) is the demand function and c is the unit production cost. By
the envelope theorem, π'=-χ, and so π " = -dx/dt. From the first-order condition it is easily
shown that x is decreasing in t, and so π is convex in t. Since the boundary separating the
X and Fn regions is defined by f=π(0)-π(t), it follows that it must be concave in t.