Foreign Direct Investment and the Single Market

facing competition only from the local firm in each market.

Consider first the case where τ is below ⅛. If the multinational establishes a plant in
only one country, its profits become:

Π^f' = π[0,(n-l)τ] -/+ (n-l)π[τ,(n-l)τ]             ⁽²⁸⁾

Now the effects of a reduction in τ on the profitability of FDI are ambiguous. Differentiating
(28) with respect to τ:¹¹

d29    ( (n-l) ∣πj + {π°+(n-l)π⅛}]                    ⁽²⁹⁾

As in Section 2 (see equation (10)), lower internal tariffs make it more profitable to establish
a single union plant, since it gives preferential access to all other n-1 union markets.
However, by comparison with (10), lower internal tariffs also tend to lower the profitability
of FDI, since they increase competition within the union. The net effect is ambiguous. In
the linear-demand case, equation (29) becomes:

≤f! = - ⅛1> ri-(_n÷3)τ]                    (30)

dτ            {n.2γ ^{l           j}

So, for internal tariffs higher than 1/(n+3), the competition effect outweighs the market access
effect. Figure 4 is drawn for an internal tariff of 0.1 and for two firms, so the market access
effect dominates and the locus between the O and the FDI regions shifts up as τ falls.
However, even in this case, the quantitative expansion of the FDI region is much less than
in Section 2.

¹¹ The notation for the partial derivatives of π is hopefully obvious. The superscript on π
denotes the tariff facing the multinational at which the derivative is evaluated: either 0 or τ;
while the subscript indicates the partial derivative: "1" for the (negative) derivative with
respect to the tariff which the multinational firm itself faces, and "2" for the (positive)
derivative with respect to the sum of the tariffs facing its rivals.

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