Foreign Direct Investment and the Single Market

different firms. My approach draws on Dixit (1986) and is related to the literature on cost
changes in oligopoly. (See, for example, Kimmel (1992) and Zhao (2001).) The demand
function is (11) with x replaced by x, the total sales of all firms in market i. (The superscript
i can be suppressed without ambiguity.) Irrespective of how the market is served, the
equilibrium can be calculated as follows. Write the operating profits of firm k in market i
as:

^πfc ⁼ (¹~^tk~ (1^xk                             ⁽¹³⁾

where t_k is the access cost which firm k faces on sales in market i: it equals zero for a local
firm (k=i); t for the multinational (k=0) if it is located outside the union; and τ for a firm
located in a partner country (0<k=/ i). Differentiating (13), the first-order condition for output
by firm k can be written as:

⅞ ⁼ (4)k~^{x                        (14)}

which implies from (13) that equilibrium profits equal the square of output: π_k=(x_k)².

Equilibrium can now be calculated easily. Consider the case where it is profitable for
all firms to serve the market. (Recall that n is the number of partner countries, so n+1 is the
total number of firms.) The results apply with minor amendments to cases where some firms
are inactive. Summing (14) over all active firms we can solve for total sales in market i:

- ₌ n5i-t                             (15)

n+2

where t is the sum of the access costs of all firms in market i: t≡Σt_k. Substituting back into
(14), the output of each firm is:

10

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