Foreign Direct Investment and the Single Market

_ 2÷ε-[2-(_n-l)ε-,⅜tεε._t              (43)

‘             (2+ε)(2-nε)

This confirms, as required, that x_k is increasing in t_-k,, the sum of the access costs of all firms
excluding firm k. By contrast, the sign of the effect of own access cost on sales appears to
be ambiguous. However, it can be shown that it must be negative. The substitutability
parameter ε in (41) cannot be a primitive one, since if it was then demand for good k would
increase without bound as the number of goods increased. It is shown in Neary (2000) that,
if demands are generated by a symmetric quadratic utility function with substitutability
parameter e, then ε and e are related as follows: ε=e/[ 1+(n-1 )e]. Making this substitution,
the coefficient of t_k in (43) can be seen to be unambiguously negative, as required. It is also
sufficiently negative to offset the effects of an increase in t_-k=(n-1 )t_k.: the result in (18)
continues to hold.

A.2 Cournot Competition with General Demands

Return to the Cournot case, with homogeneous products, but now allow for a general
demand function: p=p(X). The first-order condition for firm k is: bx_k=p-t_k; where b is
(minus) the demand slope: b≡-p'(x). Summing over all n-1 firms and totally differentiating
gives:

(n+2+r)bdx = -dt                          ⁽⁴⁴⁾

where r≡xb'/b is a measure of the concavity of the demand function, and the coefficient of
dx must be positive for stability. Next, totally differentiating the first-order condition for firm
k:

bdx,_k = - (l+a_kr)bdx - dt_k                         (⁴5)

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