Foreign Direct Investment and the Single Market

implications of trade liberalisation and FDI on factor markets in individual member countries
and in the union as a whole.

Appendix

The key result of Section 3.1 was that, in Cournot competition with linear demands,
each firm’s sales in each market are decreasing in its own access cost and increasing in the
sum of its rivals’ access costs. The purpose of this Appendix is to show that these properties
also hold in Bertrand competition with linear demands, and in Cournot competition with
general demands (except when demands are highly convex and the firm in question has a
relatively small market share).

A.1 Bertrand Competition

Assume a symmetric linear demand system. The direct demand function for sales by
firm k in any market i is:

x_jt = 1 - [(l+ε)p_fe-εp]                            ⁽⁴¹⁾

where ε is an inverse measure of product differentiation and p is the sum of the prices
charged by all n-1 firms. Proceed as in Section 3.1. Operating profits of firm k in market
i are π_k=(p_k-t_k)x_k; the firm’s first-order condition is: x_k=p_k-t_k; and so profits equal the square
of output: π_k=x²_k. Summing the first-order condition over all active firms gives:

- ₌ n2i+t                             (42)

2-nε

where, as in Section 3.1, t is the sum of the access costs of all firms in market i: t≡Σt_k..
Combining this with (41), we can solve for the output of each firm:

24

<<   23   24   25   26   27   28   29   >>

More intriguing information