The model used to assess the validity of the potential indicators is a generalization of the 'reciprocal dumping' model used in international trade analysis (see Brander, 1981; Brander and Krugman, 1983). A homogeneous product is produced by individual firms i e I, located in countries j e J; with the subset of firms located in a particular country being denoted by I and the number being denoted by the parameter Nj. The product is purchased by consumers located in distinct markets k e K; where the latter are defined geographically. For simplicity, it is assumed that there is a one-to-one correspondence between countries and markets.7 Consequently, the number of markets is equal to the number of countries; with producers in each country having a 'home market' and K - 1 'export markets'. In each market, the firms compete as quantity-setting Cournot oligopolists facing a market-specific linear inverse demand function: Pk = ak — bkX k, where Pk is the market price, Xk is the aggregate value of market sales, and ak is the 'choke price' (i.e. the price at which sales fall to zero).8
All firms have a constant unit cost of production cij and a fixed cost Fji , both of which differ between firms. In addition, they incur market-specific constant unit transportation costs (rjk) which are assumed to be the same for all firms in a particular country. For simplicity, it is assumed that the transportation costs are equal to zero for all home-market sales.
7 This does not have to be the case, so long as each market is distinct. For example, there may be several regional or local markets within a country, or a single market may span several countries. However, this complicates the definitions of countries' import penetration and export intensity.
8 With distinct (i.e. segmented) markets and Cournot conjectures, firms make separate quantity choices for each market under the assumption that all other firms hold their output constant.
The following three definitions of average production cost are used in the analysis:
• average of unit production costs for firms in country j e J
\ieIl average production cost of sales in market k e K by firms located in country j e J
• average of unit production costs for all firms
where Xjk and xjk are respectively the aggregate and individual sales in market k e K by firms located in country j e J. Under the assumption of country-specific unit transportation costs, within each country, firms with lower unit production costs will have higher market shares in all markets and hence it follows directly that cj > cjk.
The competitiveness of a firm is defined to improve if the increase in its unit production cost is less than the average increase in unit production costs of all other firms, or if the reduction in its unit production cost is greater than average reduction of the other firms. Conversely, it will lose competitiveness if its unit production cost increases by more than its competitors, or reduces by less. This definition can be extended to the sectoral level, with a country gaining competitiveness if the average increase (decrease) in the unit production costs of its constituent firms is less (greater) than the average increase (reduction) of firms in all other countries, and losing competitiveness if the reverse is true.9 Formally, the necessary and sufficient condition for sector j e J to gain (lose)
9 By definition, the average change in unit production costs of constituent firms (i.e. X(Ac!)/Nj) is the same as the change in the average of the unit production costs (i.e. £(Acj/Nj)).
competitiveness is that:
\ieIl which can be rearranged to yield the following condition:
For small changes in unit costs, the condition can be expressed in terms of differentials:
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