The validity of each of the four measures as an indicator of changes in competitiveness for a particular country is assessed by deriving a necessary and sufficient condition for the measure to increase, expressed in terms of the average change in unit production costs for that country relative to the global change (i.e. dc1 — dc).10 If this condition coincides with the competitiveness condition (C1b), then the measure is a robust indicator of changes in competitiveness. However, if it diverges significantly, then it is a poor indicator that should be used with caution, or not used at all.

In addition to changes in unit production costs, the analysis allows for the possibility that markets may be growing or shrinking over time. This is achieved by allowing the choke price in each market ak to vary independently, while keeping the slope of the inverse demand curve (bk) constant.11 All of the other exogenous parameters in the model are held constant. In particular, the number of firms in each sector is fixed—that is, there is no entry or exit as a result of the changes in unit costs.

Share of global production

A necessary and sufficient condition for share of global production (ct1) of country j e J to increase (decrease) is that:

10 Details of the derivation of the conditions are provided in the Final Project Report, which can be downloaded from:<http://www2.dmu.dk/cometr/COMETR_Final_Report.pdf>.

11 Thus, the (inverse) demand curve may shift outwards (or inwards) over time, but the slope does not change.

10 Details of the derivation of the conditions are provided in the Final Project Report, which can be downloaded from:<http://www2.dmu.dk/cometr/COMETR_Final_Report.pdf>.

11 Thus, the (inverse) demand curve may shift outwards (or inwards) over time, but the slope does not change.

where pi is the country's share of total number of firms (i.e. Nj/N) and dâ= E

dak bk

The expression on the right-hand side of condition (C2) is not generally equal to zero—only being so if the country's share of global production is equal to its share of the total number of firms (i.e. aj = pj); or if the weighted average change in the choke prices in the various markets is equal to the average change in the unit costs of all firms.12 Neither of these two conditions is likely to be true in general, although the country shares of global production and number of firms will be similar if there is little variation in the average scale of firms between countries. In general, the expression may be positive or negative. However, if the total number of firms is relatively large, then the right-hand side of (C2) will be approximately equal to zero.13 For most sectors, this is likely to be the case and hence the direction of change of a country's share of global production provides a good indicator of its change in competitiveness. If a sector gains competitiveness, its share of global production increases; if it loses competitiveness, it declines (see Figure 4.114).

Share of global production

Competitiveness dûj > 0

increasing increasing dûj < 0

decreasing decreasing dcj - d c < 0 0 dcj - d c > 0

Figure 4.1. Changes in competitiveness and global market share

12 The changes in the choke prices are weighted by the slopes of the respective demand curves (i.e. 1/bk).

13 The assumptions that are made in the derivation of (C2) impose an upper bound on the global number of firms (N), which is dependent on the relative values of the choke price and the unit costs (including transport costs) in each market. Details are provided in the Final Project Report.

14 In Figures 4.1-4.3, it is assumed that the value of the right-hand side of the condition is positive. However, this need not necessarily be the case.

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