A higher-cost region excessively attracts firms

Abstract

This study examines the economic efficiency associated with firm location in a non-traded goods industry. This industry comprises of two segmented regions (markets) and a fixed number of potentially identical, oligopolistic firms. We consider the following two-stage game. In the first stage, firms determine the region in which they want to locate simultaneously and independently. In the second, given the pattern of firm location, every firm engages in Cournot competition in each market. If a potentially identical firm is located in a different region, the firm has a different cost function, and therefore, different fixed and marginal costs. Thus, the cost function of each firm is not firm-specific but region-specific. We define welfare as the sum of the region's social surplus, which includes consumer surplus and producer surplus. We obtain the following results. First, when only the marginal costs differ across regions, from a welfare perspective, an insufficient number of firms are located in the higher-cost region. Second, when only the fixed costs differ across regions, an excessive number of firms are located in the higher-cost region. Third, when a region has sufficiently higher fixed and marginal costs than another, an excessive number of firms are located in this region.

Keywords:

• Firm location
• non-traded goods
• difference in costs
• social efficiency

JEL classifications:

• L13
• F12

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Although services are tradable in terms of accounting, they are often regarded as typical examples of non-traded goods: service itself is invisible and not storable nor transportable.

2 In this paper, we focus only on supply-side factors to clarify their effect. Market size – a demand-side factor that has been investigated in previous studies – is another factor that is critical for firms when choosing locations. For example, Behrens (2005) showed that the home market effect is always exhibited in the traded goods industry; however, that effect depends on the degree of product differentiation in the non-traded goods industry. Kurata, Ohkawa, and Okamura (2011) demonstrated that from a welfare viewpoint, too many firms are attracted to a region with a larger market under an oligopoly. In reality, firm location is affected by demand-side factors (e.g. market size) as well as supply-side ones (e.g. cost). We briefly discuss this point in Section 5.

3 It has been observed that firms locate in multiple regions simultaneously. However, because firms face managerial resource constraints, they often cannot locate in multiple regions. Even if firms locate in multiple regions, their timing is usually different.

4 This property is termed the strategic aspect of location choice (Kurata, Ohkawa, and Okamura 2011). This aspect has been overlooked in previous studies about location because it has been analyzed mainly with respect to the new economic geography, which particularly considers monopolistic competitive markets.

5 This assumption is adopted in the literature on subsidy games (e.g. Barros and Cabral 2000; Fumagalli 2003).

6 When the condition is satisfied, Cournot eqilibrium is stable in both markets (Hahn 1962).

7 These properties appear in the literature on excess entry (e.g. Mankiw and Whinston 1986).

8 d'Aspremont et al. (1983) is a pioneering work using such kind of inequalities as the equilibrium conditions.

9 This implies that we ignore the ‘integer problem’. This approach has often been adopted in research on oligopolies (e.g. Suzumura and Kiyono 1987; Elberfeld 2003).

10 In this paper, we exclude the case with perfect agglomeration, because equilibrium conditions of the corner solutions (i.e. perfect agglomeration) are different from that of the interior solutions. In particular, equality of net profit (i.e. condition (ii')) is not satisfied. Furthermore, under perfect agglomeration, it is straightforward to see that the number of firms at the equilibrium location to the region with both higher marginal and fixed entry costs (we call it ‘higher-cost region’) cannot be excessive from the welfare viewpoint. Our main contribution is to clarify the possibility that firm excessively locate in the higher-cost region, we thus exclude the perfect agglomeration and confine our attention on the case with at least a single firm locates in each region.

11 The details are explained in Appendix 2.

12 The effect to consumers is induced only by a change in price. A decline in price by a marginal movement of a firm raises consumer surplus; simultaneously, it decreases producer surplus by the same amount.

13 If the inverse demand is linear (i.e. $\alpha =0$), both regions have a common price-cost margin.

14 This assumption implies that the difference in marginal costs is not extremely large.

Additional information

Funding

This work was supported by JSPS KAKENHI [grant numbers JP17K03734, JP19K01609].