Abstract
In this chapter, we investigate the relationship between firms’ regional location choices and the subsidy policies of regional governments in an imperfectly competitive third-market model. The seminal paper by Janeba (J Int Econ 44(1):135–153, 1998) has found that no subsidies are given to firms, and we check whether this result continues to hold when we extend the model in two ways. First, we incorporate the distributions of firms’ shareholders across regions to examine whether the difference in these distributions affects the zero-subsidy result. We demonstrate that even if firms’ shareholders are located in both regions, the zero-subsidy result continues to hold. Second, we consider the situation in which regional governments have concerns about the regional employment associated with firms’ locations, and we examine whether these governments’ consideration of employment affects the zero-subsidy result. We find that when regional governments have concerns about regional employment, the subsidy competition has no subgame perfect Nash equilibrium.
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Notes
- 1.
- 2.
Throughout the chapter, single and double primes denote first and second differentiation, respectively, with respect to a variable.
- 3.
\(s_{k}>0\) (\(s_{k}<0\)) represents a specific subsidy (tax).
- 4.
More specifically, \(\alpha _{11}\) (\(\alpha _{12}\)) is the fraction of firm 1’s profit shared by region 1’s (2’s) residents, respectively, and, likewise, \(\alpha _{22}\) (\(\alpha _{21}\)) is the fraction of firm 2’s profit shared by region 2’s (1’s) residents, respectively.
- 5.
In the original model, region i’s social welfare is \(W_{i} =pq_{i}-C_{i} =\widehat{\pi }^{i}\), which is equal to firm i’s profit before any subsidies. In contrast, in our extended model, social welfare is not necessarily equivalent to firm i’s profit before any subsidies.
- 6.
Source-based taxation is assumed in Janeba’s (1998) original setting.
- 7.
The subscripts of the profit function denote partial derivatives with respect to outputs. For example, \(\pi ^{1}_{2} \equiv \partial \pi ^{1}\!/\! \partial q_{2}\).
- 8.
The second-order condition is \(\pi ^{i}_{ii} =2p'+p''q_{i}-C_{i}''<0\).
- 9.
\(\pi ^{i}_{ii} =2p'+p''q_{i}-C_{i}'' < \pi ^{i}_{ij} =p'+p''q_{i}\le 0\).
- 10.
Janeba (1998) investigated tax competition under an assumption that he similarly called limited cost divergence.
- 11.
\(\pi ^{i}_{ii}<\pi ^{j}_{ji} \Leftrightarrow p'+p''(q_{i}-q_{j})-C_{i}''<0\). If demand is linear, that is, if \(p''=0\), then the above inequality always holds. If \(C_{i}(\cdot )=C_{j}(\cdot )\), the equilibrium outputs of the firms are identical, that is, \(q_{i}=q_{j}\). Furthermore, in this case, \(p'+p''(q_{i}-q_{j})-C_{i}'' =p'-C_{i}''<0\) holds.
- 12.
This logic is quite similar to that of the Bertrand paradox when two firms with the same constant marginal cost engage in price competition in a homogeneous-good market. In the Bertrand paradox, the price is equal to the marginal cost in the equilibrium because neither firm can obtain positive profits by changing its price. Likewise, in the laissez-faire equilibrium, neither regional government can obtain more welfare by changing the subsidy level.
- 13.
This assumption can be also interpreted as the constant existence of unemployment in each region such that firms’ labor demand can be always absorbed within each region.
- 14.
Note that we do not consider the situation in which the subsidy is given to regional employees because we do not explicitly introduce labor income or utility into the model to keep the analysis simple.
- 15.
Albert (1993) first classified the practice of capitalism in developed countries into two types: Anglo-American capitalism and Rhine (German-Japanese) capitalism. Aoki (1980, 1988) demonstrated that the objective of Japanese companies is endogenously determined by Nash bargaining between shareholders and employees. Several studies (Aoki 1990; Imai and Komiya 1995) regard German-Japanese firms as employee-controlled firms.
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Acknowledgements
The authors wish to thank the participants in the seminars of the Theory of Local Public Economics held at Aichi University, Kyoto Sangyo University, and Nagoya University for their valuable suggestions. This work was supported in part by JSPS KAKENHI Grant Numbers No. 16K03615 and No. 16H03612 (Kojun Hamada), No. 17K18563 and No. 17K03762 (Mitsuyoshi Yanagihara), and No. 15K03449 (Kojun Hamada and Mitsuyoshi Yanagihara). The authors are solely responsible for any errors.
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Hamada, K., Ogawa, Y., Yanagihara, M. (2019). Subsidy Competition Between Regions: An Extension to Cross-shareholding and Employment Concerns. In: Kunizaki, M., Nakamura, K., Sugahara, K., Yanagihara, M. (eds) Advances in Local Public Economics . New Frontiers in Regional Science: Asian Perspectives, vol 37. Springer, Singapore. https://doi.org/10.1007/978-981-13-3107-7_4
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