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2023 | OriginalPaper | Chapter

1. The Effect of Regulation on a Dominant Firm to Protect Fringe Firms in a Local Market

Author : Akio Torii

Published in: Industrial Location and Vitalization of Regional Economy

Publisher: Springer Nature Singapore

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Abstract

A model of competition between a large-scale dominant firm and fringe firms is analyzed to examine the effect of market share regulation on the dominant firm to protect the small firms. One feature of the model is that the dominant firm and the small firms provide close but different services to consumers. Because business stealing effects are possible for both the dominant firm’s and small firms’ entries, the effect on social welfare is generally indefinite. When small firms face the danger of extinction because of the expansion of the dominant firm, it is demonstrated that the effect is evaluated solely by the excessiveness of the number of small firms. As small firms tend to enter excessively when there is spatial competition, the market share regulation on the dominant firm prevents efficient outcome unless small firms are eliminated. In most regional retail markets in Japan, small ordinary stores are far from total elimination, so a restriction on the expansion of large-scale stores is not needed.

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next chapter Corporate Taxation and Regional Economic Development in Japan: A Panel Analysis of Prefectural-Level Data
Footnotes
1
Schenzler et al. (1992).
 
2
MITI was reorganized into Ministry of Economy, Trade and Industry (METI) in 2001.
 
3
Large Store Law was replaced in 2000 by Large-scale Store Location Law. The new law regulates location, layout, and operational method of the facilities of large-scale stores. The role of regulating store openings has receded.
 
4
Gravitation Law in Retail assumes that consumers incur trip costs in determining where to shop. However, where to shop is determined probabilistically, and the probability is inversely associated with trip costs. Theories explaining these conducts assume that consumers maximize a class of utility function. It is parallel to minimizing the total shopping cost for a given amount of service.
 
5
Specifically, assuming there are two dimensions in distribution services,\(({v}^{1},{v}^{2})\), Type L supplier supplies \(({v}^{1L},{v}^{2L})\) with price \({p}^{L}\), and Type s supplier supplies \(({v}^{1s},{v}^{2s})\) with price \({p}^{s}\). For example, the simplest form of these two dimensions is (width of assortment, convenience of the location of the store). The large store offer \((q,-{x}^{L})\), whereas small stores offer \(({q}^{s},-x)\), where \({q}^{s}\ll q\) and \(x\ll {x}^{L}\). The total distribution service required to buy a good is \(({v}^{1T},{v}^{2T})\), which costs a consumer \(C({v}^{1T}-t{v}^{1L}-(1-t){v}^{1s},{v}^{2T}-t{v}^{2L}-(1-t){v}^{2s})\), where \(t\) is the ratio the consumer buys from small stores. Then, the total consumer cost, which is the sum of the price and service cost, is \(t{p}^{s}+(1-t){p}^{L}+C\), whose derivative is \({p}^{s}-{p}^{L}+{C}_{1}\cdot ({v}^{1s}-{v}^{1L})+{C}_{2}\cdot ({v}^{2s}-{v}^{2L})\), where the suffixes of \(C\) represent partial derivatives. If the components of \(({v}^{1s},{v}^{2s})\) and \(({v}^{1L},{v}^{2L})\) are quite different and \({C}_{11}\) and \({C}_{22}\) is sufficiently large, as expected in retail markets, the total cost can be maximized internally at \(0<t<1\).
 
6
We can regard the quality of the large-scale store as the average distance from consumers. Consider a broader market with several large-scale stores and scattered small stores, if a new large-scale store enters the market, the average distance from consumers to large-scale stores decreases, which improves the convenience of large-scale stores. Therefore, the share of the large-scale stores would increase. In this story, \(q\) is positively associated with the number of large-scale stores, and the share of the large-scale stores is an increasing function of \(q\). Furthermore, the radius of the circle would shrink as new large-scale stores enter the market.
 
7
If we consider \(q\) as the number of large-scale stores, as described in Footnote 6, \(q\) is not chosen but determined by some entry mechanism of them.
 
8
If we assume the situation described in Footnote 6, we have to consider the total distribution cost from unit arc as follows:
$$DC(q)\hspace{0.25em}=\hspace{0.25em}\frac{F(q)}{r}+\frac{{F}_{s}}{D(q)}+TC(q,D(q)).$$
We have to redefine \(F(q)\) as \(F(q)/r\), which is the fixed cost of the large-scale store for a unit supplying area. Then, the following analysis is valid for this story setting \(r\) as \(1\).
 
9
See Greenhut et al. (1976).
 
10
Torii (1993) demonstrated that if only the distribution cost is considered, under free entry and elastic demand, the number of stores will be excessive whether the type of competition is Zero Conjectural Variation or Lösch as the same amount of goods can be distributed by smaller number of stores. This implies that the inside of the parenthesis of the second term of Eq. (1.1) is negative.
 
11
I aggregated the number of stores to 10 km mesh because 1 km mesh is too small as an area to consider the competition between retail stores, especially those in rural areas. I surveyed 65,710 1 km mesh areas, finding that 21,552 areas have only one store. The reason I used the number of retail workers in the areas and did not use the retail sales as the proxy for retail activities is that in many areas, the sales data are kept confidential because of the small number of stores. Grocery specialty stores are those who sell 50% or more of their sales in food product, except for grocery supermarkets, chain convenience stores, and department stores.
 
Literature
Economides, N. (1989). Symmetric equilibrium existence and optimality in differentiated product markets. Journal of Economic Theory, 47(1), 178–194.CrossRef
Greenhut, M. L., Hwang, M., & Ohta, H. (1975). Observations on the shape and relevance of spatial demand function. Econometrica, 43(4), 669–682.CrossRef
Hosono, S. (1987). Shutten-Kisei no Seiji-Keizaigaku (in Japanese, Political Economy of Restriction of Large-Scale Stores) In K. Kan and K. Kurokawa (Eds.) Seifu no Keizaigaku (Economics of Government), Yuhikaku: Tokyo.
Mankiw, N. G., & Whinston, M. D. (1986). Free entry and social Inefficiency. Rand Journal of Economics, 17(1), 48–58.CrossRef
Nishimura, K. G. (1994). Product Innovation with mass-production: Insufficient or excessive. Japan and the World Economy, 7(4), 419–442.CrossRef
Salop, S. C. (1979). Monopolistic competition with outside goods. Bell Journal of Economics, 10(1), 141–156.CrossRef
Schenzler, C., Siegfried, J. J., & Thweatt, W. O. (1992). The history of the static equilibrium dominant firm price leadership model. Eastern Economic Journal, 18(2), 171–186.
Suzumura, K., Kiyono, K., Okuno, M., & Itoh, M. (1988). Sangyo Seisaku no Keizairiron (in Japanese. Economic Analysis of Industrial Policy), Tokyo University Press.
Torii, A. (1990). Gendai Nihon no Kouri Shijo no Kyoso Kozo to Sannyu Kisei (in Japanese, Competitive Structure and Regulations on Japanese Retail Market). In Y. Nakata et al. (Eds.) Marketing no New Wave (New Wave of Marketing Theory), Dobunkan: Tokyo.
Metadata
Title
The Effect of Regulation on a Dominant Firm to Protect Fringe Firms in a Local Market
Author
Akio Torii
Copyright Year
2023
Publisher
Springer Nature Singapore
Book
Industrial Location and Vitalization of Regional Economy

Print ISBN: 978-981-19-8127-2

Electronic ISBN: 978-981-19-8128-9

Copyright Year: 2023

DOI
https://doi.org/10.1007/978-981-19-8128-9_1