## Abstract

In many developing countries such as China, the typical marketplace is a cluster of small shops or booths. We investigate an economic model in which circular causality, including search and matching between buyers and sellers, forms agglomeration forces. We find that an authoritative third party that reduces search costs is important in sustaining a large marketplace. However, it is unnecessary to reduce search costs to zero. Finally, the low capital requirement of setting up a firm helps to sustain a large marketplace owing to its increased product heterogeneity.

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## Notes

Larsson and Öner (2014) employ geo-coded data at a fine spatial resolution for Sweden’s metropolitan areas to assess retail co-location and clarifies which types of retail clusters one can expect to find in a metropolitan region.

This information was sourced from http://sc.yiwugou.com/html/market/spc/1715.shtml (accessed Nov. 30, 2015).

The formation of marketplaces without circular causality is well understood. Wang (1990) has shown, by solving the social planner’s optimization problem, that a unique welfare-maximizing equilibrium marketplace is located near the residences of buyers who prefer spatial factors. Wolinsky (1983) developed a monopolistic competition model of buyer searches under the assumption that the marketplace and place of residence are separated. Wolinsky (1983) admitted a clustered market area and allowed for examination of whether a shop emerges outside the marketplace. Fischer and Harrington (1996) derived, extending the search model of Wolinsky (1983), the circumstances in which some firms cluster, but many more are located away from the cluster as a result of the entry and exit of firms. Anderson and Renault (1999) derived a model setup required for the existence of an equilibrium under monopolistic competition and in other competitions, rigorously examining Wolinsky (1986) from the viewpoint of industrial organization. Konishi and Sandfort (2003) examined the externalities produced by an anchor store with an established brand name.

This means that our model does not rely on the distance between a given ideal product and the realized product as in Salop models.

The mechanism of circular causality in this paper seems to be similar to what on the labor market. In the case of job matching like Helseley and Strange (1991), the huge labor supply in a larger city attracts more firms and more demand for labor implies smaller gap between the skill a worker has and the ideal skill an employer seeks for, which means that less training is required. In this paper, the demand side in our paper does not need to pay the cost depending on the result of matching like the cost for training workers. In the case of search and matching like Wasmer and Zenou (2006), the bargaining between firms and labor determines the wage payment, dividing the profits produced by firms and labor after search process. In this paper, the price of a variety is determined as the result of the combination of search process and the competition among firms. Thus, the mechanism is different between this paper and what on the labor market.

Mushinski et al. (2014) also show that the importance of a retail trade industry to the economy of a rural place depends on its market area.

Anderson and Renault (1999), Fischer and Harrington (1996), Konishi (2005), and Wolinsky (1986) and this paper are regarded as the paper based on Wolinsky (1983). Monopolistic competition itself is not a new approach in the literature since Fischer and Harrington (1996) and Wolinsky (1986) are focused on monopolistic competition. However, literature keeps the constant product heterogeneity.

This point is based on comments by Yukio Watanabe, professor emeritus at Keio University.

Information on the logistic system was sourced from: http://www.zjt.gov.cn/art/2008/12/31/art_71_36589.html (accessed October 17, 2013).

Each buyer is bound to his or her place of residence, which means that the buyer cannot relocate.

In reality, the major buyers in the Yiwu marketplace are small merchants. For this reason, we believe that this assumption is reasonable.

Match values are assumed to be independent across sellers and varieties.

In Maier (2006), consumers are assumed to search for a product at the lowest overall costs where suppliers are spatially distributed. Thus, the expected result of the shopping decision is linked with the quantity decision relating the customer’s location via bid prices for land with the expected costs of buying the product.

It is readily verified that \(\partial \left[ 1-F(\widehat{x}+\Delta )\right] /\partial p=-f(\widehat{x})/\mu \) holds. Thus, the derivative of demand for seller

*i*with respect to \(p_{i}\), evaluated at \(p_{i}=p^{*}\), is given by \(\partial D(p^{*},p^{*})/\partial p_{i}=-\theta \sqrt{n/2c\mu }<0.\)The equilibrium price increases with the search cost,

*c*, as in Proposition 1 and with product differentiation, \(\mu \), as in Proposition 2 of Anderson and Renault (1999).The case when prices become higher after the search process of consumers in Marshall (1920) is as follows: “He[the consumer] will go to the nearest shop for a trifling purchase; but for an important purchase he will take the trouble of visiting any part of the town where he knows that there are specially good shops for his purpose. Consequently shops which deal in expensive and choice objects tend to congregate together; and those which supply ordinary domestic needs do not.”

A price trend comparison between the Yiwu marketplace and other sectors supports this result. As already mentioned, continually decreasing search and transport costs in the Yiwu marketplace could be expected to lower market prices there. However, the price index of the Yiwu marketplace increased from 100 in 2008 to 101.42 in 2012 at an annual growth rate of 0.37%, whereas the producer price index for daily-use articles in Zhejiang Province increased from 100 to 100.51 at an annual growth rate of 0.15% (www.ywindex.com accessed December 2, 2014; Zhejiang Statistics Yearbook 2012). Furthermore, it can be observed that the products become more differentiated as the number of sellers in the Yiwu marketplace increases.

From (13), the function, \(\theta =\Psi _{r}(\lambda )\), emanates from the origin with a gradually decreasing positive slope. By combining (5) and (14), we obtain \(\partial \Psi _{U}(\lambda )/\partial \lambda >0\). Thus, the slopes of \(\theta =\Psi _{r}(\lambda )\) and \(\theta =\Psi _{U}(\lambda )\) are positive.

A unique root \((\widetilde{\lambda },\widetilde{\theta })\in (0,+\infty )\times (0,+\infty )\) of the system given by (13) and (14) is readily verified because, from (13) and (14), the quadratic function of \(\sqrt{\lambda }\), \(\Psi _{U}(\lambda )-\Psi _{r}(\lambda )=\sqrt{\lambda }(\mu \sqrt{\lambda }/\phi t-2\sqrt{2c\mu }/\sqrt{\phi } t-\phi \bar{r}/\sqrt{2c\mu })\) takes 0 at \(\lambda =0\) with a negative slope around \(\sqrt{\lambda }=0\) and tends to infinity as \(\lambda \) approaches infinity.

An outcome is not used for expressing a stable equilibrium, but a root of the system.

North (1986) stressed the role of the third party in reducing the costs of contract enforcement, which include the measurement costs of contracting and costs of enforcement. However, our search costs represent the ex-ante costs of searching and contracting.

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## Acknowledgements

Zhu acknowledges the financial support from the National Natural Science Foundation of China (Grants-in-Aid for Science Research 71373235 and 71503232). An earlier version of this paper was entitled “Search, matching, and self-organization of a marketplace” (Discussion paper no. 396, Institute of Developing Economies-JETRO, 2013, Japan).

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## Additional information

An earlier version of this paper was presented at the Second International Conference on “Industrial Organization and Spatial Economics” organized by The Higher School of Economics, Center for Market Studies and Spatial Economics in St. Petersburg in July 2013, the Third Asian Seminar in Regional Science, Hualien, in August 2013, the 60th Annual North American Meetings of the Regional Science Association International, Atlanta, in November 2013, the Tohoku Symposium on Spatial Economics in Sendai in January 2014, the Association of American Geographers’ Annual Meeting in Tampa in April 2014, and the 28th Annual Meeting of the Applied Regional Science Conference in Okinawa November 2014. We thank Shota Fujiwara, Shiro Hioki, John Miron, Tomoya Mori, Jun Oshiro, Frederic Robert-Nicoud, Jacques-François Thisse, Chao-En Yu, and Dao-Zhi Zeng as well as conference participants, for their constructive comments.

## Appendices

### Appendix 1: Stability of corner solutions

In this appendix, we start from the full agglomeration case. Full agglomeration implies \(\lambda =1\). By substituting \(\lambda =1\) into (12) and solving \(U(1,\theta )=0\), we obtain \(\theta =\Psi _{U}(\lambda =1)\). Since \(\theta \gtreqqless \Psi _{U}(\lambda =1)\), which implies \(\overset{.}{\theta }\lesseqqgtr 0\), the economy is stable at \(\lambda =1\) and \(\theta =\Psi _{U}(\lambda =1)\) if and only if \(\Psi _{U}(\lambda =1)>\Psi _{r}(\lambda =1)\), which implies \(\overset{.}{\lambda }>0\) around \(\left( \lambda ,\theta \right) =\left( 1,\Psi _{U}(\lambda =1)\right) \).

Next, we examine the no-marketplace case. By setting \(\lambda =0\) in (12), we obtain \(U(0,\theta )<0\). Likewise, by setting \(\theta =0\) in (10), we obtain \(r(\lambda ,\theta =0)<\bar{r}\).

### Appendix 2: Stability of the interior outcome

In this appendix, we examine the stability of the interior outcome \((\widetilde{\lambda },\widetilde{\theta })\). Linearizing (3) around (\(\widetilde{\lambda }\), \(\widetilde{\theta }\)) with (10) and (12) yields

where

Thus, we obtain a characteristic equation \(a^2+ [c\bar{r}\mu ^3/\phi (\phi \bar{r}t+4c\mu )^2+t]a-c\mu /\phi ^2(\phi \bar{r}t+4c\mu )\) and find two eigenvalues, \(a_1\) and \(a_2\); \(a_{1}<0\) and \(a_{2}>0\). Hence, the interior outcome (\(\widetilde{\lambda }\), \(\widetilde{\theta }\)) is a saddle point. The simple calculation yields an eigenvector for each of \(a_1\) and \(a_2\):

which is derived by using \(a_{1}<0\);

which is derived by using \(a_{2}>0\), where \(A\equiv 4c\mu ^2/\phi (\phi \bar{r}t+4c\mu )\) and \(B\equiv c\bar{r}\mu ^3/\phi (\phi \bar{r}t+4c\mu )^2\). Since \(\eta _{1}^{(1)}<0\) and \(\eta _{1}^{(2)}>0\), the slope of a stable saddle path is negative and the slope of an unstable saddle path is positive around (\(\widetilde{\lambda }\), \(\widetilde{\theta }\)).

### Appendix 3: The equilibrium condition for full agglomeration

In this appendix, we derive the equilibrium condition for full agglomeration. First, we focus on the amount of capital required for a firm. By rewriting (17), which is equivalent to \(\Psi _{U}(\lambda =1)>\Psi _{r}(\lambda =1)\), we obtain \(h(\phi ^\frac{1}{2})\equiv -t\bar{r}\phi ^\frac{3}{2}-4\mu c\phi ^\frac{1}{2}+\sqrt{2 c}\mu ^\frac{3}{2}> 0 \), which is a cubic function of \(\phi ^\frac{1}{2}\) and has a negative discriminant and \(h(0)>0\). Thus, we find that \(h(\phi ^\frac{1}{2})> 0\) iff \(\phi \) is between zero and only one real root of \(h(\phi ^\frac{1}{2})=0\), which can be solved explicitly by using Vieta’s substitution. Next, we examine the impact of lowering the search costs for sellers. Furthermore, by solving \(h(\phi ^\frac{1}{2})\) on \(c^\frac{1}{2}\), we find that a marketplace is sustained when \( \frac{\mu -\sqrt{\mu ^2 - 8 \bar{r} t \phi ^2}}{4 \sqrt{2\mu \phi }}< \sqrt{c}< \frac{\mu +\sqrt{\mu ^2 - 8 \bar{r} t \phi ^2}}{4 \sqrt{2\mu \phi }}\) if \(\mu >\phi \sqrt{t \bar{r}}\), which satisfies condition (5). Finally, we find the impact of the transport costs and/or outside options of capital in (17). By rewriting condition (17), we obtain \(\bar{r}t < (\sqrt{2 \mu }-4\sqrt{c \phi }) \mu \sqrt{c}/\phi \sqrt{\phi }\).