The Price Effect on Spatial Structure: Revisiting the New Economic Geography Model

Abstract

This paper adds a factor of production, land, to the standard core-periphery model of the New Economic Geography to analyse the effect of land rent on the price index and spatial structure. The result indicates that when production of the manufacturing sector has high dependence on land, and high demand elasticity for differentiated goods, the price index of the core region is higher than that of the periphery, and that the price index could rise with a degree of agglomeration. Meanwhile, the market forces cannot generate a core-periphery structure, which indicates the significance of the price effect on spatial structure.

Résumé

la présente communication ajoute un facteur de production, le terrain, au modèle standard centre-périphérie de la nouvelle géographie économique, pour analyser l'effet des loyers fonciers sur l'indice des prix et la structure spatiale. Le résultat indique que lorsque la production du secteur industriel présente une forte dépendance des terrains, et une élasticité élevée sur le plan de la demande en produits différenciés, l'indice des prix au centre est plus élevé que celui de la périphérie, et que l'indice des prix pourrait augmenter avec un degré d'agglomération. D'autre part, les forces du marché ne peuvent produire une structure centre / périphérie, ce qui témoigne de l'importance de l'effet des prix sur la structure spatiale.

Extracto

Este estudio añade un factor de producción, terreno, al modelo centro-periferia estándar de la nueva geografía económica para analizar el efecto de la renta de terreno sobre el índice de precios y la estructura espacial. El resultado indica que cuando la producción del sector de fabricación depende en gran medida del terreno y de alta elasticidad de la demanda de productos diferenciados, el índice de precios de la región centro es más alto que el de la periferia, y que el índice de precios podría subir con un grado de aglomeración. Mientras tanto, las fuerzas del mercado no pueden generar una estructura centro-periferia, lo que indica la importancia del efecto del precio sobre la estructura espacial.

摘要

本文向新经济地理学的标准核心-边陲模型添加了一个生产因素 : 土地 , 以分析地租对物价指数和空间结构的影响。结果表明 , 当制造业的生产活动对土地具有 较高依赖性 , 且对差异性产品具有较高的需求弹性时 , 核心区域的物价指数高于外围的物价指数 , 并且物价指数会随集聚程度而上升。同时 , 市场力量无法形成核心-边陲结构 , 这表明了价格对空间结构的影响非常显著。

Keywords:

• price index
• land rent costs
• core-periphery
• New Economic Geography

JEL classification:

• F12
• F22
• R12

We are indebted to Dao-Zhi Zeng, the editor, and two referees of this journal for useful comments.

We are indebted to Dao-Zhi Zeng, the editor, and two referees of this journal for useful comments.

Notes

1. Krugman's cost-of-living effect relies heavily on constant markups over marginal costs, while Behrens & Murata (2007) and Melitz & Ottaviano (2008) highlight lower markups, which is the so-called ‘pro-competitive effect’, to show that profit-maximizing prices are decreasing in the mass of competing firms, and to get a stronger cost-of-living effect. Moreover, a framework based on Behrens & Murata (2007) may get a stronger circular causation mechanism than one based on Melitz & Ottaviano (2008), since the former embeds income effects.

2. See Pflüger & Tabuchi (2010, p. 487) Proposition 3, which covers both cases of land as a consumption good and land as a factor in production.

3. Pflüger & Tabuchi (2010, p. 481): ‘However, land has been included as a production factor in addition to labour in the ‘traditional’ constant returns sector in Fujita & Krugman (1995), Fujita et al. (1999) and in Puga (1999)’. Moreover, in Murata (2008), agricultural goods are also produced under perfect competition by land input and farmers.

4. First, PT gets rid of the costlessly traded good, and hence, their model does not involve factor-price equalization. Second, all workers are mobile in PT (i.e. their model is based on Helpman (1998), so there is no class of immobile unskilled workers). Third, the technology considered in PT allows land and labour to enter both as fixed and variable inputs.

5. In PT, the bell-shaped curve of spatial development is defined as follows: the dispersion equilibrium prevails for high transport costs, a partial agglomeration equilibrium holds for intermediate transportation costs, and re-dispersion equilibrium prevails for low transportation costs. Moreover, Alonso (1980) identifies five possible bell-shaped paths of development in history: economic growth, social inequality, regional inequality, geographic concentration, and population growth.

6. PT's insights about the bell-shaped curve of spatial development are two-fold. First, the bell-shaped curve is ruled out if land is used for housing only. Second, the PT model does not involve the immobile workforce which is the common explanation for the bell-shaped curve. PT stresses that ultimately there is only one immobile resource, land.

7. PT and Murata (2008) use an assumption of perfect labour mobility.

8. The meanings of housing congestion implied in the PT model are two-fold. First, it intensifies the competition in the land market due to incorporating land use for production. Second, the cost-of-living effect (i.e. the local price index) of the PT model contains both the housing rents and the price index of differentiated goods. It is difficult to clarify the variation of price index of the increasing returns sector and how the variation affects the economic mechanism.

9. In this paper, all scale returns are absorbed by the mobile factor (skilled labour), like the FE model. Hence, there is a complete market-size effect but a transformed price index (i.e. cost-of-living effect of the FE model) in the system.

10. There is no ‘structural change’ for the price index of differentiated goods if land is a consumption good only or a fixed input for production. That is, the larger region always has a lower price index of differentiated goods than the smaller region.

11. Partial agglomeration prevails for high transportation costs, whilst a symmetric equilibrium prevails for low transportation costs, i.e. agglomeration→dispersion.

12. Basically, the agricultural sector in the two regions is a single market, since the agricultural good is homogenous and freely traded, and uses the same technology for production. Following this concept, we assume that rents of agricultural land in the two regions are symmetrical to avoid a complicated framework and to keep the simplicity and focal point as the FE model.

13. The assumption used in the PT model is more reasonable since production takes place with labour and land, both of which enter the fixed and the variable costs, especially in an increasing returns to scale specification. In this paper, however, there are two reasons for abstracting from land as a fixed input of production. First, we focus on the issue of the local price index, which is independent of the fixed costs. Second, all scale returns are transformed into the wage of skilled labour, which is the same setting as the FE model. These let us keep the maximum ‘market size effect’ and allow easy comparison with the results of the FE model.

14. Although many papers are very specific about the use of capital in industrial production, to simplify the analysis we shall assume only two factors of production, land and labour.

15. This concept comes from Krugman & Venables (1995, p. 863).

16. We have tried the setting that shares add to one (i.e. use 1 − γ on unskilled labour) but found this case analytically intractable, as the analytical solutions could not be found for the nominal wage below. Therefore, without loss of generality, we choose the present setting to keep the model's simplicity.

17. This result stems from the fact that w _i,H − w _j,H ∣ _{h = 0} > 0, w _i,H − w _j,H ∣ _{h = 1} < 0, w _i,H − w _j,H ∣ _{h = 1/2} = 0 and ∂²(w _i,H − w _j,H )/∂h²∣ _{h = 1/2} = 0, where h ≡ H _i /H.

18. In terms of the periphery region, its composite price index is a trade-off between ‘increasing transportation costs’ and ‘saving land costs’.

19. Since the analysis of Δu is complex, the full technical details about (28), (29), (30) and Figure 4 are not reported here to save space, but are available from the authors upon request.

20. Pflüger & Tabuchi (2010, p. 486): ‘The Helpman model: agglomeration is strongest at prohibitive trade costs and this agglomeration is then gradually reduced through economic integration until economic activity is completely dispersed at φ₂ (the break point)’.

21. In the FE model, full agglomeration prevails for all φ ∊ (0, 1] if the black hole condition σ < 1+ µ holds. This means that the agglomeration force is too strong and then there is no stable dispersion equilibrium.

22. This fact stems from three distinct features: (1) there are no meaningful solutions of φ _bp1 and φ _bp2 (i.e. the bifurcation points) (Appendix A: Figures III, IV and V); (2) full agglomeration does not exist (its proof is relegated to Appendix B); and (3) the steady state h=1/2 is the unique stable equilibrium before it changes stability due to ∂²Δu/∂h²∣ _{h = 1/2, φ} = 0.

23. We also prove that ∂Δu/∂h < 0 holds when 1 + λ < 0 (see Appendix C).

24. The ‘market effect’ here refers to the net effect of the ‘market size effect’ and the ‘market crowding effect’ stated by Forslid & Ottaviano (2003).