Space and Economics Chapter 4: Modern Location Theory of the Firm Author Wim Heijman (Wageningen, the Netherlands) July 23, 2009

4. Modern location theory of the firm 4.1 Neoclassical location theory 4.2 The neoclassical optimization problem in a two dimensional space 4.3 Growth poles 4.4 Core and periphery 4.5 Agglomeration and externalities 4.6 Market forms: spatial monopoly 4.7 Spatial duopoly: Hotelling’s Law generalised 4.8 Optimum location from a welfare viewpoint

4.1 Neoclassical location theory In the Weber model substitution of input factors is not possible: Leontief production function In neoclassical analysis of the locational problem of the firm, substitutability of production inputs is assumed: e.g. Cobb Douglas production function.

4.1 Neoclassical location theory Figure 4.1: Location of a firm along a line

4.1 Neoclassical location theory

Assume: Then:

4.1 Neoclassical location theory

Figure 4.2: Spatial production curve. 4.1 Neoclassical location theory

4.2 The neoclassical optimization problem in a two dimensional space

Step 1:

4.2 The neoclassical optimization problem in a two dimensional space

Figure 4.3: Spatial costs curves in the neoclassical model.

4.2 The neoclassical optimization problem in a two dimensional space Figure 4.4: 3-D presentation of the neoclassical cost function.

4.3 Growth poles A growth pole is a geographical concentration of economic activities Growth Pole is more or less identical with: ‘agglomeration’ and ‘cluster’ 4 types of growth poles: technical, income, psychological, planned growth pole

4.3 Growth poles Technical growth pole: geographically concentrated supply chain based on forward and backward linkages.

4.3 Growth poles Income growth pole: location of economic activities generates income which positively influences the local demand for goods and services through a multiplier process, also called trickling down effect.

4.3 Growth poles Psychological growth pole: the image of a region is important. Location of an important industry in a backward region may generate a positive regional image stimulating others to locate in the area.

4.3 Growth poles Planned growth pole: Government may try to stimulate regional economic development for example by a policy of locating governmental agencies in backward regions.

4.3 Growth poles Figure 4.6: Types of growth poles.

4.4 Core and periphery Gunnar Myrdal ( ): Core periphery theory: economic growth inevitably leads to regional economic disparities.

4.4 Core and periphery Economic growth is geographically concentrated in certain regions (the core) In the core regions polarisation plays an important role. Myrdal calls that “cumulative causation”

4.4 Core and periphery The core regions attract production factors (labour, capital) from the periphery: “backwash- effects” If the cumulative causation continues, congestion appears in the core regions (traffic jams, high land prices, high rents, high wages, etcetera). This will generate migration of land-intensive and labour-intensive industries from the core to areas outside: “spread effect”. In most cases, areas close to the core profit most from this effect: “spill over areas”.

4.4 Core and periphery Alfred Weber’s theory on location Figure 4.7: The principle of cumulative causation

Gunnar Myrdal ( )

4.5 Agglomeration and externalities Figure 3.12: Spatial margins to profitability. Economies of scale: costs per unit product decrease if the scale of production increases Two types of externalities: - internal; - external. Internal economies of scale take place within a firm external economies of scale, a form of externalities, take place between firms External economies of scale may arise in a cluster or agglomeration

4.5 Agglomeration and externalities

Figure 4.8: Stable spatial equilibrium.

4.5 Agglomeration and externalities Figure 4.9: Unstable spatial equilibrium.

4.5 Agglomeration and externalities

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4.6 Market forms: spatial monopoly Figure 4.12: Spatial demand curve.

4.6 Market forms: spatial monopoly

4.7 Spatial duopoly: Hotelling’s Law generalised Figure 4.13: Spatial duopoly with two mobile selling points (MSP).

4.7 Spatial duopoly: Hotelling’s Law generalised

The cooperative solution :

4.7 Spatial duopoly: Hotelling’s Law generalised competitive solution: The competitive solution represents a so-called Nash equilibrium.

4.7 Spatial duopoly: Hotelling’s Law generalised

4.8 Optimum location from a welfare viewpoint In case of monopolistic competition the products offered are almost perfect substitutes for another For example, restaurants may offer exactly the same meals, but on different locations. Everything else being equal, one prefers a meal in a restaurant on a location which is close by to a meal in a restaurant far away.

4.8 Optimum location from a welfare viewpoint Figure 4.14: Six restaurants in a circular space.

4.8 Optimum location from a welfare viewpoint

Figure 4.16: Cost functions

4.8 Optimum location from a welfare viewpoint Figure 4.17: Cost functions and Total Revenue function if the price of a meal equals €