Space and Economics Chapter 3: Classical Location Theory of the Firm Author Wim Heijman (Wageningen, the Netherlands) July 21, 2009

3. Classical location theory of the firm 3.1 Minimization of transportation costs: one final product 3.2 Minimization of transportation costs: one resource, one final product 3.3 Trans-shipment costs 3.4 Other location factors 3.5 Alfred Weber’s theory on location of the firm 3.6 The Theory of the market areas 3.7 Spatial elasticity of demand 3.8 Market forms: spatial duopoly 3.9 Application

3.1 Minimization of transportation costs: one final product Location of one ice cream vendor on the beach Customers equally distributed over the beach Customers have equal preferences for ice cream The lower the average distance between ice cream vendor and customers the more ice cream will be sold

3.1 Minimization of transportation costs: one final product Figure 3.1: Beach with five visitors.

3.1 Minimization of transportation costs: one final product

Figure 3.3: Optimum location in a two- dimensional space.

3.2 Minimization of transportation costs: one resource, one final product Figure 3.4: Location of a firm that produces only one product with the help of one raw material

3.2 Minimization of transportation costs: one resource, one final product

Figure 3.5: Minimization of transportation costs with one input and one product. 3.2 Minimization of transportation costs: one resource, one final product

3.3 Trans-shipment costs * Trans-shipment costs are costs that are made when the transportation mode changes. * For example, in a sea port, the cargo may be transported further to the hinterland by truck, rail or inland waterways. * Trans-shipment costs are normally expressed in money units per weight unit (e.g. euro’s per ton)

3.3 Trans-shipment costs Figure 3.6: Location S of a business with transshipment location O

3.3 Trans-shipment costs

In the case of trans-shipment costs the optimum location is found with:

3.3 Trans-shipment costs If Then the firm is footloose

3.4 Other location factors Apart from transportation costs there are two other important location factors: labour costs; agglomeration benefits or external economies of scale.

3.4 Other location factors Agglomeration: a spatial clustering of interacting firms that is mutually beneficial because it generates a decrease in production costs Deglomeration: spatial deconcentration of firms because of external diseconomies of scale

3.5 Alfred Weber’s theory on location Figure 3.8: Location triangle.

Alfred Weber ( )

Pierre Varignon ( )

3.5 Alfred Weber’s theory on location Figure 3.9: The Varignon frame.

3.5 Alfred Weber’s theory on location Original Varignon Frame

3.5 Alfred Weber’s theory on location

Figure 3.10: Transportation cost optimum with isodapanes.

3.5 Alfred Weber’s theory on location Figure 3.11: Agglomeration benefits.

3.5 Alfred Weber’s theory on location Figure 3.12: Spatial margins to profitability.

3.5 Alfred Weber’s theory on location Figure 3.13: Sections in the location triangle.

3.5 Alfred Weber’s theory on location Figure 3.14: Transportation cost curves of a classical location problem.

3.5 Alfred Weber’s theory on location Figure 3.15: 3-D presentation of the transportation cost function.

3.5 Alfred Weber’s theory on location

3.6 The theory of market areas Three important authors: Walter Christaller (1934), Tord Palander (1935), August Lösch (1939).

3.6 The theory of market areas

Figure 3.17: Palander’s market areas

3.6 The theory of market areas Figure 3.18: Quantity consumed as a function of the distance to the location of the producer (O); the spatial demand function.

3.6 The theory of market areas Figure 3.19: Seven firms with their market areas.

3.6 The theory of market areas Figure 3.20: Hexagonal structure and hierarchy of central places.

3.7 Spatial elasticity of demand

Figure 3.21: Spatial demand curve with fixed spatial demand elasticity of -1.

3.8 Market forms: spatial duopoly Figure 3.22: Spatial duopoly: Hotelling’s Law.

3.8 Market forms: spatial duopoly Hotelling’s Law: spatial competition leads to clustering of competitors in the centre Hotelling’s Law is based on a zero spatial demand elasticity: In terms of game theory Hotelling’s Law describes a Nash Equilibrium Hotelling’s Law is also used by political scientists to explain the positioning of candidates running for a political position: htm

Harold Hotelling ( ) =jILgxeNBK_8&list=UUsooa4yR KGN_zEE8iknghZA

3.9 Application Figure 3.23: Location of sugar factories in the Netherlands in 1992