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# Chapter 9: Transportation and Migration of Firms

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• 1. Space and Economics Chapter 9: Transportation and migration of firms Author Wim Heijman (Wageningen, the Netherlands) September 8, 2009
• 2. 9. Transportation and migration of firms
• 9.1 The concept of gravity
• 9.2 Linear Programming (LP): Minimizing transportation costs
• 9.3 Graphs in regional economics
• 9.4 Markov chains and firm migration
• 9.5 Application
• 8.6 Application: Tourism in Slovenia
• 3. 9.1 The concept of gravity
• Economic gravity models are analogies of the physical gravitation law developed by Isaac Newton in his book “Philosophiae Naturalis Principia Mathematica” (1687).
• Interaction between locations is determined by “weights” and distance.
• Economic weights can be determined in several ways, for example number of inhabitants or GDP.
• 4. 9.1 The concept of gravity Isaac Newton (1643-1727)
• 5.
• 9.1 The concept of gravity
Generally speaking the interaction between two locations can be described by the following formula:
• 6. 9.1 The concept of gravity
• A useful application of the model is the so-called doubly-constrained gravity model :
This model is solved with the so-called RAS-procedure
• 7. 9.1 The concept of gravity
• 8. 9.1 The concept of gravity
• 9. 9.1 The concept of gravity
• 10.
• 9.1 The concept of gravity
• 11. 9.1 The concept of gravity
• 12. 9.2 Linear Programming (LP)
• This technique can be used for minimising transportation costs (target function), with the given constraints of :
• maximum capacities of the production units and
• minimum quantities required at demand locations
• 13. 9.2 Linear Programming (LP)
• 14.
• 9.2 Linear programming (LP)
St
• 15. 9.2 Linear programming (LP): Simplex Procedure
• 16. 9.2 Linear Programming (LP)
• 17. 9.3 Graphs in Regional Economics
• A graph consists of a set of points and a set of relationships between pairs of points
• An example of this is the spatial economic main structure in North West Europe
• The points consist of the main economic regions in North West Europe (Randstad, London etc.)
• The ‘relationships’ consist of the megacorridors including railways and highways connecting these regions
• 18. 9.3 Graphs in Regional Economics
• Figure 9.1: Spatial economic main structure North West Europe
• 19. 9.3 Graphs in Regional Economics Figure 9.2: Graph of North West European main economic structure
• 20. 9.3 Graphs in Regional Economics
• 21. 9.3 Graphs in Regional Economics
• 22. 9.3 Graphs in Regional Economics
• 23. 9.3 Graphs in Regional Economics
• 24. 9.3 Graphs in Regional Economics - Accessibility Index (AI): Sum of Row in Accessibility matrix - The higher AI the more accessible a point is - According to AI Region 4 (Brussel-Antwerp) is the most accessible
• 25. 9.3 Graphs in Regional Economics
• 26.
• Figure 9.3: Tokyo subway map
• 27. Figure 9.4: Density of European Road Network (kilometres of road per 100 km2 in 2005) 9.3 Graphs in Regional Economics
• 28. 9.4 Markov Chains
• The basic framework of the Markov model is a matrix with the observed probabilities, named transition probabilities Matrix p
• With the help of Matrix p it is possible to move from one state of a system to the following state.
• Markov chain model is suited to study migration patterns.
• 29. 9.4 Markov Chains
• Example:
• Ireland
• 30. 9.4 Markov Chains Initial State:
• 31. 9.4 Markov Chains
• 32. 9.4 Markov Chains
• The steady state arrives when the proportional distribution of the firms over the regions remains constant
• 33. 9.4 Markov Chains
• 34. Figure 9.6: Fictive proportional distribution of firms over the four Irish provinces over time
• 35. 9.5: Application: Firm migration in the Netherlands
• 36. 9.5: Application: Firm migration in the Netherlands
• 37. 9.5: Application: Firm migration in the Netherlands Figure 9.7: Proportional distribution of firms over the twelve provinces in 2005 and 2095