Spatial Interaction Modelling A Regional Science Context
In this book, the author's strong commitment to the multi-disciplinary field of regional science emerges to provide a unifying framework between spatial modelling traditions from quantitative geography and those from spatial economics, whereby each is enh
- PDF / 2,365,930 Bytes
- 23 Pages / 439.37 x 666.142 pts Page_size
- 84 Downloads / 244 Views
2.1 Some Important Theoretical Advances 2.1.1
UrbanIRural Model and Urban Land Models
The classical land use models provide an excellent introduction to the role of space in microeconomics, as well as to the differences between short run price adjustments and long run locational equilibria. Two of the most significant models in this class are introduced below.
The UrbanIRural Model of von Thonen. This model was first published in 1826 and further clarified by Launhardt (1885). The reader is referred to von Thiinen (1966) for a recent translation. The main purpose of the model is to explain the distribution of land use for different agricultural commodities around a single town, accounting for relative production costs, relative yield per unit area and relative transport costs. The model makes the following simplifying assumptions: (i) the town is a point on a homogeneous plain, (ii) all commodities are shipped to the town, (iii) the transport network is homogeneous with transport costs linearly proportional to distance, (iv) producers pay the transport costs, (v) there are no scale economies in production, (vi) there are two separate crops, (vii) the geometry of the land use is radial, (viii) at any given radius out from the town, only the higher rent-producing commodity is produced and (ix) demand for each commodity is a non-increasing function of price (the classical assumption). Despite the above restrictions, the model is of fundamental importance. We start with the following notation: r = Distance out from town Prj = Equilibrium land rent per unit area of crop j at radius r Qj = Yield of crop j per unit area Vj = Unit selling price for crop j Zj = Unit production cost for crop j tj = Unit transport cost for crop j per unit of distance r' = Radial extent of inner crop (j=l) if two crops present rm = Radial extent of outer crop (j=2) if present (where rent drops to zero) D(vj) = Demand function for crop j in terms of its price Vj Consider first the long run locational equilibrium, where profits must be zero at all points. [If profits were positive anywhere, existing producers may shift location or new producers may enter the market. If they were negative, some producers
J. R. Roy, Spatial Interaction Modelling © Springer-Verlag Berlin Heidelberg 2004
52
2 Key Insights in 'Space' and Microeconomics
must quit the market.] Thus, at any radius r, the zero profit condition for either crop j implies that the land rent must equal revenue minus production and transport costs, yielding (2.1)
In examining the function (2.1) in terms of the geometry of the system and the question of whether one or two crops exist at equilibrium, refer to Fig. 2.1 below, existing at any radial cross-section. Rent Prj
Radius r Fig. 2.1
Rent distribution and extent of cultivation over rural hinterland
It is seen from both the function (2.1) and the above figure that two crops can exist in equilibrium if and only if the crop with the greater rent POI at the centre of the circle also has the greater unit transport cost (Q} t}), that
Data Loading...
