Chapter 6: Theoretical Analysis of Urban Structure
1. Why are downtown area used more intensively than suburban areas? Why are certain goods and services produced in downtown areas and others in the suburbs? Why is it important that downtown locations permit the substitution of capital and labor for land?
2. This chapter presents the basic ingredients for urban structure and gross spatial patterns of urban areas. The next chapter sees how well the facts fit the theory presented in this chapter.
Urban Area with a Single Industry
1. Suppose a region possesses a comparative advantage in the production of a single commodity that is produced for export (economic base).
2. Production is as close to the point of shipping (railhead or port) as possible in order to economize on transportation costs. (Distribution cost to the railhead and assembly costs from the railhead will increase with the distance from the shipping point.)
3. A space of u miles from the point of export results in potential production sites within a geographic area that produces goods that must be transported to the point of export for all shipping.
4. Assume that labor costs are uniform throughout the area. (This assumption will change with the location of households that will be considered later on.) Also, assume constant returns to scale but with a production function that allows substitution between capital and land in order to produce a given output.
5. Although capital can be substituted for land, there is diminishing returns to the use of additional capital with a fixed amount of land. This is because of the need for stronger walls or offsets, heavier foundation, and space for elevators and stairs that caused output per square foot to decrease as the number of floors increases.
6. Assume input and output markets are perfectly competitive so that their prices are given to the firm.
7. Finally, assume that shipment costs are linearly related to distance, independent of the place of origin or distance traveled.
8. The dependent variables in the model are the amounts of capital employed on different plots of land, the rental rates of the various plots of land, and the total output and price of the commodity.
9. In equilibrium, the value of marginal product of capital will equal the cost of capital (interest rate); and the value of marginal product of land will equal its rent. In each case the value of marginal product is the marginal physical product multiplied by the net price = price - t u (where t is the unit-mile transport cost to the point of shipment and u is the miles shipped)
The Bid Rent Curve
1. The bid-rent curve is the rent that producers will pay at alternative locations. The highest rent will take place when the distance traveled, u, is the lowest. However, with the higher rent, employers will substitute capital for land.
2. The net profit to the firm is the same at each location because of competition; but in more distance locations, more of the cost is in the form of transport costs rather than rent. Also, at more distant locations capital will be used less intensively, since less capital will be substituted for land.
Implications of the Model
1. All land available within the urban area must be used to produce the commodity.
2. The production function indicates how much of the commodity is produced by land and capital at each distance, u.
3. Overall supply and demand are equal in the urban area, but demand is the sum of local demand plus export demand.
4. Finally, urban areas compete for land versus its next best alternative, say agricultural use. The value of land (rent) that will be paid for transport cost savings is just equal to the marginal productivity of land for urban versus rural use.
5. Note that the model is only applicable for profit maximizers and is unrealistic because it does not consider the cost of labor or the location of households.
Households in an Urban Spatial Context
1. The theory of household location is centered on maximization of utility rather than profits. But, it also considers the cost of commuting from distant locations to the CBD, where jobs are located.
2. Housing services are also produced with land, labor, and capital inputs. The construction industry produces housing structures that vary in intensity at different locations based upon the amount of capital inputs substituted for land.
3. In a competitive housing market, rent represents the value of a stream of housing services that households are willing to pay. The bid-rent curve will be the highest when transportation costs savings are maximized and will decline to zero at the edge of the city.