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.

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)

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.

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.

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.

4. At the edge of the city agricultural use outbids urban access to the CBD as the most productive use of land.

5. The housing market may not be perfectly competitive due to racial discrimination and tax advantages. Also, market imperfections occur because of neighborhood externalities and interdependencies in the value of land due to the proximity of neighbors.

1. The theory of household choice is based upon utility theory that introduces the subjective cost of commuting (time, fatigue, strain, boredom) along with other characteristic of housing and non housing services.

2. Households maximize their satisfaction with respect to the consumption of housing, goods, and commuting, subject to a budget constraint (cannot exceed total income).

3. Tradeoffs occur because the value of housing services (rent) is high near the CBD but commuting costs are low. The land-rent function will be nonlinear because of the substitution of capital for land nearer the center of the city.

4. The consumer model has two very realistic implications. First, suburbanites consume more housing than residents close to the urban center. Second, because land is cheaper relative to other housing inputs in the suburbs than it is close to the urban center, suburban housing uses lower capital to land ratios than does housing close to the urban center.

1. Each economic activity has a bid-rent curve (rent-offer curve), the slope of which is determined by the importance of transportation cost savings at more central locations and the abilility or inability to substitute for transport costs.

2. In equilibrium, "excess" profit will be zero for each bidder, when the rent actually paid is indicated by the higher of alternative rent-offer functions, i.e. the "envelope" of the rent-offer curves.

3. It is conceivable that rent offer curves could intersect more than once, especially for commercial versus relatively flat residential uses.

1. While there is only one zero profit function for business firms, there are numerous constant utility curves for households. Each rent-offer curve exists for each utility level, based upon the combination or "bundle" of goods and services offered.

2. The lower the rent-offer curve the higher the utility level since paying less for land rent leaves more money to spend on housing services or other goods and services.

3. Which rent-offer curve is relevant? The relevant curve is the one that equates supply and demand for labor provided by these households. Supply and demand determines the wage rate received by area workers. If labor demand exceeds supply, the new workers will be attracted into the area resulting in a higher rent-offer curve, and lower utility by existing workers, until labor supply equals labor demand.

1. Firms seek access to the CBD for two reasons: First, they area able to lower transport cost associated with the CBD export facility. Second, they are able to achieve agglomeration economies.

2. More distant locations provide the firm with two alternative advantages. First, they face lower land rents. Second, they are able to pay lower wages.

3. Intermediate locations involve a tradeoff between these benefits for CBD versus more distant locations.

4. Although households may benefit from more proximate work locations, they can expect to receive lower wages, even though their net wages (after commuter costs) remain the same. The reason is that at the same wage rate, workers would prefer to work in suburban locations; hence, the greater relative labor supply would force wages down in the suburbs and up in the CBD for the same occupation.

5. More proximate work locations would not affect the rent-offer curve of households unless the aggregate demand and supply of labor changed in the area.

1. Interurban migration from other cities has been used to equate the local demand and supply of labor in order to identify a given household rent-offer curve.

2. Interurban migration from urban area B to urban area A considers any wage, rent, and communting differences that may exist between the two areas.

3. An important prediction emerges from the open-city model: wages vary among urban areas as compensation for differences in land rent, commuting costs, and other amenities.

1. An increase in population growth will shift the rent gradient upward, reflecting higher transport costs at every location and greater benefits from agglomeration in the CBD.

2. An reduction in transport costs will flatten the rent gradient (substitution effect) and shift the rent gradient upward (income effect). However, the net effect will be a flatter rent gradient and lower rent in the CBD, although higher in the suburbs.

3. A change in income will flatten the rent gradient if the income elasticity of the demand for space is greater than the income elasticity of the demand for transport cost savings. Also, with higher income, the fixed cost of commuting is a smaller percentage of total income, which may lower the income barrier to commuting by upper income groups.

4. Agglomeration economies in the suburbs result in other peaks and mountains that affect the general shape of the rent gradient originating in the CBD.