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An Introduction to Regional Economics
Edgar M. Hoover and Frank Giarratani
6
Land Use

6.1 WHAT IS "LAND"?

In Chapter 4, competition for scarce local inputs was identified as one of the factors limiting spatial concentration and favoring the dispersal of activities. We are now ready to see how this works.

The present chapter deals with the dispersive effects of competition for land, which first and foremost denotes space. Every human activity requires some elbowroom. The qualities of land include, in addition, such attributes as the topographic, structural, agricultural, and mineral properties of the site; the climate; the availability of clean air and water; and finally, a host of immediate environmental characteristics such as quiet, privacy, aesthetic appearance, and so on. All these things—plus the availability of such local inputs as labor supply and community services, the availability of transferable inputs, and the accessibility of markets—enter into the judgment of what a particular site is worth for any specific use.

Labor, as a local input will be discussed in Chapter 10. The present chapter focuses almost entirely on space per se as the prototype of scarce local input. But it is appropriate to keep in mind that in an increasingly populous and urban economy, more and more of what were initially the free gifts of nature (such as water, clean air, and privacy) are assuming the character of scarce local resources, and this scarcity constrains the concentration of activities in somewhat the same way as does the inherent scarcity of space itself. Competition for space in an urban area is highly complex because of the many ways in which an activity affects its close neighbors. Such neighborhood effects or local externalities were touched on in Chapter 5 and will be further explored in Chapter 7 as basic features of the urban environment.

6.2 COMPETITION FOR THE USE OF LAND

Most land can be utilized by any of several activities. Even an uninhabitable and impassable swamp may have to be allocated between the competing claims of those who want to drain or fill it and those who want to preserve it as a wetland wildlife sanctuary. The normal multiplicity of possible uses means that in considering spatial patterns of land use, we can no longer think in terms of the individual location unit (as in Chapter 2) or of one specific activity (as in Chapters 4 and 5) but must move up to another level of analysis: that of the multiactivity area or region.

Competition for land plays an important locational role in areas where activities tend to concentrate for any reason. Locations having good soil, climate, and access to other areas, and areas suitable for agglomeration under the influence of local external economies, as discussed in Chapter 5, are in demand. The price of land, which is our best measure of the intensity of demand and competition for land, varies with quality and access, and rises abruptly to high peaks in the urban areas. Anything we can discover about the locational role of land-use competition, then, has particular relevance to the urban and intraurban problems that have become so important in recent years.

On the other hand, there are activities that need large expanses of land in relation to value of output and are, at the same time, sensitive to transfer cost considerations—agriculture being the most important, though the same considerations apply to forestry and some types of outdoor recreation as well. These activities require so much space that although they do not effectively compete for urban land, their location patterns are strongly affected by competitive uses. Such activities are a second important area of application for land-use analysis.

In societies in which land use is governed through a price system, the price of using land is identified as rent,1 and in principle each parcel of land goes to the highest bidder. Owners of the land will, if they want to maximize their economic welfare, see to it that the land goes to that activity and specific "occupant" (firm, household, public agency, or other) that will pay a higher rent than any other. At the same time, occupants will ideally compare different sites on the basis of how much rent they could afford to pay for each if it were utilized in the most efficient way available to them, and will look for the site where the rent they could afford to pay exceeds by the largest possible margin what is charged.

Needless to say, land markets are not in fact so perfect in their allocation, nor are owners or users possessed of omniscience or exclusive devotion to the profit motive.

It is almost equally obvious that allocation of the land based purely on individual profit maximization, even if competition worked more efficiently than it does, could not produce a socially optimum pattern of land use—not even in the sense of maximizing the gross national product, to say nothing of more comprehensive criteria of welfare. Here, as in every other area of economics, some social intervention is required to take account of a wide range of costs and benefits that the existing price system ignores. Just because a paper mill can outbid any other user for a riverside site, it does not follow that it is socially or economically desirable that it should preempt the river from other users who would refrain from befouling it. Direct controls on land use (including zoning ordinances, urban renewal subsidies, and condemnation or reservation of land for public use) are vital elements of rational public policy even where free competition is most enthusiastically espoused.

Socialist countries initially nationalized all land and attempted to assign it without using any system of market or imputed prices. A retreat from this doctrinaire position has been in evidence in recent years in some of these countries (notably Yugoslavia), with competitive market forces being given an increasing role in land-use allocation, though severe constraints prevail as to the amount of land any one individual may own.

In 1966, four Soviet legal experts pointed out the economic waste involved in allocating land without explicit regard to its productivity in alternative uses. In a striking departure from orthodox Soviet doctrine, they proposed "that we speed the introduction of a land registry, which would incorporate the registering of land use, a record of the quantity and quality of land, and an appraisal of its economic value." They proposed, further, that the price of land be included in cost estimates of construction projects. "Only thus will a true picture of economies in construction become apparent. Let the economists work out the form, but it seems to us that the attitude that land costs nothing must be decisively rejected."2

Despite the fact that Soviet planners had even earlier adopted the practice of including an interest charge on plant and equipment in evaluation projects, the guardians of Marxist orthodoxy have apparently thus far balked at using a price system to guide land use, or even setting any quantitative value on land. A 1968 statement of land-allocation policy in the U.S.S.R. explicitly rejected land pricing in these terms: Use of the land free of charge is one of the greatest achievements of the Great October Socialist Revolution."3

The difficulties involved in maintaining such a policy are extensive. Kenneth R. Cray has pointed out that in the absence of an explicit assignment of land rents in the Soviet Union, agricultural procurement prices paid by the state have been used as the main mechanism by which land rents can be extracted; instead of charging rents directly, to some extent rents are recovered by differentiation of official purchase prices. Thus prices paid to farms in different regions for identical products may vary substantially.4

Still another situation applies in many less developed countries. A few large landowners own the bulk of the land and have been able to stave off or subvert any efforts to achieve land reform. The adverse effects of this concentration of ownership would be far less if the owners were primarily concerned with maximizing returns from use of the land. But they have generally been either inert in the face of such economic opportunities or convinced that their long-term interests are better served by blocking the industrial and political changes that might follow a breakup of the static feudal order in which they attained their positions.

In order to understand the way in which land is allocated to various activities, we shall first ask what determines how strong a bid any particular activity can make for the use of land—that is, the maximum rent per acre that that activity could pay for land in various locations. In a society that uses prices, costs, and profits as a principal mechanism for allocating resources, this line of inquiry will help explain actual location patterns. It will also provide a rough guide as to which location patterns represent an efficient allocation of resources from the standpoint of the economy as a whole. Later (particularly in Chapters 7 and 13), we shall give more explicit attention to the important problem of divergences between individual interests and the general public interest.

6.3 AN ACTIVITY’S DEMAND FOR LAND: RENT GRADIENTS AND RENT SURFACES

There are countless reasons why an individual, firm, or institution will pay more for one site than for another. A site may be highly desirable because of its mineral resources, soil quality, water supply, climate, topography, agreeable surroundings, good input-output access (that is, access from input sources and to markets), supply of labor, supply of public services, prestige, and so on. In fact, the number of possible reasons for offering more for one site than for another is equal to the number of relevant location factors, less one (the price of the site).

For any particular activity, or kind of land use, there is a geographical pattern of site preference, represented by the amounts that practitioners of that activity would be willing to pay or "bid" for the use of each of the various sites. If we picture such a pattern, with the activity’s bid rent (or rent bid) represented by height, we have a rent surface, with various hollows at the less useful sites and peaks at the more useful sites. A cross section of this surface, representing rent bids for sites along a specific route, is called a rent gradient. The rent surfaces and gradients will vary in their conformation according to the type of land use, and we shall see later how space can be allocated among alternative uses on the basis of their bids.

First, however, it will be useful to see a bit more clearly how an individual user’s pattern of rent bids arises. For this purpose, we shall consider a particularly simple kind of situation, in which site desirability reflects just the one location factor of access to a single given market. We shall ignore, for the time being, all other distinguishing features of sites. The sites being compared are all within the supply area of a single market center: For example, they might be dairy-farm sites constituting an urban milkshed. For still greater simplification, we shall assume that there are so many individual producers in this supply area that each must take the market price as given in deciding about his or her own output and locational preference.

6.3.1 Rent Gradients and Surfaces with Output Orientation

Figure 6-1 shows a plausible relationship between the various possible amounts of a particular kind of output on an acre of land and the cost of the inputs (other than the land itself) required to produce that output. There are some fixed costs (F), and some variable costs, which rise more and more rapidly as the intensity of use approaches its feasible maximum. Total costs are as shown by TC, and in symbolic terms,

TC=F+aQb

where b is some exponent larger than 1. The average unit cost curve, AC, is of the familiar U shape. Figure 6-1 is drawn with F =100, a =1, and b =3.

It hardly needs to be said that the cost/output formula offered here is purely illustrative, not based on specific empirical investigation. The formula does, however, conform to generally accepted norms for the shape of production functions.5

 

The total cost (TC) curve of Figure 6-1 reappears in Figure 6-2, where we discern how the user of the site can rationally determine the output per acre that will maximize his or her rent-paying ability. The three white lines show receipts at three possible net prices for the output at this site. They rise proportionately to output, since we are assuming that the demand for the output of this producer is perfectly elastic. This is generally the case in agricultural or other activities involving many relatively small sellers.

At the highest of the three prices, which might reflect a location rather close to the market, the receipts curve (total revenue minus transfer costs on the output) is OL and the largest surplus of receipts over nonland costs is BC, with an output of OA. Accordingly, BC represents the maximum rent that this activity could afford to pay for the use of this acre. It will be noted that at point C, the total cost curve, TC, has the same slope as the total receipts curve at that rate of output. In other words, at that rate of output, marginal costs are equal to marginal receipts, or price, and therefore the excess of revenues over costs is maximized (or losses are minimized). Because the total cost curve includes the opportunity cost of capital; that is, a "fair" return on capital, BC represents potential excess, or economic profits. For rent payments less than BC, economic profits will be realized, but the land user would be willing to bid up to BC for rent at this location, recognizing that he or she could still earn normal profits with this rental payment.

At a location more remote from markets, the receipts curve will be OM, reflecting a lower net price because of higher transfer costs. In that situation, the best rate of output is again the one for which the receipts and cost curves have the same slope; but here, the maximum rent-paying potential of the acre (the bid rent of this activity) is zero. At any rate of output smaller or larger than OE, the land user could not cover costs even on rent-free land, and this acre will consequently be worth precisely zero to him or her.

At a less advantageous location, where the net price is still lower (receipts curve ON), there is no rate of output that would cover costs, to say nothing of providing anything for rent. The minimum subsidy, or negative rent, required to make it worthwhile for this activity to use the land would be HJ, at an output of 0G. Once again, this is the output at which the receipts and cost curves are parallel.

Let us assume, then, that our land user acts rationally and so adjusts the intensity of his or her land use and the output per acre as to maximize the excess of receipts per acre over costs exclusive of rent, and that this excess represents the most he or she would bid as a rent payment for the acre.6

Now let us compare the situation at sites located at different distances from a market, as in Figure 6-3. At each site, the net price received per unit of output is reduced by the costs of transfer to market. It will be observed that the curve showing rent in relation to net price, in the upper panel of the figure, is concave upward—in other words, the rent falls more rapidly near the market and more gradually farther out. This characteristic feature of rent gradients reflects the fact that we have allowed for some flexibility in the intensity of land use in this activity. Output per acre is larger at locations close to the market. The reason for this is that land rents increase for locations closer to the market, and this implies that the price of land will be rising relative to the price of other factors of production as distance to the market diminishes, other things being equal. As this happens, we should expect more intensive use of land; more of the other factors of production will be used per acre of land, and output per acre will increase. This means that the revenue per acre, and therefore the rent that can be earned, is more sensitive to transfer cost at such nearby locations than at more remote locations where a smaller amount of output is shipped from each acre. Of course, if there were complete flexibility in intensity (that is, immunity from diminishing returns), all of the activity could best be concentrated in a single skyscraper at the market. The rent gradient would be almost vertical.

The lower panel of Figure 6-3 shows the same rent gradient, but this time charted in relation to distance from the market. Because of the characteristic economies of long-haul transfer discussed in Chapter 3, the net price of the product will fall more and more slowly with increasing distance: Each extra dollar per ton buys more and more extra miles of transfer as we go farther from the market. Consequently, we can expect rent as a function of distance to have the accentuated concavity shown in the figure.7

Over a geographic area, we have a rent surface whose basic shape is a concave-sloped "cone" with its peak at the location of highest possible rent; in the cases discussed so far, that peak is at the market.

But for a number of reasons, real rent gradients and surfaces are never so smooth and regular as our diagrams suggest. In the first place, we have been assuming throughout that all the land is of equal quality for this particular kind of use, in all respects save access to market. A location or zone of locations with some superior advantages (for instance, higher soil fertility or cheaper labor) would be marked by a hump on the rent surface, and a place with higher costs by a dent (or even a complete gap in the surface if for some reason that activity could not be practiced there at all). The rather common stepwise variation of transfer rates produces a corresponding terracing of rent surfaces. Rent gradients will be flatter along routes of cheaper or better transfer; so if we think of a rent surface around a market as a mountain, it will fall away in sloping ridges along such routes and more abruptly elsewhere. Finally, there is usually more than just one market; thus the rent surface of an activity over any sizable area will rise to a number of separate peaks.

6.3.2 Rent Gradients and Rent Surfaces with Input Orientation

One may well ask at this point why the theory of land use places so much stress on access to markets. Why not access to the sources of transferable inputs? In such a case, of course, we should have rent gradients and rent surfaces peaking at such sources, rather than at markets.

Such patterns do occur. Residents (particularly in resort areas but to some extent elsewhere too) have a tendency to cluster around certain foci of consumer attraction, such as beaches. The activity here is residence, which requires space for which it is willing to bid rent. The input is enjoyment of the beach, which is more easily available the shorter the distance. The intensity of land use is measured by the degree of crowding of residents (persons per acre). In addition, we observe characteristic gradients of intensity and rent. If there are no considerations of desirability except access to the beach, and if the residents are not too unlike in incomes and tastes, the land values will be lower and the lot sizes larger the greater the distance from the beach. If the beach is a long one, equally attractive throughout its length, the rent surface will rise not to a peak but to a ridge or cliff along the shore, falling away to landward.

We should expect to find an analogous situation in an urban external-economy activity if the principal attraction of a cluster lies in better access to production inputs, such as supplies and services. A location in the center of such a cluster is more valuable than one on the periphery.

By and large, however, rent gradients are much more often focused around markets than around input sources. The great space-using activities are agriculture, forestry, and livestock grazing. They produce bulky transported outputs but require relatively insignificant amounts of transported inputs; consequently, their transfer orientation is overwhelmingly toward markets. The basic reason for this is that their main inputs are nontransferable ones: solar energy, water, and organic properties of the soil. They have a large stake in being close to markets but a very small stake in being close to sources of any transferable input, such as fertilizer or pesticide factories.

On the urban scene, the greatest land-using activity is residence, and the transfer orientation of residences is mainly toward markets for labor services; that is, toward employment locations. Only a household consisting wholly of consumers, without any members employed outside, is free to orient itself exclusively to amenity "inputs." And even in cities known as recreation or retirement centers, the great majority of households contain at least one worker. Although within urban areas we do see neighborhood rent gradients rising toward parks or other amenity locations, the overall pattern of rents and land values appears to be shaped to a greater extent by access to jobs. High densities of urban population occur almost exclusively in areas close to major job concentrations.8

The various business and government activities of an urban area, insofar as they serve the local market, are strongly market-oriented because their transferable outputs are so much more perishable and valuable than their transferable inputs. Consequently, they have a large stake in access to the distribution of residences, jobs, or both. Once again, we have rent gradients rising in the direction of markets; in this case, generally toward the center of the urban concentration.

Finally, manufacturing industries oriented toward sources of transferable inputs are mainly those engaged in the first-stage processing of rural products (crops, including timber, and minerals). They are input-oriented, as noted in Chapter 2, because their processes characteristically reduce weight and bulk, and sometimes (as in the case of canning and preserving operations) perishability as well. But these processing activities themselves are not extensive land users in a rural context. In fact, they are highly concentrated relative to their suppliers, and they have supply areas rather than being part of market areas. Consequently, their locations are not significantly affected by land costs; but each of the units of such a primary processing activity may represent a peak in the rent surface of the activity supplying it with inputs.

The foregoing discussion has justified the application of the rent gradient and rent surface concepts primarily to output-oriented activities, with the gradients and surfaces rising as we approach the market for the activity’s transferable output.

6.3.3 Rent Gradients and Multiple Access

It is best to keep in mind that a land user’s willingness to pay rent for the use of a site need not depend solely on that site’s access to some single point.

The pure supply-areas case identified in Chapter 4 conforms most nearly to that situation. Each market is served by many scattered sellers, and each seller disposes of its entire output in just one market. Rural land uses, and in particular agriculture, are the classic example. The multiplicity of sellers sharing the same market, moreover, implies relatively pure competition. Any one seller’s output is small compared to the total purchases of any one market; thus it has a perfectly elastic demand for its output and can sell as much as it chooses to produce without affecting the price.

As has already been suggested, however, real-life situations are often more complex. Specifically, the access advantages of a location may depend upon nearness to more than one other point. Even small producers, particularly if their outputs are not completely standardized, may sell to more than one market. In addition, with respect to other kinds of access also—for example, supply of transported inputs or labor, or the serving of customers who are themselves mobile, such as retail shoppers—the true access advantage of a location is often a composite reflecting transfer costs to a number of points. In such a situation, the rent surface may well have a number of peaks, hollows, and ridges, and may even peak at points of maximum access potential that are intermediate between actual centers.

6.4 INTERACTIVITY COMPETITION FOR SPACE

Although we have explained why any one activity can afford to pay a higher price for land in some locations (primarily, closer to market), and why that activity’s intensity of land use shows a similar spatial pattern of variation, nothing has been said yet about land requirements as a factor influencing the relative locations of different activities.

If we consider a number of different activities, all locationally oriented toward a common market point, a comparison of their respective rent gradients or rent surfaces will indicate which activity will win out in the competition for each location.

6.4.1 A Basic Sequence of Rural Land Uses

The foundations for a systematic understanding of the principles of land use were laid more than a century and a half ago by a scientifically minded North German estate owner named Johann Heinrich von Thünen.9 He set himself the problem of how to determine the most efficient spatial layout of the various crops and other land uses on his estate, and in the process developed a more general model or theory of how rural land uses should be arranged around a market town. The basic principle was that each piece of land should be devoted to the use in which it would yield the highest rent.

In von Thünen’s schematic model, he assumed that the land was a uniform flat plain (not too unrealistic for the part of the world where he farmed), equally traversable in all directions. Consequently, the various land uses could be expected to occupy a series of concentric ring-shaped zones surrounding the market town, and the essential question was the most economical ordering of the zones.

A set of rent gradients for three different land uses, extending in both directions from a market, is shown in the upper part of Figure 6-4; and in the lower part of the figure this arrangement is translated into a map of the resulting pattern of concentric land-use zones. Each land use (activity) occupies the zone in which it can pay a higher rent than any of the other activities. In the case shown, it appears that the land nearest the market town should be devoted to forestry, the next zone outward to wheat, and the outermost zone to grazing. The land beyond the pasturage zone would not have any value at all in agricultural uses to supply this market town.10

The gradient of actual land rents and land values in Figure 6-4 is the black line following the uppermost individual-crop gradient in each zone. Such a composite gradient will necessarily be strongly concave upward, since the land uses with the steeper gradients get the inner locations, and the gradients are flatter and flatter for land uses located successively farther out.

Finally, we may note that this solution of the crop location problem can be applied regardless of whether (1) one individual owns and farms all the land, seeking maximum returns; (2) one individual owns all the land but rents it out to tenant farmers, charging the highest rents he or she can get; or (3) there are many independent landowners and farmers, each seeking his or her own advantage. In a perfectly competitive equilibrium, the rent going to landowners and the value of land would be maximized, and rents would be set at the maximum that any user could afford to pay; as a result, landowners and tenants could all be indifferent as to which zone they occupied, since the rate of return on capital and labor would be the same in all of the zones used.

6.4.2 Activity Characteristics Determining Access Priority and Location

In von Thünen’s basic model (which assumes that each crop has the same delivered price and transfer rate, and a fixed intensity of land use regardless of location or rent), the rule for determining the position of a particular land use in the sequence is a simple one. The activity with the largest amount of output per acre has the steepest rent gradient and is located closest to the market, and the other activities follow according to their rank in per-acre output.

The situation is not quite so simple, however, when we recognize that land-use intensity and output per acre can vary for any given activity; that the outputs of the different activities are transferred at different rates of transfer cost per ton-mile; and that the rent gradients themselves are characteristically curved rather than straight, so that conceivably any two of them might intersect twice rather than just once. Accordingly, we need to look more closely into what characteristics of the various activities determine their location sequence in relation to the market.

The question can be posed as follows: If the rent gradients for two different activities intersect (that is, they have the same rent level at some given distance from market), and if we know something about the characteristics of these two activities, what can we say about which activity is likely to have the steeper gradient at the point of intersection and, consequently, the land-use zone closer to the market?

It was suggested earlier that a reasonable form of cost function for any one of the activities is

TC=F + aQb

where TC is the cost of nonland inputs on an acre, F the fixed cost per acre, and Q the output of the acre; a and b are coefficients characterizing the technology of the activity. More specifically, a large value for a means that variable-cost outlays are high relative to output and to fixed costs; a large b value means that variable costs per unit of output rise rapidly with increased intensity (i.e., as more variable inputs are applied to a fixed amount of land) because of the law of diminishing returns (see footnote 5).

According to this formulation of the relationship between output per acre and nonland costs per acre, the rent gradient for the activity is, as shown in Appendix 6-1,

R = a(b 1)[(P tx)Iab] b/(b-1) F

where R is the maximum rent payable per acre, P is the unit price of the activity’s output at the market, t is the transfer charge per unit of output per unit distance, and x is the distance to the market.

Each of the various identifying characteristics of an activity (a, b, F, and t) affects the shape and slope of the rent gradient in some way; and from that effect we can surmise how each of these characteristics affects the likelihood of the activity’s being a prime candidate for the occupancy of land near the market.

The effects are shown in Figure 6-5 in a series of four diagrams (see Appendix 6-1) for explanation of the underlying calculations and a proof of the general validity of the relationship shown). In the first panel (upper left), we have intersecting rent gradients for two activities that differ only with respect to the value of a in their production functions (i.e., all other factors influencing the slope of the rent gradient are held constant). The steeper gradient (implying location in the inner zone) is that of the activity with the smaller a; that is, the activity in which a given outlay per acre yields a larger amount of product. This makes sense, since such an activity could be expected to have a larger stake in proximity to markets than an activity producing small amounts of transported outputs per acre.

The upper right panel in Figure 6-5 shows, in like fashion, the locational effect of the b coefficient—which, as mentioned above, measures the strength of diminishing returns to the more intensive use of land. The steeper gradient is that of the activity with the smaller b (in other words, the activity with the greater flexibility in intensity, permitting higher intensities nearer the market).11 For example, activities able to use high-rise buildings can generally bid more for central city land than can activities that must have a one-story layout.

The lower left panel indicates that higher fixed costs per acre are associated with steeper gradients and close-in locations. When a large proportion of costs are fixed, regardless of output per acre, the rise in unit variable costs with higher intensity has less effect on rent-paying ability.

The locational effect of differences in transfer rates is shown in the last panel of Figure 6-5. As expected, an activity whose product is bulky, perishable, valuable, or for any other reason expensive to transfer has an especially strong market orientation and can pay a high premium for locations near its market.

Thus transfer and production characteristics help to determine the ability of an activity to bid for locations at various distances from the market center. The savings in transfer costs associated with more central locations depends crucially on two factors: (1) the quantity of transported output produced for a given total outlay and (2) the transfer rate per unit of output. Production cost advantages accrue at more central locations to those activities that (1) can use land more intensively and (2) have higher fixed costs per acre.

6.5 RURAL AND URBAN LAND USE ALLOCATION

The general principles of land-use competition and location of space-using activities that we have developed thus far are relevant to the highly extensive rural land uses to which this theory was originally addressed and also to the relatively microscale land-use patterns within urban areas. These principles can also be used to explain how land is allocated between rural and urban uses.

In order to appreciate how these principles may be applied in a rural/urban context, it is only necessary to realize that the activities which compose an urban area have assumed relatively central locations because they have been successful in bidding that land away from competing uses. As in the preceding discussion of land-use competition among rural activities, our explanation of this outcome rests on identifying the transfer and production characteristics that cause urban land users to place high value on access considerations.

6.5.1 Some Characteristics of Urban Economic Activity

One special feature of activity in urban areas is the important role played by the movement of people and the necessity of direct and regular face-to-face contact in location decisions. A crucial function of cities is to enable large numbers of people to make contact easily and frequently—for work, consultation, buying and selling, negotiation, instruction, and other purposes. People are more expensive to transport than almost anything else, mainly because their time is so valuable. Accordingly, intracity locations are governed by powerful linkage attractions operating over short distances and emphasizing speed of travel.

Another feature of urban locations is the intense interdependence caused by proximity and by competition for space and other nontransferable inputs. Every activity affects many neighbors, for better or for worse: External economies and diseconomies are always strong.

Both of these features imply that the advantage of physical proximity, as measured by money and time saved, is of the utmost importance to many types of economic activity within urban areas. The primary function of an urban concentration is to facilitate access, and time costs are a major determinant of access advantage in the urban setting.

Access linkages among nonresidential activity units involve in part interindustry transactions.12 Thus business firms have an incentive to locate with good access to their local suppliers and their local business customers. Some important interbusiness linkages, however, do not directly involve such transactions at all. Local branch offices or outlets of a firm are presumably located with an eye to maintaining good access to the main local office, while at the same time avoiding overlap of the sublocal territories served by the branches (for example, the individual supermarkets of a chain or branch offices of a bank). There are strong access ties between the central office of a corporation and its main research laboratory, involving the frequent going and coming of highly paid personnel. Additionally, as we saw in Chapter 5, substantial economic advantages can accrue to some activities as a result of clustering. The nature of these agglomeration economies most often depends on close proximity.

Linkages among households are also important. A significant proportion of journeys from homes are to the homes of others. Such trips are by nature almost exclusively social and thus involve people linked by family ties or by similar tastes and interests. This observation suggests that the value of interhousehold access can also be expressed fairly accurately in terms of a preference for homogeneity. However, the pressures toward neighborhood homogeneity include other factors besides access.

Linkages between residential and nonresidential units are by far the most conspicuous. The entire labor force, with minor exceptions, is concerned with making the daily journey to work as quick and painless as possible, and work trips are the largest single class of personal journeys within an urban area.13 Shopping trips are another major category. The distribution of goods and services at retail makes mutual proximity an advantage for both the distributors and the customers. Trips to school and cultural and recreational trips make up most of the rest of the personal trip pattern. There is mutual advantage of proximity throughout. The nonresidential activities dealing with households are most advantageously placed when they are close to concentrations of population, and at the same time residential sites are preferred (other things being equal) when they provide convenient access to jobs, shopping districts, schools, and other destinations.

Thus interdependence, the importance of the movement of people, and the necessity of direct contact is significant characteristics of urban activity. Individually they suggest the crucial role played by transfer considerations in shaping urban land use decisions. Jointly, these characteristics have a substantial effect on the urban rent gradient.

As described in the preceding section of this chapter, transfer factors affect the steepness of rent gradients in two ways: Higher transfer rates per unit distance and greater quantities of output for a given total outlay both make movements away from central locations costly. Thus activities with these characteristics are willing to bid high rents for locations with access, and their bid rents fall rapidly as distance from the center increases.

For urban activities, transfer factors of this type are very important in locational decisions. The increased expenses associated with maintaining contacts and developing new ones at longer distances, as well as the lost time associated with the movement of people, are important considerations in locational decisions. Their significance is reflected in higher rent bids for locations with good access.

While it is easiest to think of output as measured in physical units (e.g., tons of steel or the number of customers served), many types of output are not so easily described. Financial or consulting services are cases in point; output measures are much less tangible in these activities. However, in some instances the frequency of personal contact is itself indicative of the rate of output. Therefore, urban land users, particularly service industries, are often not only characterized as having higher transfer rates (primarily time costs associated with the movement of people), but they may also have high rates of output (entailing many interpersonal contacts) for a given total outlay.

In addition to these transfer considerations, our earlier discussion concerning the activity characteristics determining access priority suggests that production factors may also help to explain the high value placed on central locations by urban activities. In particular, the ability to substitute easily between nonland and land inputs contributes substantially to the steepness of the urban rent gradient. Thus activities that are able to use high-rise buildings (e.g., insurance companies or corporate headquarters) can bid more for central city land than can activities that must have a one-story layout. Further, to the extent that substitutions imply more of such fixed costs as buildings and equipment per acre of land, the steepness of urban rent gradients is also enhanced.

The provision of downtown off-street parking for cars provides an interesting example of the relevance of both transfer and production advantages on urban land use. Parking services are oriented toward the destination of car users after they leave their cars, since they will be making the rest of the journey on foot. In a parking lot, the nonrent costs are mainly the wages of an attendant, although there may be some capital outlay associated with the attendant’s hut or an automatic gate mechanism. Also, the capacity of the lot has a definite limit. Here, then, we have an activity with a high transfer rate, low fixed costs, and a very limited ability to substitute nonland for land inputs. A multilevel parking garage has the same transfer rate but fairly high fixed costs, since there is now a substantial investment in a structure. Additionally, the garage can use land much more intensively by increasing the height of the building. Consequently, the parking garage will have an even steeper rent gradient than a parking lot and will be the predominant form of facility in areas where the demand for parking and the demand for space in general are greatest.

6.5.2 Equilibrium of Land Uses and Rents

The production and transfer characteristics of activities that occupy urban areas thus enable them to use land intensively and to bid high rents for central locations. We now have some explanation of the sequence in which we could expect different activities to arrange themselves around a common focal point, such as a market or central business district. However, we have yet to examine the factors that contribute to the width of an activity’s zone, and consequently our analysis of factors that might affect the allocation of land among uses is incomplete.

Since we are still assuming that land is of equal quality everywhere, the greater the demand for an activity, the larger the zone it will occupy. Thus we might think of an urban area as comprising the zones of a number of activities. If the market demand associated with one such activity increases, its bid rents will also increase. Figure 6-6 depicts an activity’s net receipts (total revenue minus transfer costs on the output), NR, and total cost (exclusive of rent), TC, at a given distance from the city center. An increase in demand may result in an increase in that activity’s equilibrium price, and therefore, it would rotate NR to NR’. As a consequence, equilibrium output per acre would increase from 0A to 0A’ (land would be used more intensively), and bid rents would be larger. In this example, the maximum rent that can be paid at this distance from the center increases from BC to B’C’.

The initial effect on the zone occupied by this activity is demonstrated in Figure 6-7. Here, the rent gradients associated with three different activities are presented. We might think of the first, with gradient aa, as being central office functions. The second and third, with gradients bb and cc, might represent light manufacturing and agriculture respectively.

Suppose that the manufacturing sector experiences an increase in demand. As explained above, it may now bid higher rents at any given distance from the market center, and its rent gradient will, therefore, shift upward to b’b’. The zone occupied by this activity widens, encroaching on each of the others. Note that the increase in demand has two immediate effects: (1) the extension of the manufacturing zone, and (2) the more intensive use of land. The increase in demand has elicited a supply response as the market allocates more resources to this activity. In our example, not only are other urban land uses affected, but the conversion of rural agricultural land also takes place.

Other effects are possible. For example, as the area occupied by agricultural activity becomes smaller, the supply of output from that sector diminishes. Also, the expansion of urban activity may cause an increase in demand for agricultural goods or central office services. The forces of supply and demand come into play once again. As new, higher equilibrium prices are established in these sectors, new rent bids can be made, forcing changes in each activity zone. Higher prices and rents result in all sectors, with greater intensity of land use in each.14

This kind of adjustment goes on all the time in the real world. In transition neighborhoods in cities, we see old dwellings and small stores being demolished to make way for office buildings and parking garages; old mansions being subdivided into apartments, replaced by apartment buildings, or converted to funeral homes; and in the suburbs, farmlands and golf courses yielding themselves up to the subdivider.

Here, the nature of the demand for land is most apparent. It is a derived demand, reflecting the interplay of the demands for various activities as well as their production and transfer characteristics. We find that the spatial distribution of resources is an integral part of the market process.

6.6 RESIDENTIAL LOCATION

The analysis of land use developed in this chapter views economic activities as differing in the value that they place on access to some central location. As indicated earlier, households are a major land-using activity, and they too are characterized by significant access linkages. Because of this, some of the principles developed thus far concerning land-use decisions are applicable to residential location decisions.

One of the first and most widely recognized efforts to explain residential location behavior is that of William Alonso.15 Alonso applies the concept of bid rent in order to isolate factors that contribute to the household’s willingness to pay for access to the central business district (CBD) of an urban area. Bid rents have been defined as the maximum rent that could be paid for an acre of land at a given distance from the market center, if the activity in question is to make normal profits. Here, however, we want to analyze residential location behavior, so the concept of profits is no longer relevant to the decision-making process. Instead, Alonso recognizes that households make choices among alternative locations based on the utility or satisfaction that they expect to realize. Consequently, the bid rent of a household is defined as the maximum rent that can be paid for a unit of land (e.g., per acre or per square foot) some distance from the city center, if the household is to maintain a given level of utility.

Figure 6-8 presents several bid rent curves labeled u1, u2, and u3 for one household. Each of these curves plots the relationship between rent bids and distance from the CBD associated with a different level of utility. 16

These curves have several important characteristics. First, they are negatively inclined. As developed earlier in this chapter, the rent gradient of a particular activity plots out decreasing rent bids as distance from the market increases because of transfer costs. Household rent bids are similarly affected by transfer considerations. An individual facing a daily commute to the CBD for work or shopping, or both, must pay lower rents in order to offset the associated transfer costs of a longer trip, if utility is to be held constant. Second, lower bid rent curves are associated with greater utility. Assuming that the household’s budget is fixed, at any given distance from the CBD, if a lower rent bid is accepted, more other goods can be consumed. Therefore, utility will increase. Finally, bid rent curves are single valued. This means that for a given distance from the CBD only one rent bid is associated with each level of utility. By implication, we may state that bid rent curves cannot intersect; otherwise they could not be single valued.

The gradient of actual rents in the city is given by R in Figure 6-8. As explained previously, this gradient reflects the outcome of a bidding process by which land is allocated to competing uses. From the household’s perspective, it provides information on the rental cost of land that the household can evaluate, in light of its preferences and budget, in order to choose a location more or less distant from the city center.

When faced with these rents, the decision makers in the household will prefer to reach the lowest possible bid rent curve in order to maximize utility; thus, a residence at location d2 would be chosen. Note that at any more central location, the rent gradient (R) is steeper than any intersecting bid rent curve such as u1. The rent gradient offers information on the actual decrease in rents with greater distance from the CBD, while the bid rent curves offer information on the decision makers’ willingness to trade off more distant locations for lower rents. Therefore, for any location to the left of d2, the decrease in actual rents with increased distance is more than sufficient to compensate the household for the greater commuting costs associated with living farther out. A location such as d1 cannot be an equilibrium location for this household: For any move away from the center, actual land rents fall faster than the bid rents necessary to maintain the utility level u1, and utility can therefore be increased by such a move.

The converse is true for locations to the right of d2. A constant level of utility can be maintained if rent payments decrease at the rate given by the bid rent curves. However, the rent structure of the city requires higher rents for these locations; therefore, utility is decreased by a move to any location more distant than d2.

Any factors that might cause the slope of the bid rent curve to increase will draw the household closer to the city center. The bid rent curves describe the household’s willingness to give up access to central locations. If they are steep, access is valued highly, and more remote locations will be accepted only at very low rents.

It is possible to isolate two factors that are important in determining the steepness of a household’s bid rent curve. The first such factor is transfer costs.17 Higher transfer costs tend to increase the slope of the household’s bid rent curve, and this tendency draws the household closer to the CBD. If each move away from the center is more costly in terms of commuting expenses, higher rent bids for close-in locations are warranted. In considering this factor, one should keep in mind that the opportunity (time) cost of commuting can be especially important in evaluating the transfer costs of a household. If each hour spent on the road is valued more, commuting becomes more dear, and rent bids fall more rapidly as distance from the CBD increases.

The second factor determining the steepness of the bid rent curve is the household’s demand for space. The larger the quantity of land occupied by the household, the more it stands to gain in moving to the outlying location. As rents fall per unit of land with increased distance from the CBD, the more units that are occupied, the more total savings are realized by such a move. It follows that bid rents will fall less rapidly with distance from the CBD if the amount of land occupied is large: A smaller decrease in rent per unit of land is required to compensate for the commuting costs associated with the more distant location. This results in flatter bid rent curves, and outlying locations are encouraged.

A number of researchers have tried to use models similar to the one developed here in order to analyze the consequences of higher income on residential location choice. In this context, we find that an increase in income will have opposing effects on the steepness of the bid rent curve. Transfer costs will certainly increase for households with higher income as the opportunity cost of commuting increases. By itself, this will tend to increase the slope of bid rent curves and should encourage high-income households to live closer to the CBD. At the same time, however, higher-income households are likely to demand more space, and this will draw the household farther away from the CBD.

In American cities, we often observe higher-income households living in suburban locations, while lower-income households occupy more central locations. We shall have more to say about this phenomenon in Chapter 7, where the spatial structure of urban areas is examined in some depth; however, the theory of residential location we have presented suggests that the income elasticity of demand for space and the income elasticity of commuting costs may be important factors underlying this spatial pattern.

Alonso does not take into account the opportunity costs associated with commuting; therefore, in his model the primary effect of higher incomes on bid rent curves is through changes in the quantity of land demanded by the household. Since he expects this quantity to increase with income, he argues that flatter bid rent curves, higher incomes, and locations more distant from the CBD go hand in hand.18

Richard Muth, however, explicitly recognizes both of the factors that we have identified as determining the slope of the bid rent curve. His analysis is developed on the basis of the quantity of housing services consumed rather than the quantity of land per so. In fact Muth’s model of residential location decisions also differs in several other respects from that presented above, but the factors underlying the income-location relationship are common to both.

Muth points out that the income elasticity of demand for housing has been empirically estimated as exceeding 1 and possibly running as high as 2—in other words, a 1 percent increase in income is associated with willingness to increase expenditure on housing by more than 1 percent. By contrast, the effect of additional income upon hourly commuting costs is almost certainly less than 1 to 1. This is so because the money costs of a given journey do not depend on income at all, whereas the time costs may be assumed to vary roughly in proportion to income. Consequently, higher income is associated with increased willingness to sacrifice access for more spacious and better housing.19

William C. Wheaton has challenged the generality of this conclusion.20 He calculates income elasticities on the basis of a sample of several thousand households in the San Francisco Bay area and finds no support for Muth’s position. These data suggest that the income elasticity of total travel costs in commuting and the income elasticity of demand for land are about equal and therefore mutually offsetting in terms of any effect on the bid rent curves. This result leads him to conclude that one must look to other factors in order to explain the suburbanization of America’s middle- and upper-income groups.

For example, another important basis for these suburban preferences is a liking for modernity as such. Dislike of old houses and neighborhoods (as well as associated externalities) and a superior mobility may go far to explain the generally positive association between income and suburbanization.

This association is especially prominent in families with school-age children, who are naturally more sensitive to differentials in school quality, neighborhood amenity and safety, open space, and neighborhood homogeneity. An analysis of residential patterns in the Greater New York area in the 1950s showed that well-to-do families with children under the age of fifteen showed relatively strong suburban and low-density preferences, while those without such children were more willing to accept the higher densities of close-in communities. Differences according to presence or absence of children were less evident for lower-income families, whose latitude of choice of residential areas is narrower.21

The foregoing examination of the factors underlying urban residential patterns serves also to remind us that we are not dealing here with any inexorable or universal law of human behavior. Indeed, an inverse relationship between income and distance from city center has prevailed in some other countries and in other historical periods. In those situations, the wealthy favor inner-city locations with good access, while the poor huddle in suburban shantytowns. Many Latin American cities, such as Rio de Janeiro, illustrate this pattern;22 and in preindustrial America, the mansions of the rich were generally found quite near the center of town.

6.7 RENT AND LAND VALUE

Our discussion of rents and competition for land has placed almost exclusive emphasis on the location of a site (relative to markets and sources of inputs) as an index of its value. Location has determined how much rent any particular activity can afford to pay for the use of a site; the purchase price has been explained as simply the capitalized value of the expected stream of future rents. At this point we need to recognize some significant complications that have until now been ignored.

6.7.1 Speculative Value of Land

First, the expected future returns on a parcel of land may sometimes be quite different from current returns, particularly in locations where radical changes of use are taking place or expected. This is generally true around the fringes of urban areas, where the change involves conversion from farm to urban uses. The price that anyone will pay for the current use of the land may be quite low in relation to the speculative value based on a capitalization of expected returns in a new use.

This point is illustrated in the results of a study of agricultural land near the city of Louisville, Kentucky, well over half a century ago (see Table 6-1). It will be observed that in the zones farther than 8 or 9 miles from the city, the current annual rent was consistently about 5 percent of the average value of the land. In other words, the value was approximately 20 years’ rent at the current rate. Closer to the city, the land was worth, on the average, well over 26 times the current annual rent; the capitalization rate was only 3.8 percent. This obviously reflected the expectation that returns on the nearby land would rise as the urbanized area spread.

Incidentally, the same table (Rows 1, 5) shows that the size of the farm unit increased consistently with greater distance from the city in terms of acreage but remained roughly constant in terms of total land rent. This is consistent with the idea that the scale of the individual farm unit is constrained by size-of-firm considerations involving management capability and financial resources. The same study showed systematically greater inputs of labor and fertilizer per acre and per farm nearer to the city.

6.7.2 Improvements on Land

A further complication is that land is ordinarily priced, sold, and taxed in combination with whatever buildings and other "improvements" have been erected on it, since such structures are usually durable and difficult (if not impossible) to move. On urban land, improvements may account for a major part of the value of the parcel of real estate; and in all cases it is probably difficult to estimate just how much of the price represents the value of space per se, or "site value." Sometimes the "improvements" have a negative value: In other words, the land would be more desirable if it were cleared of its obsolete structures.


TABLE 6-1: Acreage, Rent per Acre, and Value per Acre of Farms,
by Distance from Louisville, Kentucky
  Distance from Louisville (Miles)
 

8 or Less

9 to 11

12 to 14

15 or More

(1) Average acres per farm

102

221

256

257

(2) Land rent per acre ($ per annum)

11.85

5.59

5.37

4.66

(3) Land value per acre ($)

312

110

106

95

(4) Capitalization rate (%) (2)1(3)

3.8

5.1

5.1

4.9

(5) Rent per farm per annum ($) (1) x (2)

1210

1235

1430

1295

Source: J. H. Arnold and Frank Montgomery, Influence of a City on Farming, Bulletin 678 (Washington, D.C.: U.S. Department of Agriculture, 1918).

Such structural obsolescence is an important aspect of some of the most serious problems confronting U.S. cities today. Moreover, the distinction between site value and total real property value is crucial to an evaluation of the role of the real property tax, which is the fiscal mainstay of local governments.

6.8 SUMMARY

Competition for space and other fixed local resources (collectively termed "land") plays an important role in location, especially in urbanized areas and for activities using much space relative to their outputs. In a free market, land goes to the user who can bid the highest rent or price for it. Price represents a capitalization of expected rents.

The way in which any activity’s rent bids vary over an area (the rent surface) or along a route (the rent gradient) depends on the local qualities of the sites themselves, on their accessibility, and on other factors relevant to the activity’s locational preferences. Rent gradients and surfaces for most activities show peaks at market centers.

When several activities are competing for space around some common market point, the activities that preempt the land with the best access tend to be those that have a large volume of output per unit of space used, those whose output bears high transfer costs, and those least subject to rising operating costs with increased intensity of land use (crowding).

The production and transfer characteristics associated with activities in urban areas cause them to place high value on locations with central access. The location of these activities is especially affected by the need for movement of people and direct personal contact, with time consequently playing the major role in transfer costs and access advantage. Complex linkages among units and activities, and competition for space, are also important location factors in an urban context.

Access considerations play an important role in residential location decisions. The space occupied by a household and commuting costs (especially the opportunity or time cost of commuting) affect its willingness to bid for land with good access to central locations.

The demand for land plays an important role in the market process and is affected by changes in the demand for various activities that compete for its use.


TECHNICAL TERMS INTRODUCED IN THIS CHAPTER

Land

Rent

Intensity of land use

Neighborhood effects, or local
externalities

Rent bid, or bid rent

Central business district (CBD)

Region

Rent surface

 
 

Rent gradient

 

 

SELECTED READINGS

William Alonso, Location and Land Use (Cambridge, Mass.: Harvard University Press, 1964).

Edgar S. Dunn, The Location of Agricultural Production (Gainesville: University of Florida Press, 1954).

Johann Heinrich von Thünen, Der isolirte Staat in Beziehung auf Landwirthschaft und Nationalökonomie (1st volume published in 1826, subsequent volumes published later); Carla M. Wartenberg (tr.), The Isolated State (London: Pergamon Press, 1966).

William C. Wheaton, "Income and Urban Residence: An Analysis of the Consumer Demand for Location," American Economic Review, 67, 4 (September 1977), 620-631.

 


APPENDIX 6-1

Derivation of Formulas for Rent Gradients and Their Slopes

Let the total cost of production per acre (exclusive of rent) be

TC=F + aQ b                                                                                 (1)

where F is fixed cost per acre, Q is output per acre, and b > 1. The bid rent, or maximum rent per acre that could be paid, is

R=(P — tx) Q — aQb — F                                                                                                     (2)

where P is the unit price of the output at the market, t is the unit transfer cost per mile, and x is the distance to market.

dR/dQ =P tx abQb-1                                                               (3)
d2RIdQ2 =(1 — b) abQb-2 < 0                                                          (4)

Since the second derivative is negative because b > 1, setting the first derivative to zero will give the output that maximizes R.

P — tx — abQb-1=0                                                                       (5)

Q=[(P— tx)/ab]/1/(b-1)                                                                     (6)

Substituting in (2), and simplifying,

R=a(b — 1) [(P — tx)/ab]b/(b-1) — F                                                 (7)

This is the rent gradient with respect to distance from the market.

dR!dx=— t[(P — tx)Iab]1/(b-1) < 0                                                      (8)

Therefore, the rent gradient always slopes downward from the market.

d2RIdx2 = [t2/ab(b — 1)] [(P tx)/ab](2~b)(b-1) > 0                             (9)

By (9), the rent gradient is always concave upward.

The procedure followed in deriving the rent gradients shown in Figure 6-5, which indicate the effect of each of the parameters on the slope, was as follows:

Since the question as to which one of two activities takes the zone closer to market is determined by the relative slopes of the two gradients at their point of intersection, it is necessary to set the market prices at a level P* such that the gradients representing activities with different a, b, F, or t values will intersect. Let the coordinates (rent and distance respectively) of the point of intersection be R* and x* (which were set at 1,000 and 50 respectively in calculating the gradients plotted in Figure 6-5).

Then

R*=a(b1)[(P* tx*)/ab]b/(b-1) F

and from this,

(P* tx*)!ab =[(R* + F)/a(b —1)](b-1)/b

Substituting in (8) gives the slope (S*) at the intersection point:

S*=— t[(R* + F)/a(b — 1)]1/b

From this it is clear that

S*/ a > 0
S*/ b > 0
S*/ F < 0
S*/ t < 0

In other words, if two activities have intersecting rent gradients and are alike with respect to all but one of the four parameters a, b, F, t, the activity with the steeper (more strongly negative) slope at their intersection will be the activity with the lower a, or the lower b, or the higher F, or the higher t.

In calculating the illustrative gradients shown in Figure 6-5, the following parameters were used:

 

a

b

F

t

Standard case for comparison, which appears in each of the four panels of Figure 6-5

10

2

100

1

Larger a

20

2

100

1

Larger b

10

4

100

1

Larger F

10

2

500

1

Larger t

10

2

100

2

 


ENDNOTES

1. Through most of this discussion, we shall use the convenient term "rent" to indicate the price for the use of a piece of land. If a new user buys the land instead of renting it from an owner, the price he or she will have to pay represents a capitalization of the expected rents, at the expected rate of interest. Thus if each of them expects to be able to get a 12 percent interest return on capital invested in other ways, the buyer and the seller should agree on $40,000 as a fair price for a piece of land that is expected to yield a net rent (after all costs including property taxes) of $4,800 a year for the foreseeable future. At that price, the returns will be 12 percent of the investment.

2. The statement appeared in Pravda, 30 May 1966, and was reported in the New York Times of that date, p. 12.

3. The quotation is from a set of draft principles of land legislation submitted in a report by Deputy F. A. Surganov, Chairman of Council of the U.S.S.R. Agricultural Committee. The report was published in Pravda and Izvestia, 14 December 1968, and in a condensed translation in the Current Digest of the Soviet Press, 21, 1(22 January 1969), 12-20.

4. Kenneth R. Gray, "Soviet Agricultural Prices, Rent and Land Cadastres," Journal of Cornparative Economics, 5, 1 (March 1981), 43-59. We are indebted for this and the previously cited references on Soviet land-rent policy to our colleague, Professor Janet G. Chapman.

5. In particular, it exhibits the effect of the law of diminishing returns. Note that with b=1, TC would increase linearly with output. For b > 1, the increase in TC is more than proportional to increases in Q. As the rate of output is increased by using more of some variable factor of production with all other inputs fixed, the law of diminishing returns requires that at some point the marginal productivity of that variable factor must decline. Declining productivity at the margin implies increasing costs at the margin: Each unit of input is capable of producing less additional output than preceding units, and therefore the marginal costs of production rise. This characteristic of the relationship between productivity and costs is reflected in the total cost formula used here. As long as b > 1, the increment in total cost associated with any increase in Q will be larger the larger Q itself is, reflecting the diminished productivity of variable factors of production as the rate of output is increased on a fixed parcel of land.

6. While the preceding analysis focuses on the effect of transfer costs associated with the delivery of output to the market on the rent-paying ability of an activity, any factor that affects receipts or costs at different locations will also affect bid rent and land use.

7. Solow has constructed an interesting urban land-use model in which traffic congestion is taken into account by making transport cost per ton-mile depend on traffic density. He finds that the congestion factor makes the rent gradient even more concave upward than it would otherwise be. Robert M. Solow, "Congestion, Density, and the Use of Land in Transportation," Swedish Journal of Economics, 74, 1 (March 1972), 161-173.

8. Unfortunately, this does not mean that the inhabitants of the highest density areas in our cities necessarily enjoy adequate access to jobs, despite being located near the center. The majority of urban poor persons live in the central cities of metropolitan areas, and yet many of the jobs that they can fill have tended to move to the suburbs. This and some related problems are taken up later, in Chapter 13.

For an interesting attempt to separate statistically the access and amenity components of land value differentials, see R. N. S. Harris, G.S. Tolley, and C. Harrell, "The Residence Site Choice," Review of Economics and Statistics, 50, 2 (May 1968), 241-247.

9. See selected readings in this chapter. A thumbnail summary of the main ideas of von Thünen’s pioneer theory of land uses appears in Martin Beckmann, Location Theory (New York: Random House, 1968), Chapter 5.

Von Thünen indulged in a convenient simplifying assumption to the effect that any given activity (such as wheat growing) requires land in a fixed ratio to the other inputs and the output. In other words, the intensity of land use and yield per acre are fixed regardless of the relative prices of the land, the other inputs, and the output. Although this assumption has often been retained by later theorists, we are here trying for a little more realism by allowing variation in intensity.

10. Von Thünen did indeed assign forestry to a nearby zone as this illustration shows, which seems bizarre to us today. The explanation is that in his time the woods supplied not only construction timber but also firewood, a quite bulky necessity for the townspeople.

11. It may be noted here that the von Thünen assumption of an unchangeable intensity of land use in any given activity is most closely approached in our model if we have a very high b coefficient. The total cost curve (see Figure 6-1) then looks almostû-shaped.

12. The nature of linkages among economic activities is given detailed consideration in Chapters 9 and 11.

13. For relevant reference material, see John R. Meyer, J. F. Kain, and M. Wohl, The Urban Transportation Problem (Cambridge, Mass.: Harvard University Press, 1965); and Albert Rees and George P. Shultz, Workers and Wages in an Urban Labor Market (Chicago: University of Chicago Press, 1970). Also, for a primarily bibliographical survey of the whole question of access evaluation, see Gunnar Olsson, Distance and Human Interaction: A Review and Bibliography, Bibliography Series, No. 2 (Philadelphia: Regional Science Research Institute, 1965).

14. A somewhat more rigorous analytical basis for this type of analysis is offered in Richard Muth, "Economic Change and Rural-Urban Land Conversion," Econometricia 29, 1 (January 1961), 1-23.

15. See William Alonso, Location and Land Use (Cambridge, Mass: Harvard University Press, 1964), for a full statement of his early theoretical work on agricultural, business, and residential land uses. For a concise nonmathematical presentation of his ideas on this topic, see William Alonso, "A Theory of the Urban Land Market," Papers and Proceedings of the Regional Science Association 6 (1960). 149-157.

16. Readers familiar with indifference curve mappings will recognize that bid rent curves and indifference curves differ in important ways. As Alonso puts it ("A Theory of the Urban Land Market," p. 155): "Indifference curves map a path of indifference (equal satisfaction) between combinations of quantities of two goods. Bid rent functions map an indifference path between the price of one good (land) and quantities of another and strange type of good, distance from the center of the city. Whereas indifference curves refer only to tastes and not to a budget, in the case of households, bid rent functions are derived from budget and taste considerations."

17. For an explanation of the effect of transfer costs on the household’s bid rent using indifference curves, see Hugh 0. Nourse, Regional Economics (New York: McGraw-Hill, 1968), pp. 110-114.

18. See Alonso, Location and Land Use, pp. 106-109.

19. See Richard F. Muth, Cities and Housing: The Spatial Pattern of Urban Residential Land Use (Chicago: University of Chicago Press, 1969), pp. 29-34, for further details. He concludes that "on a priori grounds alone the effect of income differences upon a household’s optimal location cannot be predicted. Empirically, however, it seems likely that increases in income would raise housing expenditures by relatively more than marginal transport costs, so that higher-income CBD workers would live at greater distances from the city center" (p. 8).

20. See William C. Wheaton, "Income and Urban Residence: An Analysis of the Consumer Demand for Location," American Economic Review, 67, 4 (September 1977), 620-631.

21. E. M. Hoover and Raymond Vernon, Anatomy of a Metropolis (Cambridge, Mass.: Harvard University Press, 1959), Table 41, p. 180. For an analysis of the locations of various types of families in Cleveland in terms of distance from center, age, density, and industrial characteristics of neighborhoods see Avery M. Guest, "Patterns of Family Location," Demography, 9 (February 1972), 159-171.

22. "In a Latin American city rural migrants and, in general, the proletariat are not customarily crowded into a blighted area at the urban core, … but they are scattered, often in makeshift dwellings, in peripheral or interstitial zones. The Latin American city center with its spacious plaza was traditionally the residence area for the wealthy and was the point of concentration for urban services and utilities. The quickening of commercial activity in this center may displace well-to-do residents without necessarily creating ‘contaminated’ and overcrowded belts of social disorganization. The poor are often not attracted into transitional zones by cheap rents; they tend to move out to unused land as the city expands, erecting their own shacks. The downtown area becomes converted for commercial uses or for compact and modern middle- and upper-income residences." Richard M. Morse, "Latin American Cities: Aspects of Function and Structure," Comparative Studies in Society and History, 4 (1961-1962), 485. For a comprehensive discussion of such characteristic contrasts in urban form and their socioeconomic background, see Leo F. Schnore, "On the Spatial Structure of Cities in the Two Americas," in Philip M. Hauser and Leo F. Schnore (eds.), The Study of Urbanization (New York: Wiley, 1965), pp. 347-398.



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