Production Theory Of Land Rent

Environment and Planning A. 1991. volume 23. pages 955-967

Production theory of land rent

G I Thrall Homer Hoyt Institute. and University of Florida, Gainesville. FL 32611. USA Received 27 January 1989; in revised form 3 July 1990

Abstract. The production theory of land rent (PTLR) contributes to knowledge of the spatial distribution of production activities. The PTLR is a general theory of a multidimensional commercial landscape. The PTLR is a heuristic model that provides explanation and trajectory for the spatial pattern of commercial land use, land value, density, capital used, labor wages, and level of employment.

Introduction A general theory of land value for the commercial or production sector of the economy is presented. I refer to the general theory and geometric methodology as the production theory of land rent (PTLR). The PTLR defines a multidimensional commercial business zone. The PTLR is a heuristic model whose results include the spatial surfaces of land and nonland (capital and labor) factors of production, and relative land values. With few exceptions-such as Odland (1978), Ogawa and Fujita (1980), and Thrall (1988, chapter 7)-in the mathematical land-use and population density literature the central business district (CBD) is defined as a point. This limited definition for the CBD is reasonable within the context of heuristic models whose analyses are independent of the spatial organization of commercial activity and commercial land values. However, a one-dimensional CBD is too restrictive when description and explanation of the interaction between consumption and production sectors are desired. Mathematical land-rent theorists are not alone in neglecting commercial land use. In contemporary studies of industrial location generally it is assumed that the price of the spatially distributed factors of production, including land, are exogenous. Also, in the contemporary theory of the firm the role of land and location are discounted and instead capital and labor are emphasized as the sole factors of production (for discussion see Beyers and Krumme, 1974). Therefore, there is a gap in our understanding of the general forces that contribute to the spatial organization of commercial land use and land value; it is necessary to bridge this gap if we are to understand how commercial land use and land values affect other sectors and ultimately the growth of a region. This paper will serve as a step toward bridging this gap and integrating theories of the firm, location, and land. Nineteenth-century contributors t6 economic and economic-geography literature emphasized the role of land in the production process. Von Thiinen (1826) a spatial theory of land values for the agricultural production sector: bid for using land is the difference of total revenue less total production and less total transportation cost to deliver the output to a central point. depict for each product differing amounts bid to use land which in turn to differing land uses that circle the central market. Technology within each Von Thiinen reasoned, would vary by distance from the central market. writings of Von Thiinen were acknowledged by Marshall (1890) to have of the significant influences on his view of the economic world. This can be summarized in five axioms of land that relate to the production

ad in Great Britain

- - - .......

----~-------

956

G I Thrall

process: (1) Land is a factor of production and "is the foundation of much that is most interesting and most difficult in economic science" (Marshall, 1890, pages 144-145). (2) Land has area and density, and is a complement to capital and labor. "[T}here is a certain application of capital and labour to the acre which gives the highest return" (page 447). (3) The "situation value" and "site value" of land are measures of the importance of relative spatial location (page 441). (4) Land is the recipient of external economies from natural and built environments. Localization of manufacturing industry arises from agglomeration economies that result from density and scope of labor market, the spatial distribution of physical resources, and threshold demand. Concentrations of service industry arise from savings to the customer in transportation cost and time. Because of increased volume of customers and increased visibility, higher order facilities benefit by agglomerating with other higher order facilities (pages 267 - 273). (5) Land value and intensity of land use are the result of spatial equilibrium processes. The system comes to be in spatial equilibrium by way of the movement of people and industry which in turn changes density and land values (pages 429 and 449). Though geographic research on migration (for a review see Clark, 1986) and diffusion (for a review see Morrill et aI, 1988) has broadened our meaning and application of spatial equilibrium, our contemporary thinking on spatial equilibrium follows directly from Marshall's contributions. Dunn (1954) corrected several interpretive errors of Von Thiinen's geometry (for a discussion see Hall, 1966). It is Dunn's interpretation of Von Thiinen's work that is generally presented in texts and that contributions such as those by Visser (1980), Jones (1978; 1984; 1985), Jones and Krummel (1985), Cromley and Hanink (1989), and O'Kelly (1989) h'ave built upon; for a discussion see Kellerman (1989a; 1989b). Dunn (1954, pages 25-39) offered a reconciliation of Von Thiinen's agricultural theory with contemporary production theory. Dunn assumed the existence of a Ricardian rent function where the price of the least productive agricultural land increases in direct proportion to incremental increases in productivity. Based upon this reasoning, Dunn describes an iterative process in which more favorably situated agricultural land eventually settles into an equilibrium with higher land values than less favorably situated sites. Building upon Marshall's theme, Isard (1956, pages 200 and 254) describes four elements most important in determining nonagricultural commercial land values: (1 ) distance from the city center; (2) customer access to the site; (3) the location of competitors, their number, and the intensity with which they vie for sales; and (4) proximity of complementary land uses that may affect the costs of production or the volume of customers. Instead of focusing upon the development of a general theory of commercial land value, the direction that Hoyt took was to derive a correct estimate of the market value of commercial property. Assessed value is an estimation of market value. Hoyt determined the assessed value of land in retail centers by capitalizing the net income that accrues after deducting from gross rents the real estate taxes, operating expenses, maintenance, vacancy allowance, interest, and appreciation on the cost of the buildings (Hoyt, 1964; see also 1966, page 510). Within a shopping center, commercial rents are determined by the bargaining position of the individual retail store (Hoyt, 1963; see 1966, page 675). Because the externalities to the shopping center from the anchor are so great, the anchor may often obtain the land without cost. This does not mean the land has no value; rather, it reveals the bargaining position of an anchor.

& Production theory of land rent

957

Alonso (1964, pages 42-58) strove to contribute a general theory, but for land rent bid by an individual retailer. Alonso built upon the contributions of Marshall and Isard, but offered a change of fashion by way of his mathematical specification of the problem. In a graphical geometric analysis, Alonso advanced a partial solution to the commercial land-use problem; the solution was partial because Alonso assumed land values to be exogenous: given exogenously the price of land, the entrepreneur makes decisions on location and amount of land to occupy (page 46). In subsequent analysis Alonso calculated the slope of the land-price function by assuming that revenues fell and costs (apart from land) increased with movement to off-center locations: "[T]he change [between locations] in bid price is equal to the change in the volume of business minus the change in operating costs" (pages 54 and 189). Richardson (1977, page 17) writes that Alonso's system is not closed, for it is limited to the calculation of the individual firm's bid rent and not on the derivation of a spatial market equilibrium land-value function. (In contrast, the PTLR model presents a spatial equilibrium solution for the market.) Muth (1969, chapter 3) gave some attenion to the commercial land-value problem. Muth assumed that profits for all firms within an industry are identical and that there is a spatially uniform production technology. (The PTlR does not require a spatially uniform production technology.) Profits in Muth's analysis, as in Von Thiinen's, are the difference of total revenues and the total cost of production. Firms adjust quantities of inputs, including land, to maximize profit. However, Muth and the literature (Goldberg, 1970) that followed offered insignificant attention to development of a general spatial model for the production sector. Few theoretical contributions have been offered since Richardson (1977, page 33) noted the gap on the production side of the land-use literature. Following upon this theme, Hum (1988) suggested that Thrall's (1987) analysis of the household sector be applied to the production side as well. The empirical literature on commercial land values has drawn upon the population-density literature by analogy (for a review see Thrall, 1988). Schmenner (1981) applied the reasoning of Clark's (1951) population density formulation to describe empirically land values for manufacturing. Schmenner found that, as distance from the city center increased, values declined for renters, but increased for owners. He hypothesized that several explanatory factors found in the housing literature are also most important to determining the spatial behavior of manufacturing land values: access to expressways, vintage, presence of pu~lic transit, and service by utilities. Also by analogy to the housing literature, McDonald (1987) considered density-the ratio of gross employment to population-to be the best measure for identifying the location of a zone of business. McDonald did not analyze the spatial arrangement of activities within the business zone. For a strategy of measuring population density within a Hoyt sectorial model of urban land use see Haynes and Rube (1973), and for an application to the metropolitan-area-based region see Parr and O'Neill (1989). Scott (1982; 1986a; 1986b) has described the spatial arrangement of activities within a business zone (see also Gordon et aI, 1986). Gad (1985) has described the spatial distribution of offices in Toronto. Marshall (1890, page 273) wrote that manufacturing firms locate at the urban periphery where land values are comparatively low; housing is constructed for the employees of the manufacturing firms; retail sales follow the relocation of laborers. Land values are driven up so that further manufacturing expansion takes place at the new urban periphery whence the cycle begins anew. Hartshorn and Muller (1989) have confirmed Marshallian suburban growth processes in Atlanta. Scott and Angel (1988) have extended the analysis to . a global scale. >

958

G I Thrall

The empirical literature consists of attempts to ascertain what attractions the central city offers to commercial land users versus suburban locations. Hutton and Ley (1987) found the four leading reasons for Vancouver businesses to locate at the CBD were contacts with other businesses, availability of accommodations, prestige, and amenities. Hutton and Ley's business sectors are defined merely as points, implying that market forces were the same throughout the business zone. Chinitz (1984) and Kutay (1986) cite communication as the most important reason for agglomeration in the CBD, while changing communication technology is responsible for dispersal of commercial activity from the CBD. Imagability (Tuan, 1974) may also be an important component in occupancy and location of the large 'class N. office buildings. Archer (1981; Archer et al, 1990) includes status and prestige as the most important factors in the decision to rent CBD office space. The location of corporate office headquarters between cities has been evaluated by Semple and Phipps (1982). They describe the highest order places in the nation as losing headquarters to lower order but important regional subcenters. This was confirmed by Wheeler and Brown (1985) for the southeastern portion of the USA (see also Clapp, 1980). In their empirical study of productivity growth by city size, Fogarty and Garofalo (1988) focus upon value added as a function of capital, labor. and land. The most important component of land to them is density. Employment density is the ratio of labor to land; capital density is the ratio of capital to land; productivity depends upon the manner in which capital and labor density unfold across space. (The PTLR will be used to derive these ratios, and the reason why they unfold as they do will be explained.) Fogarty and Garofalo believe that cities should adopt land-use regulations, zoning, and infrastructure such as transportation, to induce appropriate densities and thereby increase the productivity of manufacturers (see also Carlino, 1985; Moomaw, 1985). Their analysis is a contemporary empirical application of the above second axiom of Marshall. The PTLR is a general theory of land value and land use for the production and commercial sectors. The style of presentation of the heuristic PTLR allows for unambiguous reasoning. Unlike ear1ier contributions, the PTLR derives endogenously the spatial eqUilibrium land values for the market, the spatial eqUilibrium quantities of land, labor, and capital used; these are used to derive the unfolding over space of capital-to-Iand and labor-to-Iand ratios. The PTLR is given in the following section. The PTLR model The landscape is like Von Thiinen's, isotropic with a perfectly malleable built environment. The market is perfectly competitive so that all producers face the same constant price (instead see Jones, 1988; Mulligan and Fik, 1989), make the same decisions under the same circumstances, make the same profit, and maximize the amount of output for a given total cost. The assumptions of the PTLR can be changed to be less restrictive or to reflect alternative environments. These conditions must be met for spatial equilibrium: within the context of the model greater output cannot be achieved by changing land inputs and nonland inputs of labor and capital; a firm can neither relocate to obtain lower costs for a given level of output, nor can the firm achieve higher output elsewhere for the same costs. As the system moves between different spatial equilibrium positions in response to a change in a condition of the model, the important· output of the heuristic PTLR is the general trajectory of endogenous terms (that is, ratios of capital and labor to land, unfolding of the spatial equilibrium land-value surface). It is the trajectory of endogenous terms that empiricists and those computing simulations should use as the basis for their experimental design. The PTLR can

ts


959

provide the logic, justification, and anticipation of effects from the inclusion of particular variables or alternative states of affairs in computer simulations (Batty et aI, 1989). A two-stage technique is adopted (Brown and Hein, 1972; Fischer and Nijkamp, 1985; Phlips, 1974). In the first stage, the firm chooses between land and the ensemble of nonland factors of production; the ensemble is capital and labor. The size of each production or commercial site is established by the market. Subsequent to first-stage decisions, in the second stage the firm evaluates which combination of capital and labor will be appropriate for the site. The twostage technique is contended to characterize more appropriately how decisions of this type are made, and contributes to the distinct treatment of land and location, distinguished from the other factors of production as suggested in Marshall's above axioms. However, it is recognized that the same equilibrium solution does not necessarily arise between two-stage techniques such as that introduced here and a possible one-stage PTLR where all choice variables are decided upon at one time with all constraints known. Differences in solutions between one-stage and twostage strategies have been demonstrated to occur when determining the costminimizing location of the firm within a Weberian (Weber, 1929) triangle (Nijkamp and Paelinck, 1973; Pace and Shieh, 1988). Stage 1 Location is measured here in relative terms; the point of reference is the port.

Definition 1: The port is a point or zone on the landscape where the summation of assembly and distribution costs are minimum. Other locations are measured relative to the port. At the port, distance s = O.

Raw materials and finished product are shipped through the port. The port may be a seaport city, the central business district. a limited access highway off-ramp or rail spur at the urban periphery. One raw material source is assumed and one ,market (however, see Moses, 1958). To produce a given level of output a fixed amount of raw material is required: Assumption 1: A fixed amount of raw materials, m, is required for a given output. The cost per unit of raw materials at its source is p. The total cost of raw :(ilaterial independent of its assembly cost is pm. fh

Assumption 1 can be changed to reflect a variety of conditions. ,~'1he production cost C' can be divided into that which can differ between rocatlons C., and that which is the same Cns • where subscripts sand ns stand for and nonspatial, respectively. In other words,

(1) the costs identified here, only pm is everywhere the same; thus, Cns = pm. of pm will be done elsewhere. Spatially variant total cost at s is the combination of payments for transportation, nonland inputs wn(s) with price (quantity n( s), land r( s) q( s) with price r( s) and quantity q( s). Producers' total then be written as (2)

= C· - Cns • Transportation cost, T(s), is the summation of assembly costs .....~"''''..." and the cost of distributing the finished product to all destinations. are compared with the price of nonland inputs. Therefore, :~~nOtion 2: w

is the numeraire 1.

G I Thrall

960

Rearranging equation (2) to express nonland inputs as a function of land inputs results in n(s) = C-T(s) _ r(s) q(s) •

w

(3)

w

with intercepts C-T(s)

(4)

w

and C-T(s) r(s)

(5)

In the earlier discussion it was argued that, when the system is in spatial equilibrium, producers cannot achieve lower costs elsewhere and also maintain the same level of output. When the system is in spatial equilibrium, producers with the same total cost will therefore be on the same isoquant. This can be restated as Definition 2: When the system is in spatial equilibrium, all producers at all shave the same total cost to obtain the same output and will select land and nonland inputs from the same isoquant.

Let I(n{s}, q{s}) represent the isoquant for producers at location s. Capitalized endogenous terms satisfy conditions of spatial equilibrium. Producers at SI have isocost line AA [figure 1, equation (3)]. Because isocost line AA is tangent to I(N{sd, Q{sd), it is the spatial equilibrium isocost line. The intercept on the abscissa [equation (5)] of AA contains the land value R(sl) that satisfies spatial equilibrium (defInition 2) at location SI' The point of tangency between spatial equilibrium isoquant and isocost identifies spatial equilibrium N and Q. How do commercial and production land values behave between locations? The significant component that differentiates locations in this illustration of the PTLR is T(s); other components that contribute to location differentiation will be evaluated elsewhere. A

.i

N, B

'0

~

Z

c

Q, Land inputs

Figure 1. Geographic equilibrium for the production sector.

r'~

961


Principle 1: When the system is in spatial equilibrium, land values for the production sector will decline with increasing T(s), other things being equal.

Given: three locations

SI