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Highest and best use: the von Thunen connection.

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In this article, a two-choice model is applied to agricultural land to illustrate a simple version of von Thunen's land-rent theory, and an expanded three-choice agricultural model is used to develop the concept of highest-valued land use. These ideas, originating nearly two centuries ago, are directly applicable to the modern appraisal concept of highest and best use. They illustrate why location, externalities, product price, productivity, and production cost all impact land-use outcomes. The ideas of yon Thunen provide a solid theoretical foundation for current definitions of highest and best use, and provide a better understanding of why the highest-valued legal and physically possible use represents the highest and best use for land.

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The topic of highest and best use (HBU) has not been at the forefront of appraisal literature for some time. The American Institute of Real Estate Appraisers published a monograph dealing with the subject in 1981, (1) and Grissom wrote about the semantics of HBU in 1983, (2) but in appraisal much of the formative discussion and debate regarding HBU and its application predate those two publications. The HBU concept, however, has recently been the topic of renewed critical thinking in the context of modern appraisal practice, particularly by Parli and Lennhoff. (3) These latest writings on HBU suggest alteration of the currently accepted definitions of HBU and have prompted much discussion and critical comment. (4)

Given the current regeneration of interest in HBU, it may be beneficial to look at the theoretical rootstock from which the concept and current definitions have grown. Hence, this article revisits von Thunen's land-rent model developed in the early to mid-1800s (5) as a means to inform current discussions regarding the meaning of HBU.

To illustrate von Thunen's ideas, this article presents a simple two-choice model and a three-choice model, with liberties taken to simplify understanding and facilitate connectivity with the modern HBU concept. (6) The article also summarizes the HBU insights that may be derived from the agricultural context of von Thunen's theories and uses these insights to develop a more complete understanding of modern HBU definitions.

Two-Choice Model--Single Crop

In the first model, two land-use choices are available: to produce or not to produce an agricultural crop. For this illustrative example, consider a one-crop agricultural economy characterized by a central market, constant and uniform costs for crop transportation, and uniform land productivity, where:

p = market price per unit of crop output at a central market location,

c = production cost per unit of crop output (including all costs except a return to the land),

t = transportation cost per unit of crop output per unit of distance,

k = distance from farm to market, and

q = crop output per acre of land.

Here, land rent (r) is the return to the land, where r = (p - tk - c)q. Letting [R.sub.L] be the appropriate land capitalization rate and defining [V.sub.p] as land value per acre for crop production use, then

[V.sub.p] = (p - tk - c)q/[R.sub.L].

Several implications arise from the simple von Thunen agricultural land-rent model. First, [V.sub.p] declines as distance from farm to market (k) increases; this is a consequence of diminished output price per unit of land at the farm location (p - tk) as farms become more distant from the market. Second, [V.sub.p] reaches zero when p - tk = c; that is, when price per output unit at the farm location is identical to production cost. Third, no production occurs at distances where p - tk [less than or equal to] c since the return to the land is negative or zero at these locations.

Referring to Figure 1, crop production land value is (p - c)q/[R.sub.L] dollars per acre contiguous to the market, where k = 0 and transportation cost is nil. Distance measure [k.sup.*] is indicative of the distance at which p - tk = c and [V.sub.p] = 0. A crop will be produced at all distances to market less than [k.sup.*] since land value for crop production use is positive. Land will lie fallow (the only other option in this simplified model) where distances to market are greater than or equal to [k.sup.*], since [V.sub.p] [less than or equal to] 0 at these distances. In the context of the modern concept of HBU, the HBU at 0 < k < [k.sup.*] is crop production and HBU at k [greater than or equal to] [k.sup.*] is fallow land.

[FIGURE 1 OMITTED]

Although the implications of this simple model are clear and intuitive, the concept of an inverse relationship between distance to market and land value provides a useful means for proceeding into a study of variation in land use by location.

Three-Choice Modern--Two Crops

Adding a second crop implies three land-use choices: produce crop 1, produce crop 2, or leave the land fallow. In order to keep the exposition clear and focused on HBU, in this model the following assumptions are initially made:

[p.sub.1] > [p.sub.2]

[t.sub.1] > [t.sub.2]

[c.sub.1] = [c.sub.2]

[q.sub.1] = [q.sub.2]

That is, the price for crop 1 is greater than the price for crop 2, transportation cost is greater for the more valuable crop, production cost per unit of output is identical for both crops, and output per unit of land is identical for both crops.

Here, the higher-priced crop will be grown on land contiguous to the market. This is because land value is greater when the higher-priced crop is grown there, as the following illustrates:

At k = 0, [V.sub.p1] = ([p.sub.1] - c)q/[R.sub.L], [V.sub.p2] = ([p.sub.2] - c)q/[R.sub.L], and [V.sub.p1] > [V.sub.p2].

In general,

[V.sub.p1] = ([p.sub.1] - [t.sub.1]k - c)q/[R.sub.L] and [V.sub.p2] = ([p.sub.2] - [t.sub.2]k - c)q/[R.sub.L].

Since [t.sub.1] > [t.sub.2], [V.sub.p1] has a steeper slope than [V.sub.p2], meaning that the crop 1 and crop 2 land-value gradients will intersect at a positive distance from the market (i.e., where k > 0). (7) This is illustrated in Figure 2.

As shown in Figure 2, [V.sub.p1] > [V.sub.p2] when 0 < k < k', where k' denotes the distance from the market where [V.sub.p1] and [V.sub.p2] intersect. Crop 1 will be produced on all land bounded by distance k'. Note also that [V.sub.p2] > [V.sub.p1] and [V.sub.p2] is positive when k > k' and k < [k.sup.*.sub.2]. Therefore, crop 2 will be grown where k' < k < [k.sup.*.sub.2]. Land farther than [k.sup.*.sub.2] from the market will lie fallow. In the context of HBU, the HBU at 0 < k < k' is production of crop 1, the HBU at k' < k < k.sup.*.sub.2] is production of crop 2, and HBU at k [greater than or equal to] [k.sup*.sub.2] is fallow land.

[FIGURE 2 OMITTED]

HBU Insights

A number of observations can be made based on the results of these simple models of agricultural land use.

* The land use that will dominate at a given location is the highest-valued use. This is because this use is capable of producing the greatest land rent; it therefore can outbid all competing uses. This is analogous to farmers who specialize in crop 1 being able to outbid farmers who specialize in crop 2 at locations up to a distance of k' from the central market, as shown in Figure 2.

* Location matters. Land value for various uses differs by location. Although the lower-priced crop is outbid up to a distance of k' in Figure 2, lower-priced crop 2 dominates higher-priced crop 1 at a distance in excess of k'. Crop 2 also dominates fallow land up to a distance of [k.sup.*.sub.2]. Neither crop represents a feasible land use beyond distance [k.sup.*.sub.2].

* Externalities can affect land values, altering which land use dominates at a boundary location. For example, an innovation in transportation of crop 1 that lowers [t.sub.1] would flatten the slope of [V.sub.p1] but leave the vertical intercept unchanged. This would push the land-use boundary (k') further from the market and alter the dominant land use for some distance beyond the prior crop 1 land-use boundary.

* Product price can affect land-use dominance. If price [p.sub.1] were to increase relative to price [p.sub.2] and all else remained unchanged, the vertical axis intercept for [V.sub.p1] would move upward while the slope remained constant. The effect would be to increase the distance to the intersection point k'. Hence, the boundary between crop 1 and crop 2 will move as relative crop (product) prices vary.

* Production cost matters. In Figure 1, a reduction in production cost per unit of crop output (c) would raise the vertical axis intercept for the crop production land-value gradient, increasing the ratio of cropland to fallow land. In Figure 2, a change in production cost per unit of crop output would push the crop 1 and crop 2 land-use boundaries outward as the vertical axis intercepts for both land-value gradients move upward. Additionally, a change in relative production cost per unit of crop output (initially assumed as [c.sub.1] = [c.sub.2]) would have an effect similar to a price change. Note that an increase (decrease) in production cost per unit of crop output has the same effect as a decrease (increase) in product price.

* Land (site) productivity affects land use. For example, relaxing the [q.sub.1] = [q.sub.2] assumption would affect the relative value of land for production of the two crops, change the two land-value curves, and change the productive/fallow land boundary.

The lessons from the agricultural models lead to important broader conclusions regarding the highest and best use concept. These can be summarized as follows: (1) HBU is the highest-valued land use; (2) the highest-valued land use is dependent on more than the price a producer receives for its product, but product price matters as well; (3) location (linkage, for example) plays a major role in which land use dominates; (4) highest and best use is not stagnant--external factors can and do affect which use dominates at a given time and location; and (5) changes in production cost for a crop (industry) affect land rent and HBU.

Agricultural Model of von Thunen Informs the Modern HBU Concept

The appraisal profession, as practiced in the United States, currently adopts several highest and best use definitions. (8) All are informed by an understanding of the foregoing von Thunen land-rent model and its [V.sub.p] land-value gradients (often referred to in economics as bid-rent curves). Consider the currently accepted definition of highest and best use of land or a site as though vacant, which in part defines highest and best use as "among all reasonable, alternative uses, the use that yields the highest present land value, after payments are made for labor, capital, and coordination." (9) This definition envisions production resulting from each potential use, production costs associated with each use, and a present land value as a function of the use and associated costs.

In the von Thunen model, production is p and production costs (land, labor, and coordination) may be viewed as c and k; [R.sub.L] converts the resulting return to the land into land value. This is consistent with the teaching in Appraisal Institute introductory courses, where the highest and best use is defined as the use that results in the highest surplus productivity of land. Uses compete for land, and the use having the greatest surplus land productivity is capable of outbidding all other uses.

All uses, however, do not compete for all sites. Hence, the more generic definition of highest and best use specifies "the reasonably probable and legal use of vacant land ..." meeting the criteria of "... legal permissibility, physical possibility, financial feasibility, and maximum productivity." (10) The first two criteria allow the appraiser to simply exclude from further consideration land-value curves (in the von Thunen context) that are not allowed (not legal or likely to become legal) or physically possible. The third criterion eliminates any remaining uses resulting in a negative land value. This is analogous to crop 1 at a distance beyond [k.sub.1.sup.*] in Figure 2. This use is not a direct factor in the land market at locations beyond distance [k.sub.1.sup.*], given the extant crop price, productivity, and production and transportation costs. Once these uses have been eliminated, one is left with feasible uses competing for a site (the site being valued or analyzed). The highest and best use is the use that is able to outbid all others, i.e., the maximally productive use or the use yielding the greatest surplus land productivity.

Another aspect of highest and best use may come into play. For an improved site, the existing use will continue unless and until another use can outbid the existing use. A different use becomes a maximally productive choice when the land value, in the alternative land use, exceeds the value of the site as improved plus the cost of demolishing the existing improvements to accommodate the alternative land use. If the existing use dominates all alternative land uses, then the highest and best use as improved comes into consideration along with any nuances regarding ideal improvements and implications for functional utility of the existing improvements. Highest and best use as improved is beyond the scope of this article. The foregoing land-rent theory, however, easily accommodates the concept of an extant use outbidding competitive, alternative land uses.

Conclusion

Although not currently emphasized in Appraisal Institute curricula or The Appraisal of Real Estate, (11) the concept of highest and best use as we know it and define it today is solidly grounded in von Thunen's land-rent theory, which may be as profound now as it was when first developed almost two hundred years ago. While it is tempting and perhaps prudent to rewrite definitions to suit the current valuation environment, it is also important to remain true to the profession's theoretical underpinnings. Land-rent theory facilitates an understanding of why certain uses are eliminated from consideration in a highest and best use analysis, provides an understandable and logical construct for the concept of financially feasible use, and illustrates why the maximally productive use must be the winner in a hypothetical auction of a given site. The maximally productive use outbids all other uses because it generates the greatest surplus productivity to the land and therefore generates more purchasing power. It is hoped that this perspective on HBU will not be lost to the dustbin of history as the profession alters its terminology to suit the modern era.

(1.) American Institute of Real Estate Appraisers, Readings in Highest and Best Use (Chicago: American Institute of Real Estate Appraisers, 1981).

(2.) Terry V. Grissom, "The Semantics Debate: Highest and Best Use vs. Most Probable Use," The Appraisal Journal (January 1983): 45-57.

(3.) Richard L. Parli, "What's Financial Feasibility Got to Do With It?" The Appraisal Journal (October 2001): 419-423; David C. Lennhoff and Richard L. Parli, "A Higher and Better Definition," The Appraisal Journal (Winter 2004): 45-49.

(4.) See letters to the editor by Lloyd D. Hanford Jr., Walter M. Kane, and Joseph F. Consoli as well as a response by David C. Lennhoff and Richard L. Parli, The Appraisal Journal (Spring 2004): 186-189.

(5.) Johann H. von Thunen, Der isolierte Staat in Beziehung auf Landwirtschaft und Nationalokonomie, 3rd ed., ed. H. Waentig (Jena: Gustav Fischer, 1930 [1826, 1843]).

(6.) For a more complete and mathematically rigorous but modern presentation of von Thunen's land-rent theories, see Donald W. Jones, "An Introduction to the Thunen Location and Land Use Model," ed. A. Ghosh and C. Ingene, Research in Marketing (Greenwich: JAI Press, 1991).

(7) To make the analysis meaningful, assume that the transportation cost difference is large enough to cause the crop 1 and crop 2 land-value gradients to intersect where both land values are positive, i.e., intersect above the horizontal distance line in Figure 2. Otherwise, crop 1 dominates crop 2 and the model reverts to the simple two-choice model.

(8.) The Dictionary of Real Estate Appraisal includes three definitions: "highest and best use," "highest and best use of land or a site as though vacant," and "highest and best use of property as improved." Appraisal Institute, The Dictionary of Real Estate Appraisal, 4th ed. (Chicago: Appraisal Institute, 2002), 135-136.

(9.) Ibid, 135.

(10.) Ibid.

(11.) Appraisal Institute, The Appraisal of Real Estate, 12th ed. (Chicago: Appraisal Institute, 2001).

Marvin L. Wolverton, PhD, MAI, is a consultant in a practice limited to issues of valuation theory and statistical modeling. He retired from academia in 2004, having taught at the University of Nevada-Las Vegas and having held the Alvin J. Wolff Distinguished Professorship in Real Estate at Washington State University. Wolverton earned his doctorate in business administration with concentrations in real estate and decision science from Georgia State University in Atlanta. He holds an MS in economics from Arizona State University and a BS in mining engineering from New Mexico Tech. He currently serves on The Appraisal Journal Editorial Board and is widely published in a variety of domestic and international real estate journals. Contact: wolverton1@cox.net
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Author:Wolverton, Marvin L.
Publication:Appraisal Journal
Date:Sep 22, 2004
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