Faustmann formula before Faustmann in German territorial states

FORPOL-01329; No of Pages 12 Forest Policy and Economics xxx (2015) xxx–xxx

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Faustmann formula before Faustmann in German territorial states Esa-Jussi Viitala Natural Resources Institute Finland, PL 18, 01301 Vantaa, Finland

a r t i c l e

i n f o

Article history: Received 9 June 2015 Received in revised form 10 November 2015 Accepted 10 November 2015 Available online xxxx Keywords: Forest economics Land valuation Optimal timber harvesting German School of forestry History of forest economic thought Capital and investment theory

a b s t r a c t A common perception in forest and natural resource economics is that the celebrated ‘Faustmann formula’ was discovered in 1849 and that the ‘Faustmann rule’ or Faustmann–Pressler solution to the optimal forest rotation age was derived from it a decade later by Max Robert Pressler. This paper shows that the modern perspective to the valuation of forests was presented in German territorial states much earlier than has previously been thought. In 1805 a competent forest mathematician Johann Hossfeld showed explicitly how forest value can be derived under both intermittent and sustained yield management, thus discovering the Faustmann formula. The study also shows that the close intellectual and professional connections among the first German ‘forest economists’ seem to have played a key role in the diffusion of modern forest economic principles from Hossfeld and his contemporaries to Faustmann and Pressler, and perhaps even more generally to modern capital theory. © 2015 Elsevier B.V. All rights reserved.

1. Introduction A common notion in forest and natural resource economics is that the celebrated ‘Faustmann formula’ was discovered by a young Hessian forester Martin Faustmann in 1849 and that the ‘Faustmann rule’ or Faustmann–Pressler solution to the optimal rotation age was derived from it a decade later by a distinguished professor of forest mathematics Max Robert Pressler (e.g. Gane 1968, Samuelson 1976, Johansson and Löfgren 1985, Hanley et al. 1997, Crocker 1999). Similar perception appears also in reviews on the development of general economics (e.g. Faulhaber and Baumol 1988). Recent research has significantly extended this understanding by showing that the economic ideas behind these innovations were presented already in the late seventeenth century England during socalled financial revolution (Viitala 2013). In his remarkable writings in 1683 and 1701, John Houghton, a London-based editor, businessman and fellow of the newly-formed Royal Society, explicitly recognized the opportunity cost of forest capital (standing timber and bare land) and compared forestry with other forms of land use employing calculations that are in line with modern capital and investment theory. While presenting these economic comparisons, he also came very close to expounding the underlying principle of the ‘Faustmann rule’ or ‘Faustmann condition’, which states that it is optimal to harvest a forest when its marginal value growth decreases under the marginal cost of forest capital consisting of standing timber plus bare land. In 1730, a competent land surveyor and accountant John Richards from Essex

E-mail address: esa-jussi.viitala@luke.fi.

contributed to this line of modern forest economic thought by calculating forest value under both intermittent and sustained yield management using discounted cash flow to infinity, and thus discovering the ‘Faustmann formula’ more than a hundred years before Faustmann (Scorgie 1996, Viitala 2013). The above findings are of particular interest considering that in natural resource economics literature Faustmann's contribution has been referred as ‘remarkable’ (Samuelson 1976, 469, 472) and Pressler has been regarded to anticipate marginal analysis (Crocker 1999, 33). Extending this line of argumentation somewhat further it has been claimed that Faustmann and Pressler produced capital theory that outplayed and was developed even earlier than its cousins within the economic discipline (Löfgren 2012). This argument finds some implicit support in Irving Fisher's famous The Nature of Capital and Income (1906) in which Fisher presents the idea that the value of a capital at any instant should be derived from the value of the future income which the capital is expected to yield. His celebrated book includes a brief but curious comment that such appraisement of young forests is already worked out with considerable precision in Germany and some other countries.1 The significance of the Faustmann formula and condition is not restricted to forestry. As pointed out by Gaffney (2008), the Faustmann

1 “The fundamental principle which applies here is that the value of capital at any instant is derived from the value of the future income which that capital is expected to yield. Other classical examples [of this principle] are wine, the value of which is the present worth of what it will be when ‘mellow’ and ready for consumption; and young forests, which are worth the discounted value of the lumber they will ultimately form. In Germany and in other countries, such appraisement of forests is now worked out with considerable precision.” (Fisher 1906, 188, 205)

http://dx.doi.org/10.1016/j.forpol.2015.11.004 1389-9341/© 2015 Elsevier B.V. All rights reserved.

Please cite this article as: Viitala, E.-J., Faustmann formula before Faustmann in German territorial states, Forest Policy and Economics (2015), http://dx.doi.org/10.1016/j.forpol.2015.11.004

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formula ostensibly deals with timber growth but can be adapted to deal with all capital assets, with any time-patterns of inputs and outputs whatsoever. Another relevant point is that although the economic problem of handling natural resources is as old as civilization (e.g. Lowry 1965), the Faustmann model (encompassing both the formula and the condition) has been regarded as perhaps the oldest formal description of natural resource use that is still considered to be theoretically valid (e.g. Tahvonen and Salo 1999). It appears that in early natural resource economics only the works of Johann Heinrich von Thünen (1966, 1850, 1863) contain similar theoretical sophistication with regard to capital valuation and marginal analysis as the writings of Faustmann, Pressler and other early German forest economists. To fully acknowledge the potential merits of the early German agriculturalists and foresters in anticipating some fundamental aspects of modern resource economics it is useful to note that in the history of economics Thünen has been regarded as the first to use the calculus as a form of economic reasoning (Schumpeter 1954, 441). Blaug (1968, 321) goes a step further by asserting that Thünen's rudimentary development of the concept of marginal productivity, applied to wages as well as to the revenue of capital, his use of differential calculus and marginal reasoning to provide equilibrium solutions of economic variables make him the first truly modern economist. The potential role of forestry in the formation of modern resource economics calls for a more extensive analysis of the early development of forest economic thinking. One of the most interesting questions is whether it is plausible that the fundamental principles related to forest valuation, opportunity cost of forest capital and optimal forest rotation age were introduced in Central Europe only approximately 150 years after they had been discovered in England. Since Faustmann and Pressler did not refer to Houghton, Richards or other English scholars, seeking an answer to this question requires that one examines in more detail the evolution of forest economic thought in German territorial states before Faustmann and Pressler. This examination is of wider interest because the origins of many long-standing controversies in forest management and planning, typically related to the role of opportunity cost of forest capital, can be traced back to this particular period. Previous studies have examined the development of the fundamental forest economic principles almost exclusively within the space of some decades after Faustmann and Pressler. Löfgren (1983, 1990, 1993, 1995, 2002) and Löfgren and Mattsson (1995) have provided interesting information on the Swedish contributions and development, while Helles and Linddal (1997) have explored early Danish insights to forest economics. One of the most interesting findings has been that a Danish count Christian Reventlow made calculations on the optimal rotation age of oak and beech with a marginal approach already in the 1810s, yet without accounting for the opportunity cost of bare land. Considering that Danish forestry had close connections with the German discipline, one may ponder whether the economic ideas Reventlow promoted had been presented earlier in the German forestry literature.2 Other studies have examined the contribution of Faustmann and Pressler in detail. Viitala (2006) analyzed Faustmann's less-known article, published three months before his classical one, and concluded that his economic thinking was remarkably modern, and that the young forester made an impressive number of valid observations related to efficient land use and forest management already in this pioneering article (Faustmann 1849). Gong and Löfgren (2010) focused on the question whether Pressler fully understood the economic implication of the celebrated indicator percent (Weiserprozent), and concluded that his

2 Several leading German foresters helped to develop Danish forestry and to establish its forestry education in the mid-eighteenth century. These foresters included, for example, Johann Georg von Langen and his private student Hans Dietrich von Zanthier (e.g. Wedekind 1835, Hess 1885, Rozsnyay 1979).

treatment of the rotation problem was not always economically fully consistent. Previous studies also have elaborated the contribution of the famous German agriculturist Johann von Thünen, often referred as the founder of the location theory. In the forest and natural resource economics literature he is usually designated as belonging to the group of famous economists who have posed an unwarranted solution to the optimal forest rotation problem – others include e.g. Jevons, Heckscher, Fisher and Boulding (see, e.g. Samuelson 1976) – whereas in general economics he is typically acknowledged for his contribution on the theory of rent and resource allocation based on the principle of marginal productivity (e.g. Ekelund and Hébert 2007, 292, 401–407). In the first volume of his influential book Isolated State, published in 1826 and treating forestry very briefly, Thünen (1966, 121) indeed proposed the unwarranted solution that accounted only for a single forest rotation and thus ignored the opportunity cost of bare land. However, less commonly acknowledged is the fact that in the third and last volume of the same book – published posthumously in 1863 (Thünen died in 1850) and dedicated solely to forestry – he maximized land rent and calculated optimal forest rotation of a normal forest (Manz 1986), yet erred in evaluating immature forest stands at their immediate sale value. As it happens, it was around at the same time when Faustmann wrote his celebrated article as a response to a teacher of mathematics, Edmund von Gehren (1849), who also had misspecified the value of young forest stands in his article in the preceding issue of the same forestry journal, Allgemeine Forst- und Jagd-Zeitung. The above studies indicate that some conscious scholars, such as Reventlow and Thünen, both estate owners and keen experimenters in forestry, were aware of the capital nature of standing timber and its opportunity cost several decades before Faustmann who started his forestry studies only in 1841. It seems quite evident that they preceded Faustmann and Pressler also in attempts to apply marginal analysis to the optimal rotation problem. Similar line of discussion on Faustmann's precursors can be found for example in Heyer (1871), Schwappach (1888), and Gane (1968), who suggest that Faustmann and Pressler probably benefited from the insights and formulations put forward by early German forest economists like Gottlob König (1813, 1835, 1842), Wilhelm Pfeil (1823) and Johann Hundeshagen (1826). Increased information about various further specifications of the Faustmann formula seems to have led to some confusion and apparently contradictory claims regarding its origins in the forest and natural resource economics literature. The idea of calculating forest value under both intermittent and sustained yield management using discounted cash flow to infinity has been referred for example as the Faustmann, König–Faustmann, Faustmann–Pressler, Faustmann– Wicksell, Faustmann–Pressler–Ohlin, and Faustmann–Ohlin– Preinrich–Bellman–Samuelson formula (see, e.g. Samuelson 1976, Johansson and Löfgren 1985). Similar type of obscurity seems to persist with regard to the correct solution of the optimal forest rotation problem, which has been designated e.g. as the Faustmann, Faustmann– Pressler, and Faustmann–Ohlin rule or condition. This study contributes to the current literature by showing that a modern perspective to the valuation of forests was presented in the German territorial states almost 50 years before Faustmann by Julius Nördlinger and Johann Hossfeld, perhaps the first ‘forest economists’ who were accustomed to use algebraic notation in their argumentation. Nördlinger proposed that net income from the forest should be considered as an interest on forest capital, and that the value of a forest should be calculated based on the ‘expected future utility’ it provides, i.e. on the income it yields over an infinite series of years. Hossfeld's contribution was even more remarkable in the sense that he showed explicitly how forest value can be derived under both intermittent and sustained yield management and how young forests should be appraised accordingly. In this respect he fully captured the capital nature of forests, an idea that would resurface in Faustmann's, Presser's and Fisher's classical

Please cite this article as: Viitala, E.-J., Faustmann formula before Faustmann in German territorial states, Forest Policy and Economics (2015), http://dx.doi.org/10.1016/j.forpol.2015.11.004

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writings several decades later.3 Hossfeld's achievement is novel in the literature, and Nördlinger's utility-based views have not received due credit in modern natural resource economics literature. The study concludes by demonstrating the close intellectual and professional connections between the early German forest economists. These interactions seem to have played a key role in the transfer of modern forest economic reasoning from Hossfeld and his contemporaries to Faustmann and Pressler, and perhaps even more generally to modern capital theory. 1.1. Research method History is socially constructed, embodying interpretative strategies that are either explicit or implicit in how historians of economic thought pursue their works. This has given rise to a variety of research methods in the field. Different research styles and methods in the history of economic thought are presented and discussed in Samuels (1983), Medema and Samuels (2001), Biddle (2003), Samuels et al. (2003) and Marcuzzo (2008). Marcuzzo (2008) identifies three broad methods in the history of economic thought: i) textual exegesis, ii) rational reconstruction, and iii) historical reconstruction. In short, textual exegesis is a search into the meaning of a text, whereas rational reconstruction refers to a method in which the ideas and arguments of past authors are reconstructed in a way that enables the interpreter to identify its relation to modern economic thought. It usually deals with a subset of a past author's work, which is translated to modern theoretical framework, in our case neoclassical economic theory. This implies that mathematical modeling techniques and theoretical concepts unknown to the original author may appear in the rational reconstruction. Historical reconstruction focuses on reconstructing the meaning of texts at specific moments in the past and on text's relation to its own social, political, cultural and intellectual contexts. Piecing together the fragments of past and reconstructing a picture that encompasses important insights and discoveries in the midst of their own familiar surroundings enables to draw on continuance of economic ideas and to explore their motivating forces. Besides published works, historical reconstruction involves perusal of biographies and other archival sources. This extends the scope of inquiry but at the same makes it more complex because it requires that ideas and their evolution are examined as part of larger political, economic and societal development. It is generally well understood that the classification of research styles and methods in the history of economic thought does not permit the drawing of any sharp distinctions between different styles; approaches are rather distinguished by the emphasis placed on different aspects. Different methods are in some respects overlapping and each method has its locus in the field. Pure rational reconstruction, for example, may provide important information in cases when the focus is confined to certain theoretical constructions in the past, but in other instances the same method may miss the benefit of a rich background of ideas and past debates and thereby lead to fragmental or narrow interpretations in the history of economics or economic thought. This study applies both rational and historical reconstruction because it not only traces new insights and ideas on the economic aspects of forestry and translates them into modern theoretical frameworks, but also connects these constructs and events to broader political developments and intellectual movements. The most interesting ideological and intellectual forces that have arguably shaped early forest economic thinking in German territorial states are cameralism and its academic form cameral science, both approaches with high ambitions to regulate domestic resources and thus diverging from the rising spirit of liberalism and political economy in England with an increasing emphasis on laissez faire type of market economy. 3 Later Fisher (1930, 55) gave another intriguing example of the connection between income and capital: “the orchard is the source of the apples but the value of the apples is the source of the value of the orchard.”

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2. Discovery of the Faustmann formula in Central Europe 2.1. The quest for proper valuation of forests A basic idea adopted by the early German game wardens and foresters was sustainability (Nachhaltigkeit) which in its simplistic form was to be obtained by dividing a forest to equal parts in area or timber volume and harvesting one at each year. Because various local forest enactments, issued at least since the fourteenth century, did not generally allow any other kind of forest exploitation, the quest for an even forest age-class distribution was to form a basis also for forest valuation practices (Bernhardt 1875, Lemmel 1936). These traditional principles and patterns were readily assimilated into the economic and administrative doctrine that prevailed in Central Europe during the eighteenth century. The doctrine of cameralism (Kameralism) was firmly based on the idea that economic action is the prerogative of the state, and economic order flows from the prudent direction of such action. Following this fundamental principle, advocates of cameralism assumed that purposive direction of all the state's important activities in industry, finance, commerce, internal affairs and the military would increase the prosperity and power of the state and its ruler, and eventually contribute to the general welfare and common good (Tribe 1988).4 An important element in cameralistic thinking was compulsion to self-sufficiency, especially with regard to those necessities and resources that were considered essential for the power of the state and its ruler. Reflecting this dominant quest that arose from the turbulent economic and political environment, cameralists subscribed to the traditional view that an even forest age-class structure was the most suitable form to produce the greatest overall benefit for the state and its subjects because it provided a constant flow of income for the state as well as domestic raw materials for households and industries. These prevailing premises and principles of governing economy and its resources tended to guide forest officials' and scholars' interest away from the questions of modern forest and capital valuation. However, already in the mid-eighteenth century one of the leading cameralists, Georg Heinrich Zincke (1755, 878–879), and his counterpart in forestry, Wilhelm Gottfried von Moser (1757, 74–81), had aptly pointed out that the method of calculating the value of a forest by assuming a normal or fully-regulated forest, and thus relying on the (constant) net income stream it would generate in perpetuity, is overly advantageous for the buyer if the initial age-class distribution of the forest was skewed towards old age-classes. A few years later an anonymous writer in one of the prime forestry journals, Allgemeines oeconomisches Forst-Magazin, raised similar concerns by claiming the conventional method of deriving the rental value of a normal forest (Waldrentierungswert) yielded too low values for carefully managed (overstocked) forests (Anonymous 1765, 212).5 This type of observations together with several alterations in the ownership of German lands called for more accurate methods to the valuation of forests (Bernhardt 1875, 297). Also the reports of rapidly rising timber prices, at least in certain areas (Lowood 1990, 318–319), 4 The early form of cameralism was predominantly concerned of creating a uniform and effective public administration to secure authority and revenues for the rulers of the territorial states, irrespective of their vassals. However, the increasing quantitative spirit of the eighteenth century, induced by the Enlightenment, gradually transformed the movement to ‘cameral science’ (Kameralwissenschaft) with more systematic aims and patterns of managing various economic activities and resources (Tribe 1988, Lowood 1991, Loughlin 2010). 5 The knowledge of compound interest can be traced back to early civilizations. However, there seems to be a consensus among historians of economic thought that it was not widely (openly) used in the ancient world, and that this practice continued in the medieval period (800–1500 CE), at least in Western Europe. In the sixteenth and seventeenth centuries it became more common to value agricultural land and other real property by using methods that resemble, or in some instances correspond to net present valuation. For discussion, see e.g. Poitras (2000), Munro (2003, 2008), and Goetzmann and Rouwenhorst (2005).

Please cite this article as: Viitala, E.-J., Faustmann formula before Faustmann in German territorial states, Forest Policy and Economics (2015), http://dx.doi.org/10.1016/j.forpol.2015.11.004

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directed increasing interest in more exact and flexible methods of forest valuation. Demand for more coherent forest valuation methods was stimulated also by the growing consciousness of the economic principles that had been put forward by the French physiocrats and their compatriots from the 1750s. These economic writers and their ideas on liberalism and primacy of agriculture had a direct influence on Adam Smith who became acquainted with the physiocrats at the height of their literary activity, while he was conducting his own inquiry into the nature and function of capital in an agricultural society (Ekelund and Hébert 2007, 84). The celebrated Wealth of Nations, published in 1776, and translated and published in German language 1776–1778, and again in 1793–1796, contained noteworthy discussion on forestry, capital and land rents but without any definite conclusions on forest valuation (Smith 1776, ch XI). Nevertheless, it was the work on which Thünen (1966) built his ideas of land rents, marginal productivity and opportunity cost of capital – also when dealing with forestry. Considering that the physiocratic doctrine spread widely to German academic circles (Tribe 1988, Backhaus 2011) and that Smith's book became a great success in England, it seems reasonable to assume that also the leading German forestry scholars, who pondered questions related to the capital nature of forests and lucrative forest resource management at the turn of the nineteenth century, became increasingly aware of the more modern type of economic reasoning. At the same time, they must have realized that the novel ideas of a self-regulating economy operating within a market system (laissez faire) deviated substantially from the core ideas of cameralism, which had provided a theoretical framework for forest regulation and its principles and patterns in the German territorial states at least since the beginning of the eighteenth century.

of construction timber) and at interest rates of four and six percent (pp. 132–133). In an annex to the article, von Burgsdorf, who was one of the original fellows of the Forest Society, established in 1797, applauded their efforts and expressed a wish that insightful writings on the same important topic would appear also in the subsequent numbers of the same journal (see Bein and Eyber 1801, 127–128). Burgsdorf's enthusiasm reflected the fact that his textbook, published some years earlier, had included two basic examples of calculating forest values under perpetual annual series of income, thus corresponding to sustained yield forest management (see Moog and Bösch 2013). Similar mathematically elementary but theoretically solid calculations on the capital value (Kapitalwert) of forests would be reiterated in Krug (1805, 153).

2.3. Nördlinger and expected utility of a forest A few years later, Julius Simon Nördlinger (1805), who had studied mathematics and acquired his practical knowledge of forestry by working as a land surveyor, followed Burgsdorf's request. He criticized Bein and Eyber's methods, as well as Johann Gottlieb Beckmann's (1769) cameralistic approach to forest valuation. In his insightful article, Nördlinger first elaborated the proposition that the net income from the forest should be considered as the interest on forest capital (p. 370) and that the value of a forest should be calculated based on the expected future utility it provides, i.e. on the income it yields over an infinite series of years: “As excellently demonstrated here, the value of a forest must be derived solely from its expected utility (hoffenden Nutzen), i.e. one has to calculate the income, and namely the utility (Nutzen), it yields over an infinite series of years.” (Nördlinger 1805, 367).

2.2. Towards modern forest valuation principles Otherwise unknown Prussian foresters Bein and Eyber (1801) contributed to the rise of more modern forest economic reasoning in Central Europe by proposing that under a fully-regulated forest the annual net timber income could be considered as interest on forest capital and that this perpetual annual series of incomes could be used to derive the value of a forest (Waldrentierungswert). In this respect, they closely followed Zincke's argumentation, yet without any explicit reference to him or Moser, another predecessor with similar perceptions. Motivated by their observation that a large part of the German forests could not be considered as fully-regulated, Bein and Eyber posed the question as to how one can determine the return of a forest capital and forest value when timber income is periodic over time rather than being annually constant: “In such cases, in which the annual income (jährliche Einnahme) from a forest changes very often, how can one determine the average sum, regarded as the perpetual income (immerwährende Einnahme) from the forest, and considered as an interest (Zins), from which the present value of the relevant capital (jetzigen Werthe angemessene Kapital) can be determined?” (Bein and Eyber 1801, 131). In their article, Some thoughts related to the determination of forest value in purchase transactions, addressed to the Prussian high forest councilor and prominent forest scholar Friedrich von Burgsdorf, they proposed that the average annual net timber income over a transition period towards a normal forest can be regarded as the perpetual annual series of net incomes, which, with an appropriate interest rate, can be used to derive the corresponding forest value. While acknowledging certain approximations in their calculations and manifesting the need for an infinite time horizon and compound interest, they presented an example in which the value of a forest was calculated with a predetermined (single) rotation period of 120 years (reflecting the dimensional requirements

Nördlinger (1805, 415–419) continued by noting that the calculations by Bein and Eyber contained several fundamental errors. The forest values attained were much too low because the Prussian foresters had used an overly simplified form of compound interest calculation in which the accumulated interest was added to the capital only every ten years. He also drew attention to the fact that calculating the ‘average annual net timber income over a single rotation period’ without fully taking account of the phasing of timber harvests and management costs, is an unwarranted approach in the case of unregulated forestry. If a forest was abnormal, the proper procedure was to calculate the value of each forest stand; the aggregate would then represent the value of the forest. A further implication of Nördlinger's advanced economic understanding was his observation that the valuation of forests should be based on the common interest rate but that at the same time consideration should be given to the fact that forest land is a less risky investment than money placed in some other financial assets, though not as secure as farmland. Since the conventional (risk adjusted) discount rate to be applied on farmland investments was three percent and on pure money capital five percent, he felt it reasonable if it was something between them for forest, thus as an integer, four percent (Nördlinger 1805, 375). Another important observation is that Nördlinger used the term ‘expected utility in perpetuity’ while discussing forest valuation. Although the idea of exploiting the forest at the highest possible utility in perpetuity had appeared in the cameralistic discourse at least since the 1780s, it was subordinate to the prevailing interpretation of sustainability and thus to various practical guidelines of forest regulation (see, e.g. Deegen and Seegers 2011). It is possible that Nördlinger found inspiration from those conscious forest cameralists who, despite focusing almost exclusively on the established tradition of forest regulation, had presented some simple calculations on the economic return of forest capital. The calculations of somewhat mysterious writer di

Please cite this article as: Viitala, E.-J., Faustmann formula before Faustmann in German territorial states, Forest Policy and Economics (2015), http://dx.doi.org/10.1016/j.forpol.2015.11.004

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Paprica (1789, 27, 255), who signed with initials C.J.M. v. C.P. (Count Constanze di Paprica), is a good example of this kind of work. 2.4. Hossfeld's definitive work Nördlinger's argumentation and calculations on forest value under constant annual income were immediately extended in the same forestry transaction (Diana) by Johann Wilhelm Hossfeld, who was one of the leading contemporary teachers of forest mathematics and highly qualified also in matters of forest taxation and mensuration. In an annex to Nördlinger's article, Hossfeld (1805b, 420–448) showed how the value of a forest can be obtained — not only under perpetual annual series but also under periodic series of income. Hossfeld's modern economic approach to forest valuation is perhaps most clearly discerned in his numerical examples (pp. 442–443). In one of these examples, a short-rotation forest stand (eichene Schlagholzwand) is expected to yield a net income of 240 Reichsthalers (Rthlr) every 20 years at an interest rate δ of four percent. He correctly pointed out that this implies that the value V of the forest land is V¼

240 ð1 þ δÞ20 −1

¼ 201 Rthlr;

ð1Þ

while the value of the same forest at the age of 14 years is V 14 ¼

240ð1 þ δÞ14 ð1 þ δÞ20 −1

¼ 349 Rthlr: 6

ð2Þ

Like Nördlinger, Hossfeld (pp. 437–438) also proposed that, under constant annual income a to infinity, forest value can be obtained from the infinite geometric series a a a a þ þ þ þ :::in infinitum 1 þ δ ð1 þ δÞ2 ð1 þ δÞ3 ð1 þ δÞ4 ¼ a=δ:

Va ¼

ð3Þ

These formulations describe the essential content of the celebrated Faustmann formula. For a comparison, Faustmann (1995) presented his specification in an algebraic form as VF ¼

At þ

Xq i¼a

t−i

Di ð1 þ δÞ t

ð1 þ δÞ −1

−cð1 þ δÞt

v − ; δ

ð4Þ

where At denotes timber income from the final harvest, Di, i = a,…q timber income from thinnings, i age of the forest at the time of thinnings, t rotation period, c regeneration costs and v annual costs. Inserting At = 240 Rthlr , t = 20 and excluding thinnings as well as regeneration and annual costs, Eq. (4) collapses into Eq. (1). Hossfeld excluded thinnings and regeneration costs because he dealt with short-rotation forest stands, but thinnings have also typically been left out of those more modern formulations that have been presented by general economists (e.g. Ohlin 1921, Samuelson 1976, Johansson and Löfgren 1985), independently of whether the rotation period is short or long. This simplification has been preferred so as to obtain an analytically solvable optimization model. In his comprehensive textbook on forest mathematics published fifteen years later, Hossfeld (1820, 581) presented an augmented numerical example, involving a 90-year forest rotation period which included a thinning. Hossfeld's major contribution was his realization that forest value at any instant can be derived from the bare land value of the same tract of

6

V¼

Hossfeld's first calculation contains an arithmetical slip, since he wrote 240 240 ¼ 1:911 ¼ 125:5 Rthlr: It is obvious, however, that the denominator 20 ð1þδÞ −1

should have been 1.1911, which approximation he used in his subsequent calculation.

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land. This is possible because all forest values reflect fundamentally the same thing, i.e. the discounted stream of net income which that scarce resource is expected to yield in perpetuity. Perhaps making use of his good economic intuition or his knowledge of the novel economic ideas that had been expounded a few decades earlier by the French physiocrats and early political economists, Hossfeld followed economic reasoning asserting that bare land is able to yield a rate of return that equals δ, which implies that the value of the forest at the age of 14 years is V(1 + δ)14 and corresponds to Eq. (2). Continuing similar argumentation, the value of the forest at the age of 20 years is 441 Rthlr [240(1 + δ)20/((1 + δ)20–1) = 441] and, after subtracting the timber income from the final harvest (240 Rthlr), we end up with the same bare land value as that derived from Eq. (1). Hossfeld's insight was remarkable, considering that with it he anticipated the essential part of the capital theory that was a century later condensed in Fisher's (1906) The Nature of Capital and Income, a work that is generally considered to be the cornerstone of modern capital and investment theory. Moreover, he was able to evade the shortcomings of those colleagues in forest and agricultural economics (e.g. Gehren, Thünen) who would value young forests simply by multiplying timber volumes by their prices. To add perspective, similar theoretically unwarranted approaches to valuing young forests have been used even quite recently in several forest economic studies. For discussion of these misspecifications in even-aged forest management, see Tahvonen and Viitala (2006), and for a similar discussion concerning uneven-aged management, see Getz and Haight (1989, 269–72), Tahvonen (2011), and Rämö and Tahvonen (2014). These papers also demonstrate how the forest valuation methods that lack solid theoretical foundations distort profitability figures.7 2.5. Evaluation of individual contributions Bein and Eyber, Nördlinger and Hossfeld published their articles in consecutive volumes of the forestry transaction Diana that had been introduced in 1797 by the newly-formed Forest Society. At the time the second volume of the publication appeared in 1801, many prominent forest scholars and officials had joined the Society: e.g., Beckmann, Burgsdorf, Cotta, Däzel, Hartig, Hennert, Hossfeld, Hundeshagen, König, Lassberg, Moser, Oettelt and Späth (Bernhardt 1875, 397). It difficult to draw a definitive conclusion on Nördlinger's original contribution, because the third volume of Diana appeared as a single issue in 1805. However, a reasonable amount of evidence seems to support the perception that Hossfeld was the first in the German tradition who laid out the Faustmann formula in both cases, that is, under perpetual annual series and periodic series of income, and understood its more general applicability in forest resource use, and perhaps also in land management. We now turn to examine this evidence in more detail. Hossfeld was an exceptionally prolific author who produced numerous articles and several textbooks, mostly in the field of forest mathematics and Forsttaxation, i.e. mix of forest inventory, accounting, analysis and planning. In addition to writing the aforementioned annex to Nördlinger's article, he contributed to the third volume of Diana also in another respect. Just preceding Nördlinger's writing in the journal, there appeared Hossfeld's (1805a) extensive article (Comprehensive System for Forest Taxation and Regulation), in which he stated as follows: “To me, the monetary value or purchase price of a forest (Geldwerth oder die Kaufsumme des Waldes) fully represents capital while the income or revenue from a forest represents an interest to this capital (Interessen dieses Kapitals).... This leads us to the art of determining the interest on the forest capital [under constant annual or periodic income, or constantly or periodically (for a number of years or

7 An incisive early remark on the issue comes from Fisher (1907, 24): “It is clear that to cut young timber which is growing very fast is like killing the goose that lays the golden egg, and to reckon the value of the growing timber as only equivalent to the wood contained in it is like reckoning a live goose equivalent to a dead one.”

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forever) increasing or decreasing income*]. One can easily understand that Interusurium [compound interest] has an important role in these kinds of calculations.” (Hossfeld 1805a, 153–154) *This was the subject Hossfeld treated in this connection. At the end of the article, Hossfeld (p. 154) briefly pointed out – evidently being aware that Nördlinger's essay would be published in the same journal volume – that he had introduced the essential principles and techniques related to forest valuation to his students already seven years earlier while acting as a lecturer in Heinrich Cotta's famous forestry school at Zillbach, Saxe-Weimar-Eisenach. This corresponds with the fact that Hossfeld lectured there from 1798 to 1800. From 1801 he acted as a lecturer at the forestry institute of Dreissigacker, situated close to Meiningen, a small town southwest of Jena, in Thuringia. Hossfeld was able to include the annex to Nördlinger's article in Diana most probably because at the time he served as the secretary of the publisher, Forest Society, affiliated with the Dreissigacker forestry institute (Bechstein 1805c, 524). Since Nördlinger visited Zillbach, Dreissigacker and other notable forestry schools and institutes in Saxony, Thuringia, Anhalt and Prussia at the early stages of his extensive study tour that started in 1804 (e.g. Bernhardt 1875, 267; Hess 1885, 255; Hess 1887, 12), there exists a clear possibility that the ideas he presented in his article originated, directly or indirectly, from Hossfeld. This may have been an important incentive for Hossfeld to compose a fairly extensive annex to Nördlinger's writing – in addition to presenting the fundamental principles of forest valuation, he gave explicit rules for forest valuation under variable, in particular increasing and decreasing annual timber income (Hossfeld 1805b, 443–448). Some years later, Hossfeld (1820, 588–592) provided also a more complete treatment of forest valuation under nonconstant timber income. Because of his good knowledge on mathematics, Hossfeld also knew how to make use of differential calculus in forestry: “I have used differential calculus when determining the point in time of highest forest growth and most advantageous forest rotation (der Zeit des größsten Zuchwachtes und der vortheilhaftesten Umtriebes). However, since only few foresters are familiar with this kind of higher mathematics, I had to find such ways that also a common calculator could determine the most advantageous forest rotation. The results of the various studies I have conducted suggest that the rotation periods of most tree species should be much longer than has been conventionally assumed.” (Hossfeld 1805a, 139–140).

An additional point here is that after Zanthier's (1764) elementary calculations on the profitability of various forest management regimes, the question of most lucrative (advantageous) forest rotation seems to have fallen out of mode. The apparently relatively scattered efforts in this direction (e.g. Anonymous 1790, Hennert 1801) did not essentially add to the subject. In England, the development was very much similar. Richard Watson (1794), the Bishop of Llandaff and himself a woodland owner, proposed the single rotation solution in his report to the Board of Agriculture, but it was not until William Marshall (1808), a well-known English agriculturist working for the same institute and reviewing Watson's report, who put forward the correct solution, also without analytical formulation (James 1981, Scorgie and Kennedy 1996). The analytical solution certainly could have been derived from the land value formulas introduced by Hossfeld, because infinitesimal calculus had already been independently developed in the 1670s by Isaac Newton and Gottfried Leibniz. Another point worth considering in Hossfeld's aforementioned passage is his remark on foresters' familiarity with higher mathematics. It very much reminds of the more modern discussion about the use and non-use of mathematics in forest economics (e.g. Löfgren 1990, 1993). Hossfeld was not the only one who paid attention to this matter. It was around the same time when Cotta (1804, v) complained that the ‘practiced algebraist’, to whom calculating the value of a forest was a trivial exercise, would not be the least bit interested in applying his art to it. He continued by claiming that most foresters, unencumbered by such mathematical sophistication, were likely to faint at the slightest scent of a mathematical problem (see also Lowood 1990, 322). 3. Hossfeld and Nördlinger: background and connections Since Hossfeld and Nördlinger explicitly presented the fundamental principles related to opportunity cost of forest capital and forest valuation, and perhaps also understood how these principles were connected to more general economic framework, it is useful to present a brief account of their life and connections. This may provide some additional insights of the factors that contributed to their forest economic thinking. Moreover, it may help to understand their role in a larger disciplinary context; the controversies that their works invoked among forest officials and scholars, but also their significance as a source of inspiration for their intellectual heirs, in particular König, Faustmann and Pressler. 3.1. Hossfeld's life, career and connections

The interesting question here is whether Hossfeld derived the rotation that maximized bare land value. Two particular points indicate that, at least in this connection, he referred to rotations that corresponded with maximum sustained yield. The first observation is that in the preceding section of the article he presented four different intentions related to the concept of ‘most advantageous forest rotation’: maximum wood production, maximum fuelwood production, production of quality timber for construction and other similar purposes, and maximum net income (p. 100). Another point in this direction is his claim that the most advantageous rotation of beech was 140 years (p. 140), which seems quite long from modern financial perspective. Although Hossfeld certainly was mathematically capable of deriving the forest rotation that corresponds with the celebrated Faustmann rule or condition, he perhaps did not actually present this line of calculations. This may have been due to the fact that he appears quite pronounced in his belief that forest management should be based on the prevailing principles of sustainability and systematic forest regulation in order to limit the scope of forest devastation and to secure a constant timber supply for domestic industries (Hossfeld 1805a, 112–113, 142). Nevertheless, his approach to use differential calculus to derive the most advantageous rotation was novel in forestry and clearly anticipated the efforts by Reventlow, Thünen, König, Faustmann and Pressler.

Hossfeld was born in 1768 in Oepfershausen, a small village situated in southwest Thuringia (Saxe-Meiningen-Coburg), famous for its dense forests. He came from a modest family: his father, a teacher in a local village school, was personally able to provide only basic education (elementary mathematics and Latin languages) for his son. From the age of 15 years, Hossfeld continued studies entirely on his own, at the same time taking care of the family household (Hess 1885). When Hossfeld turned 18 years, he applied to the local gymnasium in Meiningen and was accepted on the account of his good proficiency. However, his precocious fondness for mathematics, combined with an argumentative temperament, made him unpopular with his teachers, and soon he quit these studies (Hess 1881; Lowood 1990, 333). The duke of Saxe-Meiningen-Coburg offered him a university grant, but Hossfeld declined because he did not find the local faculties of theology, medicine and jurisprudence interesting. Following his father's wish, he continued to a local teacher seminar but soon dropped out of it as well. In 1789, the duke hired him as a land geometer and supervisor in projects involving building of country roads, but after some unfortunate incidents that involved his allegedly incompetent superior, Hossfeld returned to his parents' home. Then he moved to the countryside, took up residence in local clergyman's home and for several

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months devoted himself to the study of natural sciences, especially botany. In 1791, at the age of 23 years Hossfeld moved to Eisenach, a town just outside of the Thuringian Forest. To support himself, he accepted a position as a lecturer of mathematics in the local English business school (Hess 1885, 161). After several years of teaching there, Heinrich Cotta – one of the Forstklassikers, i.e. leading scholars in the emerging field of forest science – requested him to move some thirty kilometers southward and to begin lecturing geometry and mathematics in his private forestry school at Zillbach. Hossfeld accepted the call and begun to teach there in 1798. Two years later Hossfeld followed his father's wish and traveled back to his home village to assist him in the local school. He stayed there until his father's death in 1801. Already a few months earlier the local duke had offered him a position as an instructor in mathematics and natural sciences (physics and chemistry) in a forest institute that had been established in May 1801 by Johann Bechstein at a nearby town of Dreissigacker (Bechstein 1855, 144). Hossfeld became the first teacher in this famous institute and settled there with the title of forest commissioner (Forstkommissar). During his years in Dreissigacker, Hossfeld claimed a reputation as a highly competent mathematician and an active and inspiring teacher (Bechstein 1855, 378; Hess 1881). He enjoyed debates and was involved, for example, in several rather fierce disputes in the early 1820s with Wilhelm Pfeil, a high forest official of Prussia and another Forstklassiker (Bernhardt 1875, 360). The disputes concerned forestry curriculum at higher educational levels and its links to other disciplines, as well as more specific question like on what grounds forest rotation age should be determined (for details, see Hossfed 1822, Anonymous 1823). After Bechstein died in early 1822, Hossfeld was appointed to the forest council of Saxe-Meiningen-Coburg and was a strong candidate to succeed Bechstein as the director of the upgraded forest academy. His argumentative temperament, inclination to evaluate critically some of the management practices of the school and quest for higher teaching standards may have contributed to the decision that he was not appointed; instead, a rotation among teachers was applied to the director's position (Hess 1881; 1885; Bechstein 1855, 354). Disappointed, Hossfeld gave in his resignation, but after some administrative changes returned to office a few months later, in early 1823. He stayed in Dreissigacker until 1837 when he died at the age of 68 years. It appears that a key element in Hossfeld's thinking was his knowledge in mathematics. Available sources for him were those modern textbooks of mathematics that were aimed at foresters and dealt with his specific areas of interest, forest physics and geometry, touching also differential calculus (e.g. Späth 1797). Hossfeld may have had knowledge of various earlier works on calculus as well. Another pioneer of modern natural resource economics and marginal analysis, Johann von Thünen (2009), in this connection referred to the comprehensive textbooks by Leonhard Euler (1790, 1793). An important source of inspiration for Hossfeld could also have been Abraham Kästner's (1786b) extensive and popular textbook, which treated e.g. logarithms, arithmetic and geometric series, simple and compound interest calculations, and present values. The book contained references to the works of such notable mathematicians as Henry Briggs, Jacob and Johann Bernoulli, Leonhard Euler, Gottfried Leibniz and Simon Stevin. The connection between Hossfeld and Kästner becomes more apparent when one considers that the latter had worked out simple formulas for the volume of timber logs already in 1758 when acting as a professor of natural philosophy and geometry at Hanover's modern university at Göttingen (Kästner 1758). It is very likely that due to his academic status and works in the determination of wood volume Kästner was a familiar figure in German forestry circles — at least to those scholars who were involved in applying and improving similar type of geometrical and stereometrical analysis. Kästner (1786a, 399–400) himself seems to have been well aware of the efforts of

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some competent forestry scholars in this field. Of particular relevance Kästner's works and methods must have been to Hossfeld who became a leading proponent of this type of analysis in forestry.8 3.2. Nördlinger's life and sources of inspiration Hossfeld's contemporary, Julius Simon Nördlinger (1771–1860), was born in a small village of Pfullingen, situated near Stuttgart, in the Duchy of Württemberg. He went to a local Latin school but soon became an apprentice for his artisan father and pursued studies on his own. At the age of seventeen, he was able to make a trip to the Rheine and Black Forest regions, which proved to be a turning point for his interests and career (Bernhardt 1875, 267; Hess 1885, 254–256). After some fortunate incidents, Nördlinger found employment as a land surveyor and draftsman. A few years later in 1801, he began to study mineralogy, chemistry, entomology and botany — again on his own and in his spare time. In 1804, he set out for an extensive study tour. After touring in Saxony, Thuringia, Anhalt and Prussia, Nördlinger continued to the nearby city of Gotha (in Saxe-Gotha-Altenburg) where he turned down the professorship in cameral science that was offered to him by the Tübingen University; instead, he went on to other German cities and states. In 1807, he accepted a position in the council of mining and forestry in his home state Württemberg and later became the senior councilor in the matters of forestry in the local ministry of finances. He was regarded as a competent and active civil servant who was involved in developing manifold activities related to the use of natural resources (Bernhardt 1875, 267). Although Nördlinger was introduced plainly as ‘Forstkandidat from Stuttgart’ in the forestry journal Diana, he was also a fellow of the newly-formed Forest Society (Bechstein 1805a, x; 1805c, 525). The close affiliation to the academic and professional forestry community provides some additional indication that he indeed may have taken courses or instructions in forestry at the early stages of his study tour (1804–1806), perhaps at Dreissigacker or Zillbach. There is evidence that Nördlinger associated at least with the renowned directors of these forestry institutes, Bechstein and Cotta (Hess 1887, 12). Hossfeld and Gottlob König held senior positions at the same institutes. The forestry education at Dreissigacker certainly provided all the necessary qualifications for building a modern approach to forest valuation. The education lasted three years, and the second year included studies on algebra (incl. functions and series) and the third year infinitesimal calculus, advanced geometry, and the use of mathematics and physics in forest management and taxation (Bechstein 1805b, 472–475). Judging from various lecturers' duties and expertise (pp. 475–476), most of the above subjects were on Hossfeld's responsibility. 4. From Hossfeld to Faustmann Considering Hossfeld's and Nördlinger's seminal contributions in the formation of modern forest economic thought, it is interesting to examine whether explicit links to Faustmann can be detected. Especially interesting figures in this respect seem to be Gottlob König (1776–1849) and Georg von Wedekind (1796–1856), both who earned a reputation as eminent forestry scholars and writers in the first decades of the nineteenth century. 4.1. König's insights and achievements König had no university education but he had laid the foundation of his knowledge of forestry under Cotta at Zillbach, where he studied 8 Recalling Faustmann's invention of the Spiegel-Hypsometer in 1856 (see, Faustmann 1856, Löfgren 2000) and Richards' of the Common Quadrant and Micrometer (Richards 1730, 107–128), it is interesting that also Hossfeld, König and Pressler developed sophisticated trigonometric instruments for tree height measurements. However, Pressler's ‘Measuring jack’ (Messknecht) had also several other functions (see, Pressler 1852, 1870).

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from 1794 to 1796 (Hess 1885, Schwartz 2010), that is, some years before Hossfeld began to give lectures there. During the next few years, König qualified himself, partly by acting as assistant forester – under, among others, competent Karl Oettelt at Ilmenau, in the Thuringian area (Saxe-Gotha-Altenburg) – and partly by taking part in the Prussian arrangements for forest management (Brown 1887, 81–82). In 1802 he returned to Zillbach and became Hossfeld's (who had moved to Dreissigacker) successor as teacher of geometry and forest mathematics. After spending three years as an instructor at Zillbach, König moved to nearby town of Ruhla, also close to the Thuringian Forest. There he acted as a local forest official and began to give tuition on matters of forestry to private students. In 1813, König published his first major work, Holztaxazion, a textbook that was aimed at foresters and most likely based on his lectures at Zillbach and Ruhla forest institutes. In the last section of the book, he treated quite extensively questions related to capital and forest valuation (pp. 232–260). He correctly pointed out that the value of a forest can be divided into two elements: standing timber (Bestandswerth) and bare land (Bodenwerth) (p. 252). The first represents the capitalized value of timber income from the first rotation, and the latter the capitalized value of net income from all the rotations thereafter. Although König did not present any algebraic formulae for determining forest and bare land values, his economic reasoning and numerical calculations were almost in line with those of Hossfeld (1805b) and Faustmann (1849, 1995). The only difference is that König (pp. 257–259) considered regeneration costs only once, in the beginning of the first rotation period, while Faustmann used on a series of regeneration costs and discounted them. König's another merit is that he seems to have been the first who explicitly included income from thinnings as well as annual management costs in calculations of forest land value. A modern translation of König's calculations is presented in Appendix 1. König may have failed to understand the idea of a periodic series of regeneration costs but his treatment of the other recurring items challenges this explanation. One may ponder whether his approach to omit future regeneration costs has something to do with his critical attitude towards clear cuts. According to Hess (1885) and Schwartz (2010), he favored natural regeneration and seeding as well as native tree species and mixed forests. Perhaps reflecting these preferences, in his later works König increasingly emphasized the non-monetary benefits of forests, including their esthetic value and the opportunities for nature protection that they afford. In his most comprehensive treatise, Forstmathematik, König (1842, 133–134) showed further insight by aptly pointing out that also negative land values are possible. The reckoner was not to blame for such a result; instead measures should be taken to lower regeneration costs and to increase discounted returns, for example, by promoting mixed forests and early thinnings. If these and other measures were not effective, the land should be reallocated to agriculture or pasture. In his Forstmathematik König also addressed the critical question of the timing of harvests. He first promoted the use of “value increment percent” (Werthzunahme-Prozent), a measure that utilizes the marginal method but discards the opportunity cost of bare land. This wine aging formula left the door open for Faustmann (1853d, 365–367) to present his critique and Pressler (1860) to produce his celebrated indicator percent (Weiserprozent). However, in later sections of the book König (1842, 476–477) introduced and employed a specific notion, the “net value increment percent” (bodenfreie Werthzunahme-Prozent) which accounted for the capital cost of bare land. Although König did not present any algebraic formulae for this measure, his economic reasoning and numerical calculations demonstrate that he came quite close to providing a solution that corresponds to Pressler's indicator percent (Appendix 2). König's contributions were long overlooked in forestry, even by those scholars that thrived for more rigorous forestry. Heyer (1871, vii) attributes this to the fact that König was considered more a reckoner than a mathematician, his writings were not easy to follow, and he

published at a time when economic formulas and calculations with compound interest received little enthusiasm among forest professionals. However, König's early accomplishment in expounding the principles of efficient forest management should be evaluated against the fact that the classical article by Faustmann (1995) did not contain an explicit solution to the optimal rotation problem, and even Pressler's (1860) landmark paper in which he derived his indicator percent, relied on an incremental analysis similar to the one König used. A curious point is that according to Heyer (1871, vii), Pressler, who was initially trained as an engineer, learned forestry from König's Forstmathematik. Considering König's professional education and long teaching experience at Zillbach, as well as his membership in the fledgling Forest Society, there cannot be any doubt that he was aware of the modern forest economic ideas that had been articulated some years earlier by Hossfeld and Nördlinger. Faustmann, in turn, must have been familiar with all these seminal contributions due to his graduate studies in forestry at the University of Giessen, located in Hesse-Darmstadt. This intellectual link becomes more evident when one examines the career and affiliations of Georg Wilhelm von Wedekind, an active publisher and a close colleague of Faustmann in Darmstadt. 4.2. Wedekind's liasions Von Wedekind received basic education in the Darmstadt area but in 1812 went on to the University of Göttingen. Already in the following year he moved again to study forestry at the Dreissigacker forest institute under its most meritorious lectures Bechstein and Hossfeld. According to Hess (1885), this marked the beginning of his lifelong and devoted friendship with Hossfeld. The next year Wedekind returned to Darmstadt where he acted first as an assessor and later, in 1848, was promoted to privy senior forest councilor. As it happens, it was in the same place, Darmstadt, where young Martin Faustmann passed his qualification for state forestry in 1846 after he had finished his studies at Giessen. This professional engagement proved influential for their further cooperation – more specifically, it marked the beginning of Faustmann's career under Wedekind in Hesse-Darmstadt, both in state forestry and in scientific publishing (Hess 1885, 81). Two matters in Wedekind's background deserve special attention. First, before settling to Darmstadt in 1816, he had traveled extensively in Central Europe, and in 1827 he made trips also to England and France. It seems plausible that during these trips, at the latest, he became aware of the extensive social and economic developments in these countries and of the attempts to develop a more comprehensive resource economic theory, particularly in England. Even more interesting observation is that Wedekind edited Allgemeine Forst- und JagdZeitung (AFJZ) from 1847 until his death in 1856, and that Faustmann assisted him during this professional assignment (Mantel and Pacher 1976, 181–182). In fact, Faustmann served as an associate editor for AFJZ from 1847 to 1855 when he was called as a director of the Babenhausen forest district, situated close to Darmstadt. It was during this particular nine-year period in AFJZ when Faustmann (1849; 1853a,b,c,d; 1854; 1995) produced his most important forest economic papers. They all were published in AFJZ or in Neue Jahrbücher der Forstkunde, also edited by Wedekind. The only exception to this concurrence seems to have been the article in which Faustmann (1865) treated the question how an isolated forest stand should be valued as part of larger forest area under quest of sustainable yield. Faustmann's economic papers contained only few references: most notably Kröncke (1806), Hartig (1813, 1832, 1833), Hundeshagen (1826), and Gehren (1835, 1849). However, there cannot be any doubt that he was able to build much more extensively upon an established tradition of forest economic reasoning. Scholars like Zincke (1755), Moser (1757) and Zanthier (1764) had initiated this line of thinking, but more definite economic insights on opportunity cost of

Please cite this article as: Viitala, E.-J., Faustmann formula before Faustmann in German territorial states, Forest Policy and Economics (2015), http://dx.doi.org/10.1016/j.forpol.2015.11.004

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forest capital and forest valuation had been delivered at the turn of the nineteenth century by Hossfeld, Nördlinger and König in the forestry schools and institutes of the small states of Saxe-Meiningen-Coburg, Saxe-Gotha-Altenburg and Saxe-Weimar-Eisenach, all in today's Thuringia. Some indication of Faustmann's sources of inspiration can be found in his less-known article that dealt with optimal forest rotation. In this elegantly written paper, Faustmann (1853d) criticized König's ‘value increment percent’ (Werthzunahme-Prozent) for not accounting for the opportunity cost of bare land, and showed with elementary marginal analysis and numerical examples how optimal rotation can be derived by maximizing bare land value. It is quite evident that also in this instance he was able to build on the seminal contributions of the prominent scholars in the field, most notably Hossfeld (1805a,b; 1820), Pfeil (1823) and Hundeshagen (1826), who had laid the foundations of modern forest economics in Central Europe. 5. Discussion and conclusions This study has examined the discovery of the Faustmann formula in the German territorial states more thoroughly than previously in the literature. It has shown that in the German forestry tradition the fundamental forest valuation principles in line with the celebrated ‘Faustmann formula’ were discovered 50 years before Faustmann by a competent forest mathematician Johann Hossfeld (1805a,b). In addition to presenting the modern economic principles of capital valuation, he gave explicit rules for forest valuation under variable, in particular increasing and decreasing annual timber income, and most evidently applied differential calculus to derive the forest rotation which maximizes timber production. Hossfeld's predecessors in England, Houghton (1683, 1701) and Richards (1730), presented their remarkable insights at a time when extensive commercial and financial development pushed England towards modern market economy. The early ‘forest economists’ in the German territorial states were probably not familiar with Houghton's and Richards' writings, but they almost certainly were aware of the extensive economic progress in England (and even before in Holland) and of the economic ideas that the French physiocrats had promoted since the 1750s — ideas that inspired Adam Smith (1776) and other classical economists. An outstanding common feature in the English and German development was the personal and intellectual background of those figures that seem to have contributed most to the forest economic thought and discovery of the Faustmann formula. Hossfeld and Nördlinger were autodidacts (Hess 1885), and also Houghton's knowledge on matters of forestry was based on his own initiative and manifold individual activities (Viitala 2013). One may suggest that due to their independent education, diverse interests and professional experience in other fields than forestry, Houghton, Richards, Hossfeld and Nördlinger were especially qualified to critically scrutinize some of the core premises and patterns of contemporary forestry and to understand how the modern economic ideas of capital valuation, opportunity costs and marginal method could be applied in forest management. Another common feature in England and Central Europe seems to have been the major role of intellectual and professional societies that served as organized bodies of knowledge and promoted various fields of natural and applied science. Houghton was an active fellow of the Royal Society of London from 1680 and may have benefited from his interactions with those distinguished fellows and correspondents who were interested in forestry and, more generally, economic aspects of natural resource exploitation. Similarly, the first Forest Society some hundred years later began to enhance communication among leading German forestry scholars and professionals. The society was closely affiliated with the local forestry institute, led and operated by Bechstein and Hossfeld. The close intellectual connection between English and German agriculturists is another issue that deserves attention. The first Agricultural

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Society (situated in Celle, a commercial center of Hanover) established already in the 1790s a working relationship with the recently founded Board of Agriculture, which at the time produced systematic reviews on agriculture and farming operations in different parts of England. It was William Marshall, one of the leading English agriculturalists, who in his review of the Board's report on agriculture and farming operations in northern England, published in 1808, expressed the fundamental idea of the Faustmann condition. It is plausible that also Hossfeld benefited from this type of international contacts and dissemination of knowledge. A particularly interesting observation is that he lectured in the local English business school at Eisenach, Thuringia, from 1791 to 1798 (Hess 1881). The kaufmännische Institute für Engländer was not far from the Electorate of Hanover and its famous University of Göttingen, which in the eighteenth and early nineteenth century functioned as a gateway for the influx of British political, social and economic thinking (Lowood 1991, Biskup 2007). A key institutional factor that promoted the close administrative, intellectual and business connections between Hanover and Great Britain from 1714 to 1837 was the personal union, i.e. the countries were officially ruled by a single monarch (Simms and Riotte 2007). To complete the picture, it is useful to point out that also Johann von Thünen had close connections to the Agricultural Society at Celle. In 1803 he studied there under Albrect Thaer, the leading German agricultural writer of the time, who had close connections to the English scholars in the field. According to Hall (1966, xiv), it was from the lectures given in Celle that Thünen came to realize the importance of mathematics to the theoretical study of agriculture, and under Thaer's influence, interested himself also in agricultural statics and the related concepts of equilibrium and diminishing returns which would be important issues in his Isolated State. These concepts surfaced also in his discussion on optimal forest rotation, first briefly mentioned in 1826 and then treated more extensively in a subsequent volume, published posthumously in 1863. Thünen worked in isolation from contemporary economists (Blaug 1968, 321; 1985). Although he was a keen experimenter and improver of agricultural and forestry practices in his Tellow (Mecklenburg) estate from 1810, he may have not been familiar with William Marshall's (and Watson's and Reventlow's) earlier commitment to marginal approach in forestry. However, at the same time one may ponder whether Thünen could have been unaware of the insights of such prominent contemporary forestry scholars as Hossfeld and König, who several years earlier had demonstrated how marginal analysis can be applied in determining most advantageous forest rotation. This question is of particular interest because Pressler (1859) clearly was aware of Thünen's accomplishments in this field. A lack of modern reference practice in old German scholarly texts makes it difficult to attain definite proof of direct intellectual connections, but future inquiries involving perusal of manuscripts, letters and other archival sources could reveal to what extent the modern ideas of forest and capital valuation, and of applying marginal approach in forestry, diffused from Hossfeld and König to scholars like Thünen, Faustmann and Pressler. Although Hossfeld introduced the modern economic principles of forest valuation in 1805, or even earlier (see Hossfeld 1805a, 154), it took quite a long time until these principles were adequately incorporated into the forestry literature. Many of the able German scholars, who were to act as lead figures in the fledgling discipline of forest science during the following decades, advocated economically unwarranted principles in calculating forest values (see Heyer 1865, 14–24; Schwappach 1888, 818–828). Hartig (1812, 11, 18; 1813, 180), an active writer who in 1811 was appointed head of the Prussian forest administration, used a specification for bare land value which was based on simple interest and covered only single rotation. His argument was that most investors and forest owners needed the yearly or periodic forest income for their subsistence and thus were not able to reinvest it. Another Forstklassiker, Cotta (1804, 152–186), initially recognized the propriety of compound interest calculations, but later turned to favor so-called arithmetic mean interest (arithmetisch-mittleren Zinsen) which was a combination of simple and

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compound interest. His argument was that it was not always possible to immediately invest the attained interest return, and that in some instances compound interest calculations resulted in negative bare land values (Cotta 1818, 46; 1819, iv–v, 128). Another common, yet more general argument was that calculations that involve opportunity cost of forest capital should be confined only to those cases in which a forest has been purchased. Although this line of argumentation, found already in Zincke (1755) and Moser (1757), is essentially unwarranted from modern economic point of view, it has proven quite persistent in forestry during the last plus 250 years. The above type of argumentation places Hossfeld's insights and discoveries in a larger context and brings out their distinct nature in the early modern forest and natural resource economics. The apparent lack to adequately understand the significance of his contribution during the next decades was an important prerequisite for the fact that Faustmann was able to rediscover the same economic principles related to forest valuation and efficient land management some 50 years later. It is essentially due to this merit that Faustmann has been designated as the Founder of Forest Economics and celebrated as the forester who with Pressler produced capital theory that outplayed and were developed earlier than its cousins within the economic discipline (Löfgren 2012). To extend the perspective, the modern economic aspects of forest valuation and optimal timber production did not gain much attention during the next plus hundred years, although some conscious scholars quite consistently advocated this economic rationale (see, e.g. Pressler 1860, Heyer 1865, 1871, Dickson 1953, Gaffney 1957). Forest economic reasoning in line with modern capital and investment theory experienced a marked revival only after Samuelson's (1976) celebrated review article Economics of forestry appeared. The underlying reasons for this ‘big sleep in forest economics’ (cf. Löfgren 2012) are left for future studies, but one may assume that an essential element in this development was the deep-rooted and essentially cameralistic legacy in forestry, which tended to direct prime attention to controlling the balance of timber growth and yield over time by deriving long-term cutting budgets and working plans so that these schemes would meet the perceived needs of one extensive household, the territorial state or ‘national economy’. Similar type of desire to govern economic life and natural resource exploitation for supposed ‘common weal’ can be discerned also in those long-standing controversies in forest management and planning that relate to the role of opportunity cost of forest capital. This integral part of modern economics was in the heart of the forest valuation principles that Johann Wilhelm Hossfeld put forward some 210 years ago in the surroundings of the vast Thuringian Forest — quite appropriately German Holzland, land of wood (Backhaus 2011). For this remarkable accomplishment he deserves credit for being one of the true pioneers of modern forest economic thought. Appendix 1. König's (1813) early contribution to forest land valuation König (1813, 257–259) examined whether it is profitable to convert agricultural land to forestry. He first calculated the value of an acre of land in agriculture and obtained 18.75 fl. (Florin). The result is correct as the annual land rent was one fl., taxes 0.25 fl. and interest rate four percent (0.75 fl. / 0.04 = 18.75 fl.). König then calculated the value of the same piece of land in forestry. His economic reasoning and numerical calculations concerning the determination of land value in forestry (BK) can be expressed in an algebraic form as.

BK ¼

At þ

Xq i¼a

In König's numerical example t = 90, c =3 fl., v =1/3 fl. and δ = 0.04. For the capitalized value of the timber income at the end of the first q

t−i

rotation period At þ ∑i¼a Di ð1 þ δÞ he obtained 580.68 fl. which included income from three thinnings (at the ages of 30, 50 and 70 years). He then correctly calculated the present value of a perpetual periodic series of such timber income as 580.68/(1.0490 − 1) = 17.53 fl. from which value he subtracted the incurred regeneration (pine seeding) costs c (aufgewendete Kulturkosten) and the value of fixed annual management costs v/δ= 8.33 fl. Thus he obtained (17.53− 3 − 8.33)fl . = 6.2 fl. which he denoted ‘forest land value’ (Werth des Holzgrundstükkes). His conclusion (p. 258) was that it is not profitable to convert the piece of land to forestry. More generally, he articulated that the example showed how to calculate bare land values (Bodenwerth) in agriculture and forestry. The similarity of König's approach (A1.1) to Eq. (4), conventionally credited to Faustmann (1995), explains the designation ‘König–Faustmann’ formula in the literature. Appendix 2. König's (1842) ‘net value increment percent’ (bodenfreie Werthzunahme-Prozent). Pressler's indicator percent ρP is usually written as ρP ¼ 100

Iiþ1 −I i Ii þ B f

ðA2:1Þ

where Ii and Ii+1 denote values of i and i+1 year-old forest stands and Bf bare land value. When ρP is less than the market rate of interest δ, it is profitable to cut the forest. König (1842, 476–478) followed similar reasoning but his aim was to find out the ‘value increment percent of standing timber, net of land rent’ (thus the term bodenfreie). He did not present any algebraic form for his ρK but his reasoning implies a formulation Iiþ1 −Ii ¼

ρK Ii þ δB: 100

ðA2:2Þ

For a similar interpretation, see Heyer (1871, 38). Solving for ρK yields ρK ¼ 100

ðIiþ1 −Ii Þ−δB : Ii

ðA2:3Þ

König utilized Eq. (A2.3) in his numerical calculations and obtained that ρK = 4.2 [δ= 0.04, It+1 − Ii = 5w, Ii = 100w, B = 20w]. For comparison, ρP ≈ 4.17. The difference is due to the fact that in König's approach the capital cost δB is fixed whereas in Pressler's specification the corresponding term expresses the rate of return and is thus variable. In commercial forests close to financial maturity ρK ≈ ρP. When ρK/100 = ρP/100= δ, Eq. (A2.2)–(A2.3) collapse to the Faustmann condition. König may also have been the first to recognize the crucial role of thinnings in economic forest management: “Forest harvests [thinnings] decrease timber volumes and enhance timber growth, thus affecting the volume increment percent (Mehrungs-Prozent) from both sides [of the equation] simultaneously. … The active use of thinnings is the primary means to improve the utilization of forest capital and to make longer rotations profitable.” (König 1835, 413). References

t−i

Di ð1 þ δÞ

ð1 þ δÞt −1

 v − cþ ; δ

ðA1:1Þ

where At denotes timber income from the final harvest, Di, i = a,…q timber income from thinnings, t rotation period, c regeneration costs, and v annual costs (see also Heyer 1865).

Anonymous, 1765. Abhandlung von Holztaxen oder Vorschlag zu Holzanschlägen. Allgemeines oeconomisches Forst-Magazin VII 211–214. Anonymous, 1790. Entwicklung der Gründe, um welcher willen es für die Waldeigenthümer höchst nützlich ist, eine Holländerthanne, als ein reifes Forstproduct, so bald es den übringen Umständen nach thunlich ist, zu verwerthen. Forst-Archiv zur Erweiterung der Forst- und Jagd-Wissenschaft und der Forst- und Jagd-Literatur VII, 161–165. Anonymous, 1823. Allgemeine Literatur-Zeitung. Vierter Band. Engänzungsblätter. Num. 119, 951–952.

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Please cite this article as: Viitala, E.-J., Faustmann formula before Faustmann in German territorial states, Forest Policy and Economics (2015), http://dx.doi.org/10.1016/j.forpol.2015.11.004