Faustmann Model Research Articles

Economic Analyses of Rubber and Tea Plantations and Rubber-tea Intercropping in Hainan, China

This study uses land expectation value (LEV) as a criterion to conduct economic analyses of natural rubber (Hevea brasiliensis) and tea (Camellia sinensis var. assamica) monoculture, and rubber-tea intercropping. We calculated LEV by using the Faustmann model that combines annual revenue flow from latex production with final timber harvest of rubber trees. Production and cost data were collected from Xinwei Farm in Hainan, China. We found that rubber-tea intercropping generated higher LEV than rubber and tea monoculture under current socio-economic circumstances. Sensitivity analysis has been conducted to examine the impacts on land expectation value by interest rate, prices of natural rubber and tea, and labor costs.

Optimal Forest Taxation under Private and Social Amenity Valuation

Abstract This article analyzes the socially optimal forest taxation in the rotation framework when the government has a binding tax revenue requirement. In the Faustmann model, the optimal design of taxation consists of nondistortionary taxes, such as site productivity tax, site value tax, or profit tax. A combination of distortionary unit (or yield) tax and timber tax can also be used to collect the tax revenue in a nondistortionary way. In the Hartman model, with forest amenity services as a public good, the optimal design consists of a nondistortionary tax and a Pigouvian tax, which adjusts the private rotation age to the socially optimal one. Now only the site productivity tax is nondistortionary, while unit, yield, timber, site value, and profit taxes generally serve as corrective Pigouvian taxes. Finally, in the absence of a nondistortionary tax, if the marginal valuation of amenity services is nondecreasing with the age of forest stand, a combination of unit (or yield) and timber taxes can be used for both tax revenue collection and Pigouvian correction. FOR. SCI.49(4):596–607.

Application of real options theory to forestry investment analysis

Abstract This paper demonstrates the utility of the real options approach to forestry investment analysis. The main objectives are to discuss the real option theory and show how it can be adopted to model uncertainty and managerial flexibility in forest management and investment. Secondly, we show how to calculate the option values of selected options that may be available to managers of forest industry firms. The paper provides an empirical application, which compares a forestry investment using the static Faustmann model and the real options approach. Four management options are used for the real options approach: an option to delay reforestation, an option to expand the size of the wood processing plant, an option to abandon the processing plant if timber prices fall below a certain level or due to corporate take-over, and multiple options that evaluated all three options together. All options were evaluated using the binomial option-pricing model, where timber values are assumed to follow a multiplicative binomial process. The results show that the Faustmann analysis rejected the investments as unprofitable, while the option analysis showed that all three options were highly valuable if exercised. When real options are considered, the traditional Faustmann model for assessing the profitability of a forestry investment may fail to provide an adequate decision-making framework because it does not properly value management's ability to adjust to shocks in the economy, as well as risks and uncertainty.

Forest Taxation and Rotation Age under Private Amenity Valuation: New Results

This paper studies the impact of harvesting, property, and profit taxes on private rotation age in an ongoing rotations model, where the private landowner is interested not only in the present value of harvest revenue, but also in the private amenity services provided by the forest stand. The main finding of the paper is that conventional wisdom about the rotation effects of forest taxes, distilled from the Faustmann model, predominantly ceases to hold. This is because forest taxes distort the relative profitability of timber and amenity production in a way that is sensitive to the precise nature of amenity valuation. Therefore, the design of forest tax policy necessitates good knowledge of the landowner's objective function concerning the type of amenity services.

Tropical Deforestation, Tenure Insecurity, and Unsustainability

Abstract This article explores the effects of tenure insecurity on the migrant's decision to convert tropical frontier forestland to unsustainable agriculture. We develop and extend a Faustmann model to explore the effects of insecure property rights and unsustainability on the migrant's decision to convert tropical forestland to crop production, to maintain it for long-term timber production, or to mine the forest for timber and then abandon the land. We then provide a numerical simulation of the migrant's land-use decision based on data from the Amazon to compare the returns to mahogany plantation as opposed to agricultural conversion or timber mining. Increasing insecurity of land tenure leads to a decline in the value of timber relative to agricultural production land, thus creating an incentive for forest conversion. However, when land is easily degraded and tenure insecurity is high, timber mining and land abandonment may be a particular problem. Finally, we examine the role of private and government investment in establishing and maintaining secure land tenure. Once government “arrives” at the frontier, it can encourage sustainable timber production through providing secure harvesting rights and setting an optimal concession fee. FOR. SCI. 47(4):497–509.

Optimal forest rotation and land values under a borrowing constraint

This study relaxes the assumption of perfect capital markets in the classical Faustmann forest rotation model. A constraint on borrowing changes all the basic properties of optimal forest harvesting. Instead of a constant rotation period, an infinite chain of rotations is determined by a nonlinear difference equation. The rotation period evolves over time and approaches a stationary rotation in finite or infinite time. The length of optimal rotation, timber supply and the value of forest land depend on forest-owner-specific factors that are normally nonexistent in rotation problems. The model explains several empirical findings that cause problems for the classical versions of the Faustmann model.

Increasing rotation periods during a time of decreasing profitability of forestry — a paradox?

The profitability of forestry in Germany decreased during recent decades because of more or less constant prices for forest products, increasing input prices and limited success in rationalisation. However, the volume of growing stock increased significantly during this period since forest enterprises have chosen longer rotation periods. This is especially true for state owned and community owned forests but also at least partly for private forests. It is normally not an alternative for the owners of forest enterprises in Germany to sell the forests completely, but on a first glance increasing investments in standing timber during a time of decreasing profitability of forestry seems to be inconsistent with economic theory. On the one hand this observation could be explained as the result of non-timber values. However, this paper is focused on another approach, which is an expanded Faustmann model in line with soil rent theory and focused on timber production. Profitable rotations in the future have the effect of shortening the optimal rotation period because an investment in standing timber causes opportunity costs by delaying the establishment of the next generation of the forest. Unprofitable future rotations have the opposite effect, if the landowner is forced to reforest. In case investments in reforestations are not profitable decision-makers have good reasons not to cut the mature stands, in spite of the fact that the internal rates of return of investments in standing timber are low in comparison with investments on the financial market. Empirical data for the period 1954–1998 mostly from guidelines for forest valuation are used together with inflation corrected interest rates to show that optimal rotation length increased over time. Nevertheless we have to recognise that the observed rotation periods are distinctly longer than the calculated optimal rotation lengths. Other factors which may also explain the investments in forestry are discussed later.

Optimal Forest Taxation Under Private and Social Amenity Valuation

This article analyzes the socially optimal forest taxation in the rotation framework when the government has a binding tax revenue requirement. In the Faustmann model, the optimal design of taxation consists of nondistortionary taxes, such as site productivity tax, site value tax, or profit tax. A combination of distortionary unit (or yield) tax and timber tax can also be used to collect the tax revenue in a nondistortionary way. In the Hartman model, with forest amenity services as a public good, the optimal design consists of a nondistortionarytax and a Pigouvian tax, which adjusts the private rotation age to the socially optimal one. Now only the site productivity tax is nondistortionary, while unit, yield, timber, site value, and profittaxes generally serve as corrective Pigouvian taxes. Finally, in the absence of a nondistortionary tax, if the marginal valuation of amenity services is nondecreasing with the age of forest stand, a combination of unit (or yield) and timber taxes can be used for both tax revenue collection and Pigouvian correction.

Duality and Faustmann: Implications for the Evaluation of Landowner Behavior

Abstract This paper examines the behavioral consequences when landowners seek to minimize costs rather than maximize profits. We derive a cost function that is dual to the net present value function in the Faustmann Model. This cost function provides a theoretical foundation for studies that estimate forest production costs. We use comparative statics methodology to derive qualitative results for changes in selected policies and exogenous parameters. We find that the qualitative impacts under cost minimization are usually unambiguous. Qualitative impacts under profit maximization are usually ambiguous. This implies that behavioral impacts are usually easier to assess a priori, when landowners minimize costs rather than maximize profits. For. Sci. 46(1):132-138.

A generalized Faustmann model for the determination of optimal harvest age

This paper presents a generalization of the classic Faustmann formula for land expectation value. The generalized Faustmann formula allows the harvest age to vary from timber crop to timber crop by letting the stumpage price, timber yield, regeneration cost, and interest rate vary from timber crop to timber crop. The generalized Faustmann formula is then shown to be a dynamic programming problem that could theoretically be solved by the forward recursive solution method. To solve the problem analytically, the first-order condition for reaching the optimal harvest age is derived. The derivation yields a compact and tidy result similar to that derived from the classic Faustmann formula. This analytical result also provides a simple solution for obtaining the optimal harvest age of any particular timber crop. In addition to presenting two empirical examples, one of a southern pine pulpwood plantation for short harvest age and one of a Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) sawtimber stand for long harvest age, the paper also examines analytically the impact of changes in both the current and future stumpage price, regeneration cost, and interest rate on the optimal harvest age. The impacts are then contrasted with those obtained under the classic Faustmann formula. The paper concludes by pointing out that it would be a rewarding endeavor to examine many topics in the timber management literature under the generalized Faustmann formula.

A generalized Faustmann model for the determination of optimal harvest age

A generalized Faustmann model for the determination of optimal harvest age

Long-Run Timber Supply and the Economics of Timber Production

Abstract The analysis of long-run timber supply is hampered by the lack of a well-defined profit function. Such a function provides the foundation for deriving a theoretically consistent supply equation. Some recent studies have attempted to obtain a timber supply equation by manipulating the stand-level Faustmann model. As a result of inappropriate approaches and assumptions, their conclusions may be false. In this article, we build on the Faustmann-Smith-Samuelson model first developed by Comolli (1981) to examine aggregate timber production. We show this model to have the desired properties of a profit function that allows us to test various issues. It is then found that the general beliefs of negatively sloped per-land-unit supply curves and positively sloped aggregate supply curve are robust. Finally, we present several applications and implications of our modeling approach. For. Sci 43(1):113-120.

An investigation of the harvest decision of timber firms in the south-east United States

In the forestry literature, stochastic extensions of the classic Faustmann model have become the predominant models of optimal harvesting on even-aged timber stands. A recent attempt to estimate a stochastic version of the Faustmann model left several puzzling results unexplained (Provencher, 1995). This paper reports on new estimation and analyses undertaken to resolve these puzzles. Of particular note is the result that the value of using correct price forecasts in the harvest decision is much lower than indicated by recent simulation studies, perhaps because variability in convenience yield dampens the expected gain from exploiting stochastic variation in timber prices.

Optimal Timber Rotations with Evolving Prices And Costs Revisited

Abstract In this paper, we extend previous work that modeled the impact of evolving prices and costs to evaluate the full range of rotation length and input changes resulting from changing prices and costs. Our model suggests that if prices and costs change at the same rate, then production derisions are invariant. Any specific proportionate rate of change in prices and costs acts as an adjustment factor on the discount rate which corresponds to a constant rotation length. We also find that in the normal range of changes, namely, rates of any change less than the discount rate, the following results hold: if prices rise faster than costs, then the rotation length becomes shorter and establishment inputs increase; on the other hand, if costs rise faster than prices, then the optimal harvest age becomes longer and stand establishment inputs are reduced. These results not only extend and generalize those derived by McConnell et al. and Newman et al., but also further demonstrate the robustness of the Faustmann model. For. Sci. 41(3):477-490.

Faustmann model aplicability to forest protection

Managerial theory; basic support for forest management economy, is also applicable to the rational allocation of scarce inputs in forest protection programs. Forest protection economy is more complex because there is no marketable products, provided forest protection aims to avoid catastrophic events and to reduce damages caused by pests, diseases and other destructive agents. To quantify avoided damages is an elusive goal, but necessary in order to justify protection budgets. We propose the use of economic concepts of actuarial theory on insurance against disaster from the point of view of economic rationality. Using this idea, we try to demonstrate that forest protection decisions can be made from the concept of integrated management of forest resources.

Mathematical Bioeconomics: The Optimal Management of Renewable Resources.

Introduction. 1. Elementary Dynamics of Exploited Populations. 1.1 The Logistic Growth Model. 1.2 Generalized Logistic Models: Depensation. 1.3 Summary and Critique. 2. Economic Models of Renewable-Resource Harvesting. 2.1 The Open-Access Fishery. 2.2 Economic Overfishing. 2.3 Biological Overfishing. 2.4 Optimal Fishery Management. 2.5 The Optimal Harvest Policy. 2.6 Examples Based on the Schaefer Model. 2.7 Linear Variational Problems. 2.8 The Possibility of Extinction. 2.9 Summary and Critique. 3. Capital-Theoretic Aspects of Resource Management. 3.1 Interest and Discount Rates. 3.2 Capital Theory and Renewable Resources. 3.3 Nonautonomous Models. 3.4 Applications to Policy Problems: Labor Mobility in the Fishery. 4. Optimal Control Theory. 4.1 One-Dimensional Control Problems. 4.2 A Nonlinear Fishery Model. 4.3 Economic Interpretation of the Maximum Principle. 4.4 Multidimensional Optimal Control Problem. 4.5 Optimal Investment in Renewable-Resource Harvesting. 5. Supply and Demand: Nonlinear Models. 5.1 The Elementary Theory of Supply and Demand. 5.2 Supply and Demand in Fisheries. 5.3 Nonlinear Cost Effects: Pulse Fishing. 5.4 Game-Theoretic Models. 5.5 Transboundary Fishery Resources: A Further Application of the Theory. 5.6 Summary and Critique. 6. Dynamical Systems. 6.1 Basic Theory. 6.2 Dynamical Systems in the Plane: Linear Theory. 6.3 Isoclines. 6.4 Nonlinear Plane-Autonomous Systems. 6.5 Limit Cycles. 6.6 Gause's Model of Interspecific Competition. 7. Discrete-Time and Metered Models. 7.1 A General Metered Stock-Recruitment Model. 7.2 The Beverton-Holt Stock-Recruitment Model. 7.3 Depensation Models. 7.4 Overcompensation. 7.5 A Simple Cohort Model. 7.6 The Production Function of a Fishery. 7.7 Optimal Harvest Policies. 7.8 The Discrete Maximum Principle. 7.9 Dynamic Programming. 8. The Theory of Resource Regulation. 8.1 A Behavioral Model. 8.2 Optimization Analysis. 8.3 Limited Entry. 8.4 Taxes and Allocated Transferable Quotas. 8.5 Total Catch Quotas. 8.6 Summary and Critique. 9. Growth and Aging. 9.1 Forestry Management: The Faustmann Model. 9.2 The Beverton-Holt Fisheries Model. 9.3 Dynamic Optimization in the Beverton-Holt Model. 9.4 The Case of Bounded F. 9.5 Multiple, Cohorts: Nonselective Gear. 9.6 Pulse Fishing. 9.7 Multiple Cohorts: Selective Gear. 9.8 Regulation. 9.9 Summary and Critique. 10. Multispecies Models. 10.1 Differential Productivity. 10.2 Harvesting Competing Populations. 10.3 Selective Harvesting. 10.4 A Diffusion Model: The Inshore-Offshore Fishery. 10.5 Summary and Critique. 11. Stochastic Resource Models. 11.1 Stochastic Dynamic Programming. 11.2 A Stochastic Forest Rotation Model. 11.3 Uncertainty and Learning. 11.4 Searching for Fish. 11.5 Summary and Critique. Supplementary Reading. References. Index.

Option Pricing and Timberland's Land-Use Conversion Option: Comment

In a recent issue of this journal, Zinkhan (1991) suggests using a Black-Scholes (1973) approach to computing the value of the land-use conversion option when valuing timberlands. The value of the conversion option is the value of being able to convert from timber to some other land use such as agriculture or real estate development if such an opportunity becomes desirable at some future date.1 In the Faustmann model this conversion option is ignored; thus, Faustmann values provide a lower bound for timber stand values. While retaining the Black-Scholes framework, an alternative approach is suggested here for valuing the timberland conversion option. The approach presented here is a simpler and logically consistent model. This paper also expands the enquiry to show the optimal expiration date for the option.

Optimal timber harvest scheduling under harvest volume constraints: a comparison of two opportunity cost criteria

A simple model is developed to determine the economically optimal combination of stands to harvest in a period when there are periodic maximum harvest volume constraints. The model is formulated using concepts developed in the Faustmann optimum forest rotation model. The objective function minimizes the net opportunity cost of delayed harvest. For each stand in the forest, the model is used to determine if the stand should be harvested this period or if the harvest decision should be deferred to the next period. In the typical exposition of the Faustmann model, the opportunity costs of delayed harvest are expressed per unit area. Because of this, and the spatial orientation of forest management, it is tempting to use costs per hectare to set harvest priority. However, when harvests are constrained by some maximum harvest volume, costs per unit volume are the appropriate criterion to use. The purpose of this paper is to demonstrate the economic losses resulting from the use of the inappropriate priority criterion. The model is applied to a study area in Saskatchewan. As well as demonstrating the economic losses, the study shows that a much wider variety of species associations and site classes are scheduled for harvest when the volume-based ranking criterion is used. This mix of harvested species and sites is consistent with the observed behaviour of firms. It has been argued elsewhere that this behaviour is due largely to government-imposed behaviour (e.g., operating ground rules) or to the spatial considerations of forest management. We suggest here that at least some of this behaviour can be attributed to optimal response to harvest volume constraints.

The Long-Run Timber Supply Function

Abstract The long-run equivalent annual timber supply functions resulting from two increasingly complicated versions of the Faustmann model were derived and examined. In both cases, the expression for the equivalent annual quantity of timber supplied was identical. A second main result was the mathematical proof that the slope of the long-run timber supply curve is positive along its entire length when establishment costs are fixed and variable. Some calculations were made using a well-established yield function for jack pine in Ontario, and these supported the theoretical conclusions. In contrast, the use of V*/t* as the equivalent annual output incorporates the implicit assumption that the discount rate is zero. For. Sci. 36(1):77-86.

Timber Harvesting with Fluctuating Prices

Abstract Because of volatility in demand, timber prices tend to fluctuate from year to year. Timber owners know today's price but are uncertain about tomorrow's prices. Traditional Faustmann harvesting ignores these random annual price fluctuations and prescribes harvests on the basis of expected prices. In this paper, we adapt an asset sale model to forestry and solve for the optimal schedule of reservation prices. When current price is above the reservation price, owners should cut that age class, otherwise they should wait another year. This flexible price harvest policy significantly increases the present value of expected returns over the more rigid Faustmann model. For. Sci. 34(2):359-372.