Economies of scale and the optimality of rotational dynamics in forestry

Forest harvesting is traditionally analyzed in terms of the Faustmann rotation model. This paper considers the identification of optimal forest harvest regimes using jump controls. This approach enables the structural assumptions of clear-cut technology and identical cycles in perpetuity which are imposed in a Faustmann model to be relaxed. Jump control models permit investigation of the biological and economic conditions which favour continuous growth management regimes as opposed to clear-cut harvest regimes. A numerical solution approach to the jump control model is presented. The link between the harvest cost function and the optimal biomass path is analyzed. Economies of scale are shown to generate rotational harvest as optimal policies.      

Forest management: Are double or mixed rotations preferable to clear cutting?

We study a particular uneven-aged forest stand management pattern, variations of which are often advocated in practice to mitigate the adverse effects of clear cutting. The forest stand under consideration is similar to a Faustmann stand, with the following difference: rather than being single aged, the forest tract contains trees of two age classes so that it is submitted to a form of selective cutting. Each harvest involves all of the older trees and only a fraction of the younger ones; hence the name mixed rotation. Trees left standing at harvest help stimulate natural regeneration and improve various environmental and amenity characteristics of the forest. We model this effect by using a cost function that varies with respect to the harvest rate of younger trees. We derive the properties that this cost function must exhibit in order some form of mixed rotation to be superior to the conventional single rotation à la Faustmann; we also characterize the mixed rotation in terms of duration and the harvest rate of younger trees, and we compare its properties with Faustmann’s rule.     

On the faustmann solution to the forest management problem

This paper is concerned with optimal solutions to the forest management problem when future utilities are undiscounted. By examining asymptotic properties of such solutions, we find that (i) if the utility function is linear, then the Faustmann periodic solution is optimal; (ii) if the utility function is increasing and strictly concave, an optimal solution converges to the maximum sustained yield solution, which we characterize as a golden rule. These results may be viewed as a possible resolution to the debate in forestry economics about what constitutes an optimal policy in forest management.     

Implicit Valuation of Non-Market Benefits in Even-Aged Forest Management

Choosing the optimal harvesting time in multiple-use, even-aged forest management is an important but difficult problem. The usual formulation of the problem requires explicit knowledge of the value of the timber, plus the value of the other, non-timber and mainly non-market values. The latter are notoriously difficult to measure. This paper develops a harvesting rule that depends only implicitly on the flow of non-market values. The rule, dubbed the implicit value formula, gives the minimum stream of non-market values that would induce a landowner to adopt a given rotation length. Since harvesting decisions must be made with or without information on non-market values, the implicit value formula can provide guidance to forest managers by putting a lower bound on the non-market values for every rotation length. As a demonstration, implicit non-market values are calculated for Douglas fir. The implicit value formula indicates that preserving a forest of Douglas fir beyond the optimal rotation is much more expensive than harvesting it an equivalent length of time before the optimal rotation.     

Radiative forcing and the optimal rotation age

Forests help mitigate climate change by sequestering atmospheric carbon. However, boreal and high-latitude temperate forests may also contribute to global warming due to the albedo effect. The relative effects of carbon sequestration and albedo can be quantified in terms of radiative forcing. We present a stylized, stand-level analysis to determine the optimal rotation age when considering a tax/subsidy scheme based on radiative forcing and the notion of equivalent carbon emissions. Additional management decision variables considered include species choice and regeneration effort, since these can impact the albedo effect. We demonstrate analytically that the optimal rotation length is likely shortened when albedo-related equivalent emissions are incorporated, relative to a policy based only on carbon. Empirical results indicate that rotation ages do decrease relative to a “carbon only” policy, and approach the traditional (timber only) Faustmann rotation age as equivalent emission rates increase. Our results suggest that forestation does not necessarily provide climatic benefits in all circumstances, and that, at the margin, other opportunities for carbon reduction (e.g. abatement), or pursuing forestation in other locations, become more attractive.     

Multiple Species Boreal Forests – What Faustmann Missed

Recent research in natural sciences shows that the dynamics in boreal forests are much more complex than what many models traditionally used in forestry economics reflect. This essay analyzes some challenges of accounting for such complexity. It shows that the optimal harvesting strategy for forest owners is history dependent and for some states of the forest, more than one strategy may be optimal.This paper confirms earlier literature on shallow lakes and coral reefs and shows that this kind of phenomena seem much more common than previously thought. They are valid for a wide range of ecosystems that cover large surfaces and they do not depend on the choice of some specific function to model the non-linearity. There are also indications that theses results could be obtained even for resources with concave growth if at least one species with non-linear growth affects their dynamics.     

Wood Fuel or Carbon Sink? Aspects of Forestry in the Climate Question

This paper discusses and contrasts two mainroles of forestry in light of the debate on theglobal climate. As the main problem is relatedto the increases of the CO₂-concentrationin the atmosphere, forests may be viewed aspart of the alleviation of the problem throughtheir function as (i) a source of biomass forenergy production, which may replace fossilfuels and thus indirectly reduceCO₂-emissions, and as (ii) carbon storage,since a growing forest extracts atmosphericCO₂ and fixes it as carbon in biomass. Inthe Scandinavian forestry, logging residues areincreasingly being used for energy production.In this paper the value of forests as a sourceof bioenergy is added to the traditional timbervalue. Formulated as a joint production modelwithin the Faustmann framework, the effect ofthis addition on the optimal rotation length isdiscussed. Based on data for spruce, thedominant species in the Scandinavian forestry,it is demonstrated that the rotation length isshortened compared to the standard Faustmannmodel. Shorter rotation length implies lesscarbon storage. Therefore, in this modelwithout explicit regard to the social carbonstorage value of the forest, the gains in termsof the climate problem from utilisation offorest biomass for energy production are beingdiminished by the value of reduced carbonstorage. The carbon value of the forest is thenadded to complete the model, with the effect ofincreasing the rotation length, a result thatis well known in the literature. Finally, theempirical effects of the interaction of thesetwo climate-related value elements of theforest are discussed.     

Forest management under fire risk when forest carbon sequestration has value

We develop a multiple forest use model to determine the optimal harvest date for a forest stand producing both timber and carbon benefits under a risk of fire. An empirical application is provided for a forest owner producing maritime pine in Southwest of France. Our results indicate that a higher risk of fire will decrease the optimal rotation period. On the contrary, higher carbon prices increase the optimal harvesting age. To investigate the contradictory effects of fire risk and carbon price on forest rotation, we identify the set of carbon prices and fire risks that lead to a given rotation age. We also show that forest owner's willingness to pay for a risk reduction can be substantial (37.33 euros by ha and by year to reduce the annual fire risk from 1.26% to 0.07%).     

Harvest Decisions and Spatial Landscape Attributes: The Case of Galician Communal Forests

In recent years, forest management has moved towards a landscape approach reflecting a mix of social, environmental and economic values. In this paper, we evaluate the effect on harvesting decisions of the spatial attributes of communal forests in Galicia. We first model the forest landscape management problem within a bioeconomic framework, which allows the identification of optimal clear-cutting strategies. This framework makes it possible to model a Faustmann-type rotation at the landscape level. The empirical analysis uses data from communal forests in Galicia, Spain. Under communal ownership, members of a rural community have rights to forest resources, but not rights to the forest itself. The management of communal forests integrates multiple forest uses within the decision making process. Given the communal nature of forest rights, and given these multiple uses, we show that landscape patterns—fragmentation, diversity and clumpiness—determine rotation periods.     

Optimal Harvesting of an Age-Structured Schooling Fishery

Biologists have criticized traditional biomass models in fishery economics for being oversimplified. Biological stock assessment models are more sophisticated with regard to biological content, but rarely account for economic objectives. This study includes a full age-structured population model for studying schooling fisheries and extends the delayed difference approach used in earlier studies. We take the total harvest as the choice variable, resulting in a simple analytical structure. The model produces optimal steady states that may be higher or lower compared to the delayed-difference formulation. The model is applied to the Baltic sprat fishery. Both ecological and harvesting cost data support specifying Baltic sprat as a schooling fishery. Given nonlinear harvesting costs, the optimal solution is a path toward a steady state with smooth annual harvest and population age structure. Sensitivity analysis shows that the optimal solution is highly dependent on the population level of the sprat’s main predator Baltic cod. A linear cost function and an interest rate below 9 % imply pulse fishing instead of smooth continuous harvesting. Given nonlinear harvesting cost, the optimal steady state yield is rather insensitive to changes in the interest rate. However, under a high cod scenario, interest rates of 10 % or higher implies that no optimal steady state exists.     

The impact of recycling on the long‐run forestry

Abstract Interest in recycling of forest products has grown in recent years, one of the goals being to conserve trees or possibly increase their number to compensate for positive externalities generated by the forest and neglected by the market. This paper explores the issue as to whether recycling is an appropriate measure to attain such a goal. We do this by considering the problem of the private owner of an area of land, who, acting as a price taker, decides how to allocate his land over time between forestry and some other use, and at what age to harvest the forest area chosen. Once the forest is cut, he makes a new land allocation decision and replants. He does so indefinitely, in a Faustmann‐like framework. The wood from the harvest is transformed into a final product that is partly recycled into a substitute for the virgin wood, so that past output affects the current price. We show that in such a context, increasing the rate of recycling will result in less area being devoted to forestry. It will also have the effect of increasing the harvest age of the forest, as long as the planting cost is positive. The net effect on the flow of virgin wood being harvested to supply the market will as a result be ambiguous. An important point, however, is that recycling will result in fewer trees in the long run, not more. It would therefore be best to resort to other means if the goal is to conserve the area devoted to forestry.     

Optimal time paths with age-dependence: a theory of population policy

A mathematical model is established whereby optimal accumulation paths of population and the economy can be figured when the basic feature of population dynamics, age dependence, is taken into account. This model series links 2 previously separate disciplines and literatures - i.e., formal policy dealing with the dynamics of age and time. An integral-equation control theory is utilized. Recognition of age structure in analyzing fertility trends is important at both macro- and microeconomic levels. The present model was constructed by embedding an age-disaggregated population in a simple economic growth model where the fertility level and rate of savings can both be influenced by government policy. Such policy should balance the lifetime value of births and capital against the social costs necessary to create them. One the problem has been defined and a dynamic theory developed, optimum static theories can be establihsed where the variables are held constant over time.     

Willingness to pay for forest amenities: The case of non-industrial owners in the south central United States

We analyze the willingness to pay for non-timber values (NTV) by non-industrial private forest (NIPF) landowners of uneven-age mixed species forest stands in the south central United States. The preferences of NIPF owners are revealed by the way they manage their timber. Many NIPF owners maintain a more diverse and natural stand structure than that of a more profitable even-aged industrial plantation. In so doing, the average NIPF owner was willing to forego 60% of the timber profit for the NTV of their more natural stands compared to a less diverse industrially managed even-aged plantation.     

Discriminating Among Alternative Theories of the Multinational Enterprise

Recent theoretical developments have incorporated endogenous multinational firms into the general–equilibrium model of trade. One simple taxonomy separates the theory into "vertical" models, in which firms geographically separate activities by stages of production, and "horizontal" models, in which multiplant firms duplicate roughly the same activities in many countries. The authors nest a horizontal and a vertical model within a hybrid (unrestricted) "knowledge–capital model" and estimate the specifications with data on US foreign direct investment activity. In the nested econometric tests, the data sample cannot distinguish statistically between the unrestricted model and the restricted horizontal model, indicating that the latter captures virtually all of the determinants of FDI. The tests overwhelmingly reject the vertical model.     

Computation of non-linear continuous optimal growth models: experiments with optimal control algorithms and computer programs

In this paper we discuss the use of optimal control methods for computing non-linear continuous optimal growth models. We have discussed various recently developed algorithms for computing optimal control, involving step-function approximations, Runge–Kutta solutions of differential equations, and we suggest that the discretization approach is preferable to methods which solve first-order optimality conditions. We have surveyed some powerful computer programs by : , and for computing such models numerically. These programs have no substantial optimal growth modelling applications yet, although they have numerous engineering and scientific applications. A computer program named by is developed in this study. Results are reported for computing the Kendrick–Taylor optimal growth model using and programs based on the discretization approach. References are made to the computational experiments with and . The results are used to compare and evaluate mathematical and economic properties, and computing criteria. While several computer packages are available for optimal control problems, they are not always suitable for particular classes of control problems, including some economic growth models. The -based and , however, offer good opportunities for computing continuous optimal growth models. It is argued in this paper, that optimal growth modellers may find that these recently developed algorithms and computer programs are relatively preferable for a large variety of optimal growth modelling studies.     

Management strategies for tropical rain forests: Results of ecological models and requirements for ecological-economic modelling

In this study, we use two ecological forest models, namely FORMIX3 and FORREG, to analyse the impact of logging on tropical rain forests and to discuss needs for and problems of an economic extension of these models. The FORMIX3 model simulates spatial-temporal dynamics of tropical forests using an individual and process based approach. The main processes included are growth, mortality, competition, and regeneration of trees. The FORREG model simulates wood growth of tropical forests at landscape scale based on differential equations. Regeneration capabilities of logged forests are analysed and compared for different logging strategies. While conventional management strategies with a short logging cycle (here 20 years) produce low yields and cause severe changes in tree species composition, a reduced impact logging strategy with a longer cycle (here 60 years) leads to relatively high yields and causes moderate changes in species composition. Thus, longer logging cycles are preferable from an ecological point of view. However, also economic aspects influence logging decisions, thus a closer analysis of additional economic aspects of forest management is inevitable. We discuss which economic shortcomings of present rain forest models should be dealt with in the future and which additional data is needed as a consequence.     

OPTIMAL TAXATION ON MIXED DIAMOND GOODS: IMPLICATIONS FOR PRIVATE CAR OWNERSHIP IN CHINA

Abstract. The ‘diamond effect’ exists when a consumer's utility depends on the exchange value, not just on the intrinsic consumption effects of the good. Yew‐Kwang Ng has discussed the optimal tax on a pure ‘diamond’ good. This paper extends Ng's model to cover mixed diamond goods. It uses three mathematical models to show that the optimal tax on a mixed diamond good with both intrinsic and diamond effects depends on the proportion of the diamond effect. The result may explain the violation of the Ramsey Rule in practice, and may be used to formulate private car taxes in China.     

Managing exotic pests under uncertainty: optimal control actions and bioeconomic investigations

Using a real options framework in continuous time, we examine two problems associated with the management of exotic pests under uncertainty. First, we analyze the optimal timing of investing in a control action. Given fixed control costs, we obtain a closed-form solution for when to control an exotic pest whose density varies randomly. Second, we define an analytical framework for finding the optimal expenditures for obtaining the relevant bioeconomic data. Our numerical results, based on a wide range of bioeconomic parameters, highlight the importance of accounting for uncertainty and irreversibility when developing simple rules to manage exotic pests.     

Another reconciliation between economists and forestry experts: OLG-arguments

Foresters often claim that the goal of good forest policy is to have a sustained forest yield, or even a maximum sustainable yield. They also claim that people wish to save a few extra trees for their children. This bequest motive is not modelled in the standard approach to the optimal rotation problem. In this paper, we present a standard version of an overlapping generation model augmented with a simple tree technology. We show in particular that the market equilibrium can be dynamically inefficient, and that a bequest motive in terms of trees can correct for the overaccumulation of capital that causes the inefficiency. The bequest motive also enables us to account for a harvesting intensity varying with age (young people typically cut more than elderly people) in spite of a perfect capital market.The crux of the argument is that a bequest motive is likely to increase the equilibrium interest rate and move the economy away from a maximum sustainable yield policy. It, however, improves efficiency and is able to explain empirical regularities that are not easily explained by a traditional perfect capital market approach to forestry.The author acknowledges comments from Karl-Göran Mäler, Stockholm School of Economics, participants in the economics-forestry economics seminar at the University of Umeå, and two anonymous referees.