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Forest Value and Optimal Rotations in Continuous Cover Forestry

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Abstract

The Faustmann forest rotation model is a celebrated contribution in economics. The model provides a forest value expression and allows a solution to the optimal rotation problem valid for perpetual rotations of even-aged forest stands. However, continuous forest cover forest management systems imply uneven-aged dynamics, and while a number of numerical studies have analysed specific continuous cover forest ecosystems in search of optimal management regimes, no one has tried to capture key dynamics of continuous cover forestry in simple mathematical models. In this paper we develop a simple, but rigorous mathematical model of the continuous cover forest, which strictly focuses on the area use dynamics that such an uneven-aged forest must have in equilibrium. This implies explicitly accounting for area reallocation and for weighting the productivity of each age class by the area occupied. We present results for unrestricted as well as area-restricted versions of the models. We find that land values are unambiguously higher in the continuous cover forest models compared with the even-aged models. Under area restrictions, the optimal rotation age in a continuous cover forest model is unambiguously lower than the corresponding area restricted Faustmann solution, while the result for the area unrestricted model is ambiguous.

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Notes

  1. We use the term “continuous cover”. “Uneven-aged” is also used frequently in the literature—mostly as a direct synonymous.

  2. This only holds under the conditions of no regeneration costs and no price-dependency on tree size. Two simplifying assumptions we maintain in this paper.

  3. Morsing (2001) and as early as Muus (1921) mention the importance of distribution of area utilization between trees and the fact that in uneven-aged management more space can be occupied by larger trees that may have a higher value growth per area and time unit, relative to the Faustmann normal forest case. However, little empirical evidence exist (O’Hara and Nagel 2006) which can attribute the difference solely due to different structures.

  4. Notice that the classic Faustmann model and also our interpretation here are neglecting thinnings—of evenaged trees. In reality these may play a substantial role for the area utilization, and the setup can be expanded to that cover that situation, but at a loss of mathematical tractability in particular in the CCF case.

  5. We do not discuss the issues of competition, crown development and stem growth in more detail here. By ‘adequate’ we mean to imply a development known to result in healthy growth and good stem quality.

  6. As did Faustmann and many others. Alternatives could be size, diameter or value, but as we like Faustmann assume an identical age-size-value relationship for all individual trees—and across the forest types, age is as appropriate as size.

  7. By this assumption we avoid the need for multiple state variable models, and this eases the comparison of the models. We discuss the consequence of this assumption later.

  8. To ease interpretation, we use a slightly different notation from that in Faustmann’s original paper.

  9. In a normal forest an equal area is allocated to all T age classes and therefore T becomes both the number of age classes and the rotation period.

  10. Remember that definite integrals are defined as limits on upper and lower boundaries on integration variables. Thus, in the third term we do not integrate over i \(=\) t but only a time approximately close to i and in (21) i \(=\) t in the third term is captured by the second term. Likewise, we only get approximately close to T at the upper limit of the integral. In this way we avoid double counting because we have a discontinuity in a(t) at T.

  11. A requirement for the Taylor series approximation is continuity of the objective function with respect to a, m and t. This is also a requirement in most other economic models used for optimization (Varian 1992), including the ones earlier in this paper, and it will hold for most functional forms that can be imagined in the current setting.

  12. This function is chosen as the driving factor for both m and a is the biological growth—and limits imposed by competition for resources. For realistic assumptions of price development (e.g. that price increase by dimension, but only until dimensions are too large to handle) this general functional form is not contradicted. Thus, by working with a Gompertz function it is generalized to a relatively flexible form.

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Acknowledgements

We would like to than Colin Price and Finn Helles for constructive commenting on several previous versions of this paper, helping clearing the thoughts and for continuously urging us to finalize it. Furthermore, we would like to thank participants on the Fifth World Congress of Environmental and Resource Economists 2014 and the Biennial meeting of the Scandinavian Society of Forest Economics 2014 for comments on an earlier version of the paper. Jette Bredahl Jacobsen and Bo Jellesmark Thorsen acknowledge support from the Danish National Research Foundation to the Center for Macroecology and Climate.

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Authors and Affiliations

  1. Department of Food and Resource Economics, Faculty of Science, University of Copenhagen, Rolighedsvej 23, DK 1958, Frederiksberg C, Denmark

    Jette Bredahl Jacobsen, Frank Jensen & Bo Jellesmark Thorsen

  2. Centre for Macroecology, Evolution and Climate, Faculty of Science, University of Copenhagen, Rolighedsvej 23, DK 1958, Frederiksberg C, Denmark

    Jette Bredahl Jacobsen & Bo Jellesmark Thorsen

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  1. Jette Bredahl Jacobsen
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Correspondence to Jette Bredahl Jacobsen.

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Jacobsen, J.B., Jensen, F. & Thorsen, B.J. Forest Value and Optimal Rotations in Continuous Cover Forestry. Environ Resource Econ 69, 713–732 (2018). https://doi.org/10.1007/s10640-016-0098-z

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