Penttinen, Markku. 2000.
Timber harvesting with variable prices, costs and interest rates.

Metsäntutkimuslaitoksen tiedonantoja - Finnish Forest Research Institute, Research Papers 785. 38 p.
[ISBN 951-40-1751-X]
[Price 70 FIM - 11,70 EUR]


1 Introduction
1.1 Competing views in forest economics
1.2 Previous work on deterministic optimal rotation modelling
1.3 The aim of this study
2 Data and Methods
2.1 The optimal rotation problem definition
2.2 Optimal rotation solutions
2.3 Comparative static and sensitivity analyses
3 The numerical solution of the optimal rotation
4 Applications


This papers solves the optimal harvesting time problem of a non-industrial private forest (NIPF) owner who typically has a forest management plan and merchantable forest stands. The optimal harvesting time is defined in a volatile market situation.The infinite period problem is also formulated to allow for variable stumpage prices and reforestation costs in a two-period framework, the first of which covers the near future with dynamic price and cost functions and the second the rest of the infinite future with trend price and cost functions.

The existence and uniqueness of an optimal policy is demonstrated on the basis of the explicit quasi-concavity of the objective functions. First, the solutions are constructed with prices and costs dependent on stand age only. Both cases in which the same prices and costs hold for all periods and cases in which there are dynamic prices and costs in the first period and trend ones in subsequent periods are considered. Second, the age-dependent functions are multiplied separately by the calendar time dependent exponential terms. Solutions are provided both in the case with the same age-dependent functions and the case with dynamic functions for the first period and trend functions for the subsequent periods

The sensitivity and comparative static analyses are studied with respect to the interest rate, price and cost changes, both analytically and numerically. Optimal rotation solutions are presented with alternative competing volume growth functions. Final results are provided by a gross income growth function. Competing optimisation models are discussed, and alternative volume growth models and a value growth model are compared.

The key notion of the research is the sensitivity and comparative static analysis of the optimal rotation solutions with respect to roundwood prices, reforestation costs and interest rates. Different local market parameter and alternative growth data estimates are applied in testing the impact of price, cost and interest rate parameters. The purpose of the study is to provide tools for day-to-day decision-making in the changing world of forestry and also to compare silvicultural recommendations with the solutions.

Many NIPF owners have a tendency to try to sell only during peak price periods. Their behaviour is compared with policy results obtained using empirical data on the turbulent market place with fluctuating prices, growth models and the optimal rotation models developed.

Key words: optimal rotation, variable prices, costs and interest rates, sensitivity analysis, comparative statics, existence and uniqueness of global optimum solutions.

Publisher: Finnish Forest Research Institute
Approved: Kari Mielikäinen, Research Director, 31.8.2000.
Author's address: Markku Penttinen, Finnish Forest Research Institute, Helsinki Research Centre, Unioninkatu 40 A, 00170 Helsinki, Finland. Tel. +358 9 8570 5767, email:
Distribution & Orders: Finnish Forest Research Institute (METLA), Library, P.O. Box 18, FIN-01301 Vantaa, Finland.
Tel. +358 10 211 2201, Email:

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