# Impact of stochastic price and growth processes on optimal rotation age

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## Abstract

This paper analyses timber harvesting in the Finnish economic and wood production environment. Empirical evidence including stumpage prices, silvicultural costs, etc., since 1949 covers all non-industrial private forestry. Stumpage price and volume growth processes are proxied by GBMs. Optimal harvesting age solutions and numerical results recognising price drift, price and growth volatility, volume growth, value growth and stand establishment costs, as well as thinning benefits, are provided for Scots pine. Moreover, comparative static and sensitivity solutions, including numerical results, show the impact of the discount rate, price drift, and price and growth volatilities on optimal harvesting age. Price volatility prolonged harvesting age by some 5–9 years, and growth volatility by about 1–2, but negative price drift for discount rates from 5 to 2% fell by roughly 6–10 years. Ignoring the future thinning benefits prolonged the harvesting age only by 1–2 years, but ignoring future stand establishment costs reduced it by 2–4 years. Including the price drift and volatility violated the 70 year age limit in the Forest Act for discount rates exceeding 3.5%. The recommended harvesting age of 80 years could be established only by ignoring the price drift. In all, this study produces solutions and programs that can be incorporated into a forest management planning software product widely used in Finland (Hynynen et al. in For Ecol Manage 207(1–2):5–18, 2005).

## Keywords

Stumpage price drift and volatility Volume growth volatility Variable value growth and stand establishment cost Optimal rotation age Pressler’s indicating percentage## Notes

### Acknowledgements

The author thanks the two anonymous referees and the editor for providing many helpful comments and constructive criticism, and Dr. Roderick McConchie for revising the English.

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