Journal of Forest Economics > Vol 29 > Issue 2

Optimal rotation with negative discount rates: completing the picture

Colin Price,
Suggested Citation
Colin Price (2017), "Optimal rotation with negative discount rates: completing the picture", Journal of Forest Economics: Vol. 29: No. 2, pp 87-93.

Publication Date: 0/12/2017
© 0 2017 Colin Price
optimal rotationnegative discount ratesland expectation valueterminal valueforest rent


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In this article:
What a negative discount rate is, and is not 
Can it be done? 
Doing it by time reversal 
Armageddon at an unknown far future time 
Stochastic Armageddon 
Complications and consonances 
Normal service is resumed, in due course 


While the rotation of maximum forest rent (no discounting of revenues and costs) is sometimes discussed conceptually and calculated practically, forest economists have almost invariably focused on optimal rotation with a positive discount rate. Some circumstances, especially related to increasing marginal utility with decreasing availability per head of products, would justify use of a negative discount rate. For a logically complete suite of conditions, a means of identifying optimal rotation with such a rate is needed. Applying the usual formulation for land expectation value then produces a meaningless result. Two approaches seem to give a solution. One uses the first-order conditions for an optimum. Another uses inversion of time perspective to produce sensible-seeming results. However, for cases where the world, or the value of forest production, ends suddenly at an unpredictable time, the optimal rotation is, surprisingly, that of maximum forest rent. Where the cause of negative discount rates is of limited duration before stability or growing affluence is re-established, this “provisional optimum” can be modified responsively.