# Economic Theory for the Environment

## Essays in Honour of Karl-Göran Mäler

## New Horizons in Environmental Economics series

## Edited by Bengt Kriström, Partha Dasgupta and Karl-Gustaf Löfgren

# Chapter 16: What if Jevons Had Actually Liked Trees?

## Robert M. Solow

## Extract

Robert M. Solow We usually credit W.S. Jevons with having provided a clear statement and analysis of the problem facing a producer with an intertemporal pointinput–point-output production technology. Suppose a tree is planted (costlessly, for simplicity) at time t. The real net value of its timber (after harvesting costs) is f (a) if the tree is cut down at time t+a, that is, at age a. The producer chooses the a that maximizes e–raf (a), where r is the appropriate discount rate, usually a market interest rate. The obvious necessary condition for an interior maximum at a* is that a* satisfy f ′(a)/f (a) = r. This defines a local maximum if f ″(a) < 0. (We expect an a* to exist because the tree grows very fast when it is young, and f (a) tapers off or turns down when the tree is very old. If 1n f (a) is strictly concave, the maximum is unique.) The intuition is elementary. If f ′(a) > rf (a), the natural growth of the tree is earning a better return than the interest rate on the proceeds from earlier harvesting, so it is better to wait. If there is an initial planting cost c, a* is still the best choice once the cost is sunk. Before that point, the producer would want e–ra*f (a*) > c, or else it would be better to abandon the project altogether. If the land had alternative uses, we would be dealing with a quite different...

## You are not authenticated to view the full text of this chapter or article.

**Elgar**online requires a subscription or purchase to access the full text of books or journals. Please login through your library system or with your personal username and password on the homepage.

Non-subscribers can freely search the site, view abstracts/ extracts and download selected front matter and introductory chapters for personal use.

Your library may not have purchased all subject areas. If you are authenticated and think you should have access to this title, please contact your librarian.