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# Economic Theory for the Environment

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

Karl-Göran Mäler’s work has been a mainstay of the frontiers of environmental economics for more than three decades. This outstanding book, in his honour, assembles some of the best minds in the economics profession to confront and resolve many of the problems affecting the husbandry of our national environments.

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

## Robert M. Solow

Subjects: economics and finance, environmental economics, environment, environmental economics

## 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...