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Economic Theory for the Environment

Essays in Honour of Karl-Göran Mäler

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.
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Chapter 12: Hotelling (1925) on Depreciation

Bengt Kriström


Bengt Kriström* 1 ON DEPRECIATION According to Arrow’s (1987) review of Harold Hotelling’s contribution to economics, six of Hotelling’s ten economics papers became landmarks in the economics literature. Arrow (1987, p. 670) gives Hotelling’s (1925) pathbreaking paper on depreciation the following acclaim, Here, apparently for the first time, he stated the now generally accepted definition of depreciation as the decrease in the discounted value of future returns. This paper was a turning-point both in capital theory proper and in the reorientation of accounting towards more economically meaningful magnitudes. In this note, which is an exploration into the history of thought, rather than an attempt to provide new results, I show how an application of Hotelling’s ideas on depreciation provides several interesting results within a dynamic model. I follow Roos (1928), who gave the calculus of variation version of Hotelling’s original idea. The Hotelling result on depreciation is applied to the neoclassical investment model, models of exhaustible and renewable resources, as well as to a current controversy in resource accounting regarding how to value net changes in stocks. This note begins in Section 2 by presenting a model due to Heal (1998). I then provide a study of various special cases as illustrations of the general result in Section 3. The so-called El Serafy model (1999) for depreciation is discussed and its link to Hotelling’s theory explored in Section 4. A final section concludes. 2 A MODEL Let the vector ct∈ᑨm be a vector of flows of goods consumed...

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