Classical Turnpike Theory and the
Economics of Forestry: The Discounted Case ∗
M. Ali Khan
†Adriana Piazza
‡August 25, 2009.
Abstract
In recent work [1, 2], the authors frame the (Ramseyian) economics of forestry in the undiscounted setting of upper semicontinuous benefit (felicity) functions that are required to be price-supported at the yields of a golden-rule forest configuration, but not necessarily to be concave. Through a non-interiority condition on the convex hull of the zeroes of a resulting “discrepancy function,” they present a unified theory, one for which robust asymptotic convergence and classical turnpike theorems can be obtained.
These results are of particular interest for the general theory of intertemporal resource allocation in that they pertain to a transitional production set which does not satisfy the assumptions of inactionand free disposal.
In this paper, we trace out the ramifications of this work for the discounted setting, and thereby present a generalized theory that covers the economics of the Mitra-Wan tree farm under one rubric that moves seamlessly between the discounted and undis- counted cases, and thereby gives additional insight into both. We present results that generalize theorems of Mitra-Wan [5] and Salo-Tahvonen [6, 7], and our theorems also have a direct bearing for McKenzie’s “neighborhood turnpike theorem,” as presented
in [3, 4] for the Gale-MacKenzie model. (198 words)
Keywords Forest management, discount factor, optimal programs, value-loss, up- per semicontinuity, discrepancy function, non-interiority, existence, asymptotic conver- gence, neighborhood turnpike theorem
JEL Classification Numbers C62, D90, Q23
∗This work is to be presented at the Workshop on Mathematical Economicsto be held in Tokyo during November 13-15, 2009.
†Department of Economics, The Johns Hopkins University, Baltimore, MD 21218. E-mail[email protected]
‡Centro de Modelamiento Matem´atico, Universidad de Chile. Blanco Encalada 2120, 7 piso. Santiago, Chile. E-mail[email protected]
1
References
[1] Khan M. Ali and Piazza A., 2009. On the Mitra-Wan Forestry Model: A Unified Analysis. Publicaci´on T´ecnica CMM No. 226. Paper presented at Workshop in Economic Dynamics,National University of Singapore, July 30 to August 1, 2009.
[2] Khan M. Ali and Piazza A., 2009. Classical Turnpike Theory and the Economics of Forestry. Paper to be presented at the Department of Economics, University of Sydney, September 2, 2009.
[3] McKenzie, L. W., 1982. Turnpike theory, discounted utility, and the von Neumann facet. Journal of Economic Theory 27, 194-209.
[4] McKenzie, L. W., 1983. A primal route to the turnpike and Lyapunov stability.
Journal of Economic Theory 30, 330-352.
[5] Mitra T. and Wan H. W., 1985. Some theoretical results on the economics of forestry. Review of Economics Studies LII, 263-282.
[6] Salo S. and Tahvonen O., 2002. On equilibrium cycles and normal forests in op- timal harvesting of tree vintages. Journal of Environmental Economics and Man- agement 44, 1-22.
[7] Salo S. and Tahvonen O., 2003. On the economics of forest vintages. Journal of Economics Dynamics and Control 27, 1411-1435.
[8] Samuelson P. A., 1976. Economics of forestry in an evolving society. Economic Inquiry XIV, 466-492.
2
