On the Mitra-Wan forestry model: A unified analysis

We present a substantive and far-reaching generalization of the principal results in the economics of forestry, as formalized by Mitra and Wan (1986). Rather than a polarized dichotomy of linear and strictly concave, differentiable benefit (felicity) functions, we develop the theory in the context of functions that are supported at the golden-rule consumption and are not necessarily concave. Through a non-interiority condition on the set of zeroes of a resulting “discrepancy function,” we show the equivalence of finitely-maximal, maximal, minimal value-loss and optimal programs, and thereby answer questions left open by Brock and Mitra. Our synthesizing criterion is new to the capital theory literature, and in the concave setting, proves to be necessary and sufficient for the asymptotic convergence of good programs.  2011 Elsevier Inc. All rights reserved. JEL classification: C62; D90; Q23 ! This work was initiated during Piazza’s visit to Johns Hopkins in May 2008 and completed during her visit to the University of Illinois at Urbana-Champaign in April–May, 2009. In addition to the hospitality of Nicholas Yannelis and that of the Economics Department at Illinois, the authors gratefully acknowledge invaluable discussion and correspondence with Don Brown, Tom Cosimano, Luciano de Castro, Alex Himonas, Tapan Mitra and TN Srinivasan. Previous versions of the paper were presented at the Fourth Workshop in Macroeconomic Dynamics held at the National University of Singapore, July 31 to August 1, 2009, and at the Economic Growth Center, Yale University, December 14, 2009. This final version was completed when Khan was visiting Meisei University, Tokyo, January 3–10, 2010, and has benefitted from detailed suggestions of the Editor of JET. Adriana Piazza gratefully acknowledges financial support from Fondecyt under project # 29110254, Programa Basal PFB 03, CMM, U. de Chile and CONICYT grant ACT-88. * Corresponding author at: Department of Economics, The Johns Hopkins University, Baltimore, MD 21218, United States. E-mail addresses: [email protected] (M. Ali Khan), [email protected] (A. Piazza). 0022-0531/$ – see front matter  2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jet.2011.11.010 M. Ali Khan, A. Piazza / Journal of Economic Theory 147 (2012) 230–260 231