Optimal harvesting of forest age classes: A survey of some recent results

Mathematical Population Studies

Volumn 11, Issue 3-4, 2004, Pages 205-232

  Tahvonen, Olli ^a  

^a FINNISH FOREST RESEARCH INSTITUTE   (Finland)

Author keywords

Age classes; Normal forest; Optimal forest rotation; Vintage capital models

Indexed keywords

AGE CLASS; FORESTRY PRACTICE; HARVESTING; NUMERICAL MODEL; OPTIMIZATION;

EID: 33746285420     PISSN: 08898480     EISSN: 1547724X     Source Type: Journal    
DOI: 10.1080/08898480490513616     Document Type: Article

References (58)

1. Adams, D.M., Alig, R.J., McCarl, B.A., Callaway, J.M., and Winnett, S.M. (1996). An analysis of the impacts of public timber harvest policies on the private forest management in the United States. Forest Science 42, 343-358.
2. Andersen, E.D. and Ye, Y. (1999). On a homogeneous algorithm for the monotone complementary problem. Mathematical Programming 84, 375-99.
3. Benhabib, J. and Rustichini, A. (1991). Vintage capital and growth. Journal of Economic Theory 55, 323-339.
4. Berck, P. (1976). Natural Resources in a Competitive Economy. MIT, Ph.D. dissertation.
5. Binkley, C.S. (1987). Economic models of timber supply. In The Global Forest Sector, an Analytical Perspective, M. Kallio, D. Dykstra and C.S. Binkley (eds.). N.Y.: John Wiley & Sons, 109-136.
6. Boucekkine, R., Germain, M., and Licandro, O. (1997). Replacement echoes in the vintage capital growth model. Journal of Economic Theory 74, 333-348.
7. Boucekkine, R., Germain, M., Licandro, O., and Magus, A. (2001). Numerical solution by iterative methods of a class of vintage capital models. Journal of Economic Dynamics and Control 25, 655-669.
8. Bowes, M. and Krutilla, J. (1985). Multiple use management of public forestlands. In Handbook on Natural Resource and Energy Economics. A. Kneese and J. Sweeney (eds.), New York: Elsevier: Vol. II, pp. 531-569.
9. Bowes, M. and Krutilla, J. (1989). Multiple Use Management: The Economics of Public Forestlands. Washington, D.C.: Resources for the Future Press.
10. Brock, W.A. and Malliaris, A.G. (1989). Differential Equations, Stability and Chaos in Dynamic Economics. North-Holland: Amsterdam.
11. Cannon, M.D., Cullum, C.D., and Polak, E. (1970). Theory of Optimal Control and Mathematical Programming. New York: McGraw-Hill.
12. Caswell, H. (2001). Matrix Population Models, Construction, Analysis, and Interpretation. Sunderland, MA: Sinauer, Associates Inc.
13. Chow, G.C. (1990). Dynamic Economics: Optimization by the Lagrange Method. New York: Oxford University Press.
14. Clark, W.C. (1990). Mathematical Bioeconomics: The Optimal Management of Renewable Resources. 2nd edition. New York: John Wiley & Sons.
15. Faustmann, M. (1849). Berechnung des Wertes welchen Waldboden sovie noch nicht haubare Holzbestände für die Waldwirtschaft besitzen. Allgemeine Forst- und Jagd-Zeitung 15, 441-455.
16. Davis, L. and Johnson, K. (2001). Forest Management. 4th edition. New York: McGraw-Hill Book Company, 1987.
17. Garcia, O. (2001). Functional differential equations in sustainable forest harvesting. Journal of Forest Planning 6, 49-63.
18. Getz, W.M. and Haight, R.G. (1989). Population Harvesting: Demographic Models for Fish, Forest and Animal Resources. New Jersey: Princeton University Press.
19. Hale, C.M., Pastor, J., and Rusterholz, K.A. (1999). Comparison of structural and compositional characteristics in old-growth, and mature, managed hardwood forests of Minnesota, U.S.A. Canadian Journal of Forest Resources 29, 1479-1489.
20. Heaps, T. (1982). The optimal harvesting of a regional forest. Unpublished manuscript.
21. Heaps, T. (1984). The forestry maximum principle. Journal of Economic Dynamics and Control 7, 131-151.
22. Heaps, T. (1995). Multiple use values and optimal steady state age distributions. Natural Resource Modeling 9(4), 329-339.
23. Johnson, K.N. and Scheurman, H.L. (1977). Techniques for prescribing optimal timber harvest and investment under different objectives-discussion and synthesis. Forest Science 23, 1-31.
24. Kemp, M. and Moore, E. (1979). Biological capital theory: A question and conjecture. Economic Letters 4, 141-44.
25. Leuschner, W.A. (1990). Forest Regulation, Harvest Scheduling, and Planning Techniques. New York: John Wiley & Sons.
26. Levhari, D. and Liviatan, N. (1972). On stability in the saddle point sense. Journal of Economic Theory 4, 88-93.
27. Ludwig, D. (1993). Forest management strategies that account for short-term and long term consequences. Canadian Journal of Forest Research 23, 563-572.
28. Lyon, K.S. and Sedjo, R.A. (1983). An optimal control theory model to estimate the regional long run timber supply. Forest Science 29, 798-812.
29. Lyon, K.S. and Sedjo, R.A. (1986). Binary search SPOC: An optimal control theory version of ECHO. Forest Science 32, 576-812.
30. McKenzie, L., (1983). Turnpike theory, discounted utility, and the von Neumann facet. Journal of Economic Theory 30, 330-352.
31. Mitra, T., Ray, D., and Roy, R. (1991). The economics of orchards: An exercise in point-input, flow output capital theory. Journal of Economic Theory 53, 12-50.
32. Mitra, T. and Wan, H.Y. (1985). Some theoretical results on the economics of forestry. Review of Economic Studies LII, 263-282.
33. Mitra, T. and Wan, H.Y. (1986). On the Faustmann solution to the forest management problem. Journal of Economic Theory 40, 229-249.
34. Montgomery, C. and Adams, D.M. (1995). Optimal timber management policies. In The Handbook of Environmental Economics, D. Bromley (ed.). Oxford: Blackwell Publishers.
35. Pressler, M.R. (1860). Aus der Holzzuwachlehre. Allgemaine Forst- und Jagdzeitung 36, 173-91.
36. Reed, W.J. (1986). Optimal harvesting models in forest management - a survey. Natural Resource Modelling 1, 55-79.
37. Salo, S. and Tahvonen, O. (2001). Optimal evolution of forest age classes and land allocation between forestry and agriculture, Helsinki School of Economics and Business Administration, Working Papers W-286.
38. Salo, S. and Tahvonen, O. (2002a). On equilibrium cycles and normal forests in optimal harvesting of tree vintages. Journal of Environmental Economics and Management 44, 1-22.
39. Salo, S. and Tahvonen, O. (2002b). On the Optimality of a Normal Forest with Multiple Land Classes. Forest Science 48, 530-542.
40. Salo, S. and Tahvonen, O. (2003). On the economics of forest vintages. Journal of Economic Dynamics and Control 27, 1411-1435.
41. Solo, S. and Tahvonen, O. (2004). Renewable resources with endogenous age classes and allocation of land. American Journal of Agricultural Economics 86, 513-530.
42. Samuelson, P. (1976). Economics of forestry in an evolving society. Economic Inquiry 14, 466-492.
43. Sahashi, Y. (2002a). Optimal forestry control with variable land area. Journal of Economic Dynamics and Control 26, 755-796.
44. Sahashi, Y. (2002b). The convergence of optimal forestry control. Journal of Mathematical Economics 37, 179-214.
45. Sedjo, R.A. and Lyon, K.S. (1990). The Long-term Adequacy of World Timber Supply, Washington, DC: Resources for the Future.
46. Siitonen, J. (2001). Forest management, coarse woody depris and saproxylic organisms: Fennoscandian boreal forests an example. Ecological Bulletins 49, 11-41.
47. Stokey, N.L. and Lucas, R.E. (1989). Recursive Methods in Economic Dynamics. Harvard University Press, Cambridge, Massachusetts.
48. Tahvonen, O. (2004). Timber production vs. old growth conservation with endogenous prices and forest age classes. Canadian Journal of Forest Research, in print.
49. Tahvonen, O. and Salo, S. (1999). Optimal forest rotation with in Situ preferences. Journal of Environmental Economics and Management 37, 106-128.
50. Tahvonen, O. and Salo, S. (2000). On Faustmann rotation and normal forest convergence, Helsinki School of Economics and Business Administration, Working Paper W-243.
51. Tahvonen, O. and Salo, S. (2004). Optimal development of forest age classes in continuous time and discrete space, manuscript, Finnish Forest Research Institute, Helsinki.
52. Tahvonen, O., Salo, S., and Kuuluvainen, J. (2001). Optimal forest rotation and land values under a borrowing constraint. Journal of Economics Dynamics and Control 251, 1595-1627.
53. Walker, J.L. (1972). An economic model for optimizing the rate of timber harvesting, University Microfilms, A Xerox Company, Ann Arbor, Michigan.
54. Wan, F.Y.M. (1985). Ordered site access and optimal forest rotation. Studies in Applied Mathematics 73, 155-175.
55. Wan, Y.H. (1989a). Durable assets and replacement cycles, Cornell University, Working Paper #419.
56. Wan, Y.H. (1989b). Optimal evolution of tree-age distributions for a tree farm. In Mathematical Approaches to Ecological Problems and Environment, C.C. Chavez (ed.). Springer-Verlag.
57. Wan, Y.H. (1983). A note on boundary optimal paths. In General Equilibrium, Growth and Trade II: The legacy of Lionel McKenzie, R. Becker et al. (eds.). New York: Academic Press.
58. Wan, Y.H. (1994). Revisiting the Mitra-Wan tree farm. International Economic Review 35, 193-198.