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Binary-Search SPOC: An Optimal Control Theory Version of ECHO

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Two models for identifying the optimal harvest of old-growth forests--the supply potential optimal control model, SPOC, and the economic harvest optimization model, ECHO--are compared theoretically and numerically. Walker's ECHO restart procedure to solve convergence problems is examined and found to be theoretically sound. The primary difference between the models is that SPOC incorporates the effects of future rotations while ECHO does not. A new algorithm, binary-search SPOC, is identified which incorporates the effects of future rotations by including a difference equation for the shadow value of these rotations. This algorithm is the solution to a discrete time optimal control problem. The numerical analysis of Walker's original problem revealed that the ECHO solution was very close in the early years when the implicit land rental was low and rising, but generated the wrong long-run equilibrium. Forest Sci. 32:576-584.

Keywords: Marginal revenue; volume harvested

Document Type: Journal Article

Affiliations: Senior Fellow and Director, Forest Economics and Policy Program, Resources for the Future, Washington, DC

Publication date: September 1, 1986

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
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