This paper is
concerned with the classic topic of intertemporal resource economics: the
optimal harvesting of renewable natural resources over time by one and several
resource extractors with conflicting interests. The traditional management
model, dating back to Plourde , is overlooked both
in the simple case for which the resource stock is treated as a state variable
and in the improved case for which the harvesting equipment is treated as a
stock variable. As a result in the extended case, the equilibrium richer than
the saddle point, with bifurcations and limit cycles, is possible. While the
results of the enriched management case are consistent with the concept of the
pulse fishing, as this concept is introduced by Clark -, in the conflicting case the conditions, under
which the richer limit cycle equilibrium occurs, are not enough investigated.
Therefore, we discuss conflicts as a game with two types of players involved:
the traditional fishermen armed with the basic equipment and the heavy
equipment users. Both players have a common depletion function, considered as
harvesting, which is dependent together on personal effort and on intensity of
 Plourde, C.G. (1970) A Simple Model of Replenishable Natural Resource Exploitation. American Economic Review, 62, 518-521.
 Clark, C. (1973) Profit Maximization and the Extinction of Animal Species. Journal of Political Economy, 81, 950-961. http://dx.doi.org/10.1086/260090
 Clark, C.W. and Munro, G.R. (1975) Economics of Fishing and Modern Capital Theory: A Simplified Approach. Journal of Environmental Economics and Management, 2, 92-106. http://dx.doi.org/10.1016/0095-0696(75)90002-9
 Clark, C. (1990) Mathematical Bioeconomics. 2nd Edition, Wiley Interscience, Hoboken.
 Strobele, W. (1988) The Optimal Intertemporal Decision in Industrial Production and Harvesting a Renewable Natural Resource. Journal of Economics, 48, 375-388. http://dx.doi.org/10.1007/BF01227543
 Hannesson, R. (1983) A Note on Socially Optimum versus Monopolistic Exploitation of a Renewable Resource. Journal of Economics, 43, 63-70. http://dx.doi.org/10.1007/BF01283884
 Strobele, W. and Wacker, H. (1995) The Economics of Harvesting Predator-Prey Systems. Journal of Economic, 61, 65-81. http://dx.doi.org/10.1007/BF01231484
 Farmer, K. (2000) Intergenerational Natural Capital Equality in an Overlapping Generations Model with Logistic Regeneration. Journal of Economics, 72, 129-152. http://dx.doi.org/10.1007/BF01676980
 Gordon, H.S. (1954) The Economic Theory of a Common Property Resource. Journal of Political Economics, 62, 124-142. http://dx.doi.org/10.1086/257497
 Scott, A. (1955) Natural Resources: The Economics of Conservation. University of Toronto Press, Toronto.
 Smith, V.L. (1969) On Models of Commercial Fishing. Journal Political Economy, 77, 181-198.
 Levhari, D. and Withagen, C. (1992) Optimal Management of the Growth Potential of Renewable Resources. Journal of Economics, 3, 297-309. http://dx.doi.org/10.1007/BF01237184
 Bjrndal, T. (1987) Production Economics and Optimal Stock Size in a North Atlantic Fishery. Scandinavian Journal of Economics, 89, 145-164. http://dx.doi.org/10.2307/3440061
 Plourde, C.G. (1971) Exploitation of Common Property Replenishable Resources. Western Economic Journal, 9, 256-266.
 Liski, M., Kort, P. and Novak, A. (2001) Increasing Returns and Cycles in Fishing. Resource and Energy Economics, 23, 241-258. http://dx.doi.org/10.1016/S0928-7655(01)00038-0
 Wirl, F. (1995) The Cyclical Exploitation of Renewable Resource Stock May Be Optimal. Journal of Environmental Economics and Management, 29, 252-261. http://dx.doi.org/10.1006/jeem.1995.1045
 Lewis, T. and Schmalensee, R. (1979) Non-Convexity and Optimal Harvesting Strategies for Renewable Resources. Canadian Journal of Economics, 12, 677-691. http://dx.doi.org/10.2307/134873
 Dawid, H. and Kopel, M. (1997) On the Economically Optimal Exploitation of a Renewable Resource: The Case of a Convex Environment and a Convex Return Function. Journal of Economic Theory, 76, 272-297.
 Dockner, E., Jorgensen, S., Long, N.V. and Sorger, G. (2000) Differential Games in Economics and Management Science. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511805127
 Dockner, E. and Feichtinger F. (1991) On the Optimality of Limit Cycles in Dynamic Economic Systems. Journal of Economics, 53, 31-50. http://dx.doi.org/10.1007/BF01227014
 Dockner, E. (1985) Local Stability Analysis in Optimal Control Problems with Two State Variables. In: Feichtinger, G., Ed., Optimal Control Theory and Economic Analysis, 2, North Holland, Amsterdam, 89-113.
 Kuznetsov, Y. (1997) Elements of Applied Bifurcation Theory. Springer, Berlin.
 Grass, D., Caulkins, J., Feichtinger, G., Trangler, G. and Behrens, D. (2008) Optimal Control of Nonlinear Processes. Springer, Berlin. http://dx.doi.org/10.1007/978-3-540-77647-5
 Wirl, F. (1997) Stability and Limit Cycles in One-Dimensional Dynamic Optimizations of Competitive Agents with a Market Externality. Journal of Evolutionary Economics, 7, 73-89. http://dx.doi.org/10.1007/s001910050035
 Schafer, M. (1994) Exploitation of Natural Resources and Pollution. Some Differential Game Models. Annals of Operations Research, 54, 237-262. http://dx.doi.org/10.1007/BF02031736