TITLE:
Dynamic Modeling of the Harvesting Function: The Conflicting Case
AUTHORS:
George Emm Halkos, George J. Papageorgiou
KEYWORDS:
Renewable Resources, Exploitation of Natural Resources, Optimal Control, Differential Games
JOURNAL NAME:
Modern Economy,
Vol.5 No.7,
June
25,
2014
ABSTRACT:
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 [1], 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 [2]-[4], 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
equipment’s usage.