Nota di Lavoro, Fondazione Eni Enrico Mattei 111.2003
In previous papers we have considered the optimal mix of biodiversity in semi-arid rangelands, focusing on the steady state. This paper addresses the question of conservation in the optimal use of rangelands. That is, it considers the optimal trajectory of biodiversity change. There are two issues involved in the question of timing. One is the uncertainty associated with the fact that many changes in the flora and fauna of rangelands are 'event-driven'. They depend on stochastic parameters taking particular values before a change of state can occur. A second issue relates to the lag structure of changes. In a system that involves a mix of fast and slow variables, in which the approach to the optimum is not 'most rapid', the optimal trajectory may require the system to remain in an apparently stable intermediate equilibrium for some time before it converges to the optimum state. The paper discusses the role of conservation in the optimal use of rangeland resources.