Conservation in the optimal use of rangelands

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, where conservation is understood to mean maintenance of the system in a 'natural' state. We consider a rangeland that may exist in one of two states. In the 'natural' state, its dynamics are regulated by fire. In the 'managed' state, its dynamics are regulated by grazing pressure by livestock. We show that the optimal use of rangelands may include its maintenance in both states at different points in time, depending on initial conditions and the set of relative prices.