Efficient and Optimal Capital Accumulation under a Non Renewable Resource Constraint

Usual resource models with capital accumulation focus upon simple one to one process transforming output either into some consumption good or into some capital good. We consider a bisectoral model where the capital good, labor and a non renewable resource are used to produce the consumption good and the capital good. Capital accumulation is an irreversible process and capital is depreciating over time. In this framework we reconsider the usual results of the efficient and optimal growth theory under an exhaustible resource constraint. We show that the usual efficiency condition relates to the investment good production function and not to the consumption good production function as in the canonical model of Dasgupta and Heal. We show then that the standard Hotelling rule relating the growth rate of the consumption good to the growth rate of the marginal productivity of the resource remains valid independently of the multisectoral specification of the model. Last we explore different forms of the Hartwick rule in the context of efficient paths and optimal paths