Concorrenza perfetta e accumulazione ottimale in un modello lineare di produzione

The paper extends Samuelson's Ricardo-Marshall specific-factors model (Samuelson, 1971b) by allowing the accumulation of capital. As in the original model, the utility function is quasi-linear, with the linear component attached to "leisure". On the production side, however, we consider the technology to be of a polyhedral type. Although we use a discounted dynamic optimization problem of the Ramsey-type to describe the behaviour of the system, the dynamics of the optimal programs cannot be characterized by means of the standard tools. Indeed, the two above assumptions imply that the model is neither strictly concave nor differentiable. Nevertheless, for the case in which there is a single methods of production, we prove that an optimal path from a given initial condition is unique and has the "turnpike" property. We point out, however, that both the above dynamic properties depend on the assumption that there is no problem of choice of technique and that they do not hold in more general settings.