Optimal substitution of renewable and nonrenewable natural resources in production

A theoretical model is presented in order to study the optimal combination of natural resources, used as inputs, taking into account their natural growth ability and the technical possibilities of input substitution. The model enables us to consider renewable resources, nonrenewable, or both. The relative use of resources evolves through time according to the difference between both resources' natural growth and technological flexibility, as measured by the elasticity of substitution of the production function. Output evolves according to a version of the traditional Keynes-Ramsey rule, where the marginal productivity of capital is substituted by the ''marginal productivity of natural capital'', that is a combination of both resources' marginal growth weighted by each resource return in production