Environment and sustainable growth in a two-sector model with variable population growth rate

We investigate a closed economy in which the production depends essentially on physical capital, natural capital and labor. Contrary to the standard literature, we assume that the labor growth rate is non constant but variable over time. We show that the economy is sustainable in the long run if human activities have a net zero or positive effect on the environment. Moreover, for any given tax rate (or MPC, i.e. marginal propensity to consume), we derive the set of sustainable MPCs (or tax rates).