Sustainable growth under pollution quotas: optimal R&D, investment and replacement policies

We consider an optimal growth model of an economy facing an exogenous pollution quota. In the absence of an international market of pollution permits, the economy has three instruments to reach sustainable growth: R&D to develop cleaner technologies, investment in new clean capital goods, and scrapping of the old dirty capital. The R&D technology depends negatively on a complexity component and positively on investment in this sector at constant elasticity. First, we characterize possible balanced growth paths for different parameterizations of the R&D technology. It is shown that countries with an under-performing R&D sector would need an increasing pollution quota over time to ensure balanced growth while countries with a highly efficient R&D sector would supply part of their assigned pollution permits in an international market without harming their long-term growth. Second, we study transitional dynamics to balanced growth. We prove that regardless of how large the regulation quota is, the transition dynamics leads to the balanced growth with binding quota in a finite time. In particular, we discover two optimal transition regimes: an intensive growth (sustained investment in new capital and R&D with scrapping the oldest capital goods), and an extensive growth (sustained investment in new capital and R&D without scrapping the oldest capital).