Intellectual property rights protection in the presence of exhaustible resources

We construct a research and development (R&D) based endogenous growth model with exhaustible resources and investigate whether protection of intellectual property rights (IPR) can sustain perpetual growth. We show that relatively weak IPR protection is sufficient to sustain perpetual growth when goods production is more resource-intensive, whereas relatively strong IPR protection is needed for perpetual growth if production is less resource-intensive. If the resource intensity in goods production is medium, even the strictest IPR protection cannot sustain perpetual growth when the quality improvements brought about by innovations are small enough. In this case, we find that R&D subsidies can complement IPR protection in sustaining perpetual growth. We derive the socially optimal level of IPR protection, which is increasing in the resource intensity of goods production. Furthermore, we also consider a case where resource is essential for R&D activities and show a knife-edge condition for perpetual growth.