Science in the Third Dimension of R&D

We study a Schumpeterian model of long-run growth with endogenous fertility and with three interacting dimensions of innovation. Scientific research is the fundamental dimension of innovation that creates new technological knowledge. This is allocated over new working prototypes in the horizontal dimension. New firms finance scientific research by obtaining the property rights of new working prototypes, and existing firms invest in developing the blueprint mode of working prototypes into the more productive modes of production in the vertical dimension. Balanced growth in the standards of living is fully endogenous without scale effects, and a new parameter, i.e., the elasticity of scientific knowledge with respect to existing collective scientific knowledge, nonlinearly accelerates long-run growth. With exogenous population growth, the model generates a semi-endogenous result due to the endogenously determined bound on technological opportunity.