In this paper we analyze an inter-temporal optimization problem of a representative firm that invests in horizontal and vertical innovations and that faces a constraint with respect to total R&D spending. We find that there can exist two different steady-states of the economy when the amount of research spending falls short of an endogenously determined threshold: one with higher productivities and less new technologies being developed, and the other with more technoligies being created and lower productivities. But, for a higher amount of R&D spending the steady-state becomes unique and the firm produces the whole spectrum of available technologies. Thus, a lock-in effect may arise that, however, can be overcome by raising R&D spending sufficiently.
multiple steady-states lock-in innovations R&D constraint optimal control