In this paper we present an inter-temporal optimization problem of a representative

R&D firm that simultaneously invests in horizontal and vertical innovations.

We posit that learning-by-doing makes the process of quality improvements a positive

function of the number of existing technologies with the function displaying a

convex-concave form. We show that multiple steady-states can arise with two being

saddle point stable and one unstable with complex conjugate eigenvalues. Thus, a

threshold with respect to the variety of technologies exists that separates the two

basins of attractions. From an economic point of view, this implies that a lock-in

effect can occur such that it is optimal for the firm to produce only few technologies

at a low quality when the initial number of technologies falls short of the threshold.

Hence, history matters as concerns the state of development implying that past investments

and innovations determine whether the firm produces a large or a small

variety of high- or low-quality technologies, respectively.