Quality of knowledge technology, returns to production technology, and economic development

We incorporate a production technology that exhibits increasing returns to scale for small values of the capital stock and diminishing returns for the higher stocks at the firm level in a discrete-time version of Romer's endogenous growth model. We study the social planner's problem where the social production technology exhibits globally increasing returns to scale. The properties of the optimal paths are characterized. It is proved that for a given quality of knowledge technology, the countries can take off if their initial stock of capital is above a critical value. We analyze the effect of three factors on the critical value: initial knowledge, quality of knowledge technology, and level of fixed costs associated with production.