There are actually two very different phases in Romer’s work on endogenous growth theory. Romer (1986) and Romer (1987) had an AK model. Real output was equal to A times K, where A is a positive constant and K is the amount of physical capital. The model assumes diminishing marginal returns to K, but assumes also that part of a firm’s investment in capital results in the production of new technology or human capital that, because it is non-rival and non-excludable, generates spillovers (positive externalities) for all firms. Because this technology is embodied in physical capital, as the capital stock (K) grows, there are constant returns to a broader measure of capital that includes the new technology. Modeling growth this way allowed Romer to keep the assumption of perfect competition, so beloved by economists.
In Romer (1990), Romer rejected his own earlier model. Instead, he assumed that firms are monopolistically competitive. That is, industries are competitive, but many firms within a given industry have market power. Monopolistically competitive firms develop technology that they can exclude others from using. The technology is non-rival; that is, one firm’s use of the technology doesn’t prevent other firms from using it. Because they can exploit their market power by innovating, they have an incentive to innovate. It made sense, therefore, to think carefully about how to structure such incentives.
These two paragraphs are from my biography of Paul Romer in The Concise Encyclopedia of Economics. It is now on-line.
Read the whole thing.