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Increasing Returns and Increasing Rates of Growth

Romer (1986b) documented that industrial economies have tended to have growth rates that increase over time. Having explained why the aggregate growth models of Ramsey (1928), Cass (1965), and Koopmans (1965) fail to account for this observation, Romer proposed an alternative view of long-run prospects for growth. Combining three elements-externalities, increasing returns in the production of output, and decreasing returns in the production of new knowledge-he constructed an equilibrium model of growth. In his infinite-horizon, continuous-time analysis, qualitative conclusions were reached using the geometry of the phase plane. No examples with an explicit dynamic solution were given. The present paper provides a fully worked out example that fills this gap and that can serve as a confirmation of Romer's claim that monotonically increasing growth rates for the capital stock and for consumption can arise in the framework he specified. This paper also presents an example that can generate increasing growth rates without imposing some of the restrictions essential to Romer's model. Those restrictions are not appealing on economic grounds and were added to his paper purely for technical reasons. Any infinite-horizon model with increasing returns to scale must impose some restrictions to ensure the existence of both a social optimum and a competitive equilibrium.' Otherwise, the discounted sum of utility could go to infinity. Romer (1986b) used a production function of the form f(k, K) = AkVKW, with v + y > 1, where k is the capital stock at the level of the firm and K is aggregate capital. The