Continuing with recent posts on models with multiple equilibria, this is by Luis C. Corchón (link is to a draft)
A Malthus-Swan Model of Economic Growth, by Luis C. Corchón Departmento de Economía Universidad Carlos III de Madrid Calle Madrid, Journal of Dynamics and Games, July 2016: [Open link to working paper]: Abstract. In this paper we introduce in the Solow-Swan growth model a labor supply based on Malthusian ideas. We show that this model may yield several steady states and that an increase in total factor productivity might decrease the capital-labor ratio in a stable equilibrium.
“Why has it taken economists so long to learn that demography influences growth?” Jeff Williamson (1998)
1. Introduction. In this note we propose a model which combines the classical Solow (1956) and Swan (1956) model with ideas about population growth that are borrowed from Malthus (1798). We will refer to our model as a Malthus- Swan-Solow (MSS) model. Our model has no technical progress, no institutional change, no human capital and no land.
We assume that the rate of growth of population depends on the real wage in a continuous way. This function is a generalization of one used by Hansen and Prescott (2002).
We find that, as in the classical Solow-Swan model, there exist a steady state value of capital-labor ratio, see Proposition 1. However this steady state is not necessarily unique: Proposition 2 and Example 3 show that there might be an odd number of steady state capital-labor ratios. And only the smaller and the larger values of these capital-labor ratio are locally stable, see Proposition 4. This implies that there might be two, very different values of per capita income in the steady state: one with a small and another with a large value of per capita income. Finally we find that an increase in total factor productivity may increase or decrease the capital-labor ratio in a stable steady state (Proposition 5) but it always increases per capita income (Proposition 6).
Summing up, the consideration of endogenous population in the Solow-Swan model brings new insights with respect to the standard model regarding the number, stability and comparative static properties of steady states. ...