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The model of endogenous fertility by Barro and Becker (1989) is augmented by taking into account the heterogeneity of households in terms of capital endowments, mortality, and costs per surviving child. There exists a unique balanced growth path where the population growth rates of all dynasties are equal. An increase in mortality raises the time cost per surviving child, and enhances economic growth, while reducing parity and demographic growth. The mechanism rests on the quantity-quality trade-off of having children, summarized by the adjustment of the average rearing cost of a surviving child.

In his seminal contribution, Tirole (1985) shows that an overlapping generations economy may monotonically converge to a steady state with a positive rational bubble, characterized by the dynamically efficient golden rule. The issue we address is whether this monotonic convergence to an efficient long run equilibrium may fail, while the economy experiences persistent endogenous fluctuations around the golden rule. Our explanation leads on the features of the credit market. We consider a simple overlapping generations model with three assets: money, capital and an asset paper, which behaves as a bubble. Collaterals matter because increasing the amount of capital and asset paper in the portfolio, the household reduces the share of consumption paid in cash. From a positive point of view, we show that the bubbly steady state can be locally indeterminate under arbitrarily small credit market imperfections and, thereby, persistent expectation-driven fluctuations of equilibria with (rational) bubbles can arise. From a normative point of view, monetary policies that are not too expansive are recommended in order to rule out the occurrence of sunspot fluctuations and enhance the welfare evaluated at the steady state.

In this paper, we address the stability issue, stressing the role of labor supply, in a Ramsey model with heterogeneous households subject to borrowing constraints. Making labor supply endogenous leads us to prove the existence of two kinds of steady state: the one where everybody supplies labor, the other where only the most patient agent refrains from working. Going beyond models with inelastic labor supply, we show how preferences of impatient agents affect the saddle-path stability of each type of steady state and the occurrence of endogenous cycles. When their elasticity of intertemporal substitution in consumption exceeds one, instability and cycles are less likely, requiring lower degrees of capital-labor substitution. Conversely, elasticity values below one promote the emergence of fluctuations. We end the paper by showing the existence of the intertemporal equilibrium under market incompleteness, using a local approach based on the first-order conditions.