Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model

We study a stochastic, discrete-time, two-sector optimal growth model in which the production of the homogeneous consumption good uses a Cobb-Douglas technology, combining physical capital and an endogenously determined share of human capital. Education is intensive in human capital as in Lucas (1988), but the marginal returns of the share of human capital employed in education are decreasing, as suggested by Rebelo (1991). Assuming that the exogenous shocks are i.i.d. and affect both physical and human capital, we build specific configurations for the primitives of the model so that the optimal dynamics for the state variables can be converted, through an appropriate log-transformation, into an Iterated Function System converging to an invariant distribution supported on a generalized Sierpinski gasket.fractals, iterated function system, self-similarity, Sierpinski gasket, stochastic growth

Population Growth and Climate Change: A Dynamic Integrated Climate-Economy-Demography Model

We explore the bidirectional relationship between population growth and climate change: while population determines carbon emissions which drive climate change, climate change impacts the mortality rate and so population growth. Such population-climate feedback effects suggest that demographic policy may represent an alternative to traditional mitigation policies. We explore this possibility by introducing a population policy aiming at imposing a cap on population growth into an extended global integrated assessment model of climate-economy with endogenous fertility choices and temperature-related mortality. We show that the social costs of environmental policies, as reflected by both the social cost of carbon and social welfare, substantially increase by accounting for endogenous population change, but demographic policy allows to significantly reduce such costs. This clearly suggests that population growth does matter and so population policy may represent an effective mitigation tool to complement standard climate policies

A note on demographic shocks in a multi-sector growth model

We introduce demographic shocks in a multi-sector endogenous growth model, a-la Uzawa-Lucas. We show that an analytical solution of the stochastic problem can be found, under the restriction that the capital share equals both the inverse of the intertemporal elasticity of substitution and the degree of altruism. We show that uncertainty lowers the optimal levels of consumption and the physical capital stock, while they do not affect the share of human capital employed in production