This paper presents a tractable dynamic general equilibrium model of income and firm-size distributions. The size and value of firms result from idiosyncratic, firm-level productivity shocks. CEOs can invest in their own firms’ risky stocks or in risk-free assets, implying that the CEO’s...

We study multiplicative and affine sequences of real numbers defined byN(j+1)=ζ(j)N(j)+η(j),where {ζ(j)} and {η(j)} are sequences of positive real numbers (in the multiplicative case η(j)=0 for all j). We investigate the conditions under which the leading digits k of {N(j)} have the...

We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent α of the Pareto law obtained in stochastic multiplicative market models is crucially...

Using the uniform most powerful unbiased test, we observed the sales distribution of consumer electronics in Japan on a daily basis and report that it follows both a lognormal distribution and a power-law distribution and depends on the state of the market. We show that these switches occur...

Pareto's law states that the distribution of personal income obeys a power-law in the high income range. Its dynamical nature has been little studied hitherto, mostly due to the lack of empirical work. Using an exhaustive list of taxpayers in Japan for two consecutive years, when the economy was...

We find that area and population distributions of nations follow an inverse power-law, as is known for cities, but with a different exponent. To interpret this result, we develop a growth model based on the geometrical properties of partitioning of the plane. The substantial agreement between...

This paper investigates the effects of wealth-enhanced social status using an optimizing monetary growth model with non-separable utility function between consumption and wealth. Within this framework, we first arrive a conclusion that, in the case of no wealth effects, an increase in the rate...

This paper proposes two types of AK-style endogenous growth models to test the physical capital accumulation hypothesis in a ‘typical’ developing country with multiple regimes: a strong version, in which technological progress is fully endogenous to capital accumulation, and a weaker...

This paper deals with an endogenous growth model with vintage capital and, more precisely, with the AK model proposed in [18]. In endogenous growth models the introduction of vintage capital allows to explain some growth facts but strongly increases the mathematical difficulties. So far, in this...

This note studies the stochastic stability of the standard AK growth model under uncertain output technology. Capital accumulation follows a stochastic linear homogenous differential equation. It's shown that exponential balanced paths, which characterize optimal trajectories in the absence of...