A note on global dynamics and imbalance effects in the Lucas-Uzawa model

In the traditional literature on the Lucas-Uzawa model, it is proved that in the neighborhood of the long-run balanced growth path, human capital stock grows at a rate greater than its long-run counterpart when the ratio physical to human capi- tal is above its long run value if and only if the capital share in the production of physical good is lower than the inverse of the elasticity of intertemporal substitution in consumption. We first prove that the claim is true outside the neighborhood of balanced growth paths. More importantly, we identify a crucial asymmetry: what- ever the position of the capital share with respect to the inverse of the elasticity of intertemporal substitution, physical capital stock always grows at a rate lower than its long-run counterpart when the ratio physical to human capital is above its long run value.Lucas-Uzawa, hypergeometric functions, imbalance e®ects, global dynamics.

Growth vs. level effect of population change on economic development: An inspection into human-capital-related mechanisms

This paper studies the different mechanisms and the dynamics through which demography is channelled to the economy. We analyze the role of demographic changes in the economic development process by studying the transitional and the long-run impact of both the rate of population growth and the initial population size on the levels of per capita human capital and income. We do that in an enlarged Lucas-Uzawa model with intergenerational altruism. In contrast to the existing theoretical literature, the long-run level effects of demographic changes, i.e. their impact on the levels of the variables along the balanced growth path, are deeply characterized in addition to the more standard long-run growth effects. We prove that the level effect of the population rate of growth is non-negative (positive in the empirically most relevant case) for the average level of human capital, but a priori ambiguous for the level of per capita income due to the interaction of three transmission mechanisms of demographic shocks, a standard one (dilution) and two non-standard (altruism and human capital accumulation). Overall, the sign of the level effects of population growth depend on preference and technology parameters, but numerically we show that the joint negative effect of dilution and altruism is always stronger than the finduced positive human capital effect. The growth effect of population growth depends basically on the attitude to intergenerational altruism and intertemporal substitution. Moreover, we also prove that the long-run level effects of population size on per capita human capital and income may be negative, nil, or positive, depending on the relationship between preferences and technology, while its growth effect is zero. Finally, we show that the model is able to replicate complicated time relationships between economic and demographic changes. In particular, it entails a negative effect of population growth on per capita income, which dominates in the initial periods, and a positive effect which restores a positive correlation between population growth and economic performance in the long term.Human Capital, Population Growth, Population Size, Endogenous Growth, Level Effect, Growth Effect

Self-Consistent Random Phase Approximation - Application to the Hubbard Model for finite number of sites

Within the 1D Hubbard model linear closed chains with various numbers of sites are considered in Self Consistent Random Phase Approximation (SCRPA). Excellent results with a minimal numerical effort are obtained for 2+4n sites cases, confirming earlier results with this theory for other models. However, the 4n sites cases need further considerations. SCRPA solves the two sites problem exactly. It therefore contains the two electrons and high density Fermi gas limits correctly.Comment: 17 pages, 17 figure

On generalization closed set and generalized continuity OnIntuitionistic Topological spaces

Abstract: In this paper, we continue the study of generalized closed sets in ITS, and related to each other’s and with known’s closed sets. We introduce also, different kinds of g-continuity and related to each other’s and with known continuity in ITS

Testing significance relative to a fold-change threshold is a TREAT

Motivation: Statistical methods are used to test for the differential expression of genes in microarray experiments. The most widely used methods successfully test whether the true differential expression is different from zero, but give no assurance that the differences found are large enough to be biologically meaningful