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

Black hole thermodynamical entropy

As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy $S_{BG}$ of a $(3+1)$ black hole is proportional to its area $L^2$ ($L$ being a characteristic linear length), and not to its volume $L^3$. Similarly it exists the \emph{area law}, so named because, for a wide class of strongly quantum-entangled $d$-dimensional systems, $S_{BG}$ is proportional to $\ln L$ if $d=1$, and to $L^{d-1}$ if $d>1$, instead of being proportional to $L^d$ ($d \ge 1$). These results violate the extensivity of the thermodynamical entropy of a $d$-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is \emph{not} to be identified with the BG {\it additive} entropy but with appropriately generalized {\it nonadditive} entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle.Comment: 7 pages, 2 figures. Accepted for publication in EPJ

Genome Sequence of the Pea Aphid Acyrthosiphon pisum

Aphids are important agricultural pests and also biological models for studies of insect-plant interactions, symbiosis, virus vectoring, and the developmental causes of extreme phenotypic plasticity. Here we present the 464 Mb draft genome assembly of the pea aphid Acyrthosiphon pisum. This first published whole genome sequence of a basal hemimetabolous insect provides an outgroup to the multiple published genomes of holometabolous insects. Pea aphids are host-plant specialists, they can reproduce both sexually and asexually, and they have coevolved with an obligate bacterial symbiont. Here we highlight findings from whole genome analysis that may be related to these unusual biological features. These findings include discovery of extensive gene duplication in more than 2000 gene families as well as loss of evolutionarily conserved genes. Gene family expansions relative to other published genomes include genes involved in chromatin modification, miRNA synthesis, and sugar transport. Gene losses include genes central to the IMD immune pathway, selenoprotein utilization, purine salvage, and the entire urea cycle. The pea aphid genome reveals that only a limited number of genes have been acquired from bacteria; thus the reduced gene count of Buchnera does not reflect gene transfer to the host genome. The inventory of metabolic genes in the pea aphid genome suggests that there is extensive metabolite exchange between the aphid and Buchnera, including sharing of amino acid biosynthesis between the aphid and Buchnera. The pea aphid genome provides a foundation for post-genomic studies of fundamental biological questions and applied agricultural problems

Varieties of modules and pp-blocks of finite groups (Cohomology of Finite Groups and Related Topics)

We present a number of variants of a constructive algorithm able to solve a wide variety of variants of the Two-Dimensional Irregular Bin Packing Problem (2DIBPP). The aim of the 2DIBPP is to pack a set of irregular pieces, which may have concavities, into stock sheets (bins) with fixed dimensions in such a way that the utilization is maximized. This problem is inspired by a real application from a ceramic company in Spain. In addition, this problem arises in other industries such as the garment industry or ship building. The constructive procedure presented in this paper allows both free orientation for the pieces, as in the case of the ceramic industry, or a finite set of orientations as in the case of the garment industry. We explicitly model the assignment of pieces to bins and compare with the more common strategy of packing bins sequentially. There are very few papers in the literature that address the bin packing problem with irregular pieces and to our knowledge this is the first to additionally consider free rotation of pieces with bin packing. We propose several Integer Programing models to determine the association between pieces and bins and then we use a Mixed Integer Programing model for placing the pieces into the bins. The computational results show that the algorithm obtains high quality results in sets of instances with different properties. We have used both industry data and the available data in the literature of 2D irregular strip packing and bin packing problems

Closed-Form Solution for a Two-Sector Endogenous Growth Model with two Controls ¤

In this paper we show a method for solving in closed form a particular family of four-dimension non-linear modi…ed Hamiltonian dynamic systems, with two states and two co-states, which arises from a twosector endogenous growth model where the physical capital stock is combined with a renewable natural capital stock as essential inputs for production

Endogenous Growth, Capital Utilization and Depreciation

We study an extended version of the one-sector AK growth model introducing adjustment and maintenance costs. Agents are allowed to under-use the installed capital and to vary the depreciation rate. The model is analyzed using particular functional forms and is solved in closed-form. We find that adjustment and maintenance costs (e?- ciency) reduce (increases) investment, depreciation, capital utilization and the rate of growth; impatience reduces the rate of growth but increases depreciation and utilization, which are also negatively related to the rate of population growth; the rate of growth appears positively correlated with the depreciation rate and the rate of capital utilization.

The Reduction of Dimension in the Study of Economic Growth Models

We examine the dimension reduction method and prove that it could be isleading if we try to get some insight tinto the dynamics of the original system from the dynamics of the transformed system alone. The reduced system seemingly may give rise to a continuum multiplicity of steady states when, actually, it does exist a unique and isolated steady state or even it does not exist a steady state at all. We show how the dynamics for the primary variables that is recovered from the solution to the reduced system may be refuted by solving the original one. In our opinion there is no alternative because nothing can be regarded as a close substitute for the study of the original system. Although this method has been extensively used in studying different versions of the Lucas-Uzawa two-sector model, we will focus on one-sector models for checking its validity in the simplest way.

Solution to Non-Linear MHDS arising from Optimal Growth Problems

In this paper we propose a method for solving in closed form a general class of non-linear modified Hamiltonian dynamic systems (MHDS). This method may be used to analyze some intertemporal optimization problems With a predetermined structure involving unbounded technological constraints. The method seems specially well designed to study endogenous growth models With two controls and one state variable. We use the closed form solutions to Study either unicity or indeterminacy of the non-explosive paths in a Context charaterized by the lack of a well defined isolated steady state. Moreover, in this way we can avoid both the reduction of dimension and the linearization process even when the dynamic system offers a continuum of steady states or no steady stateat all.