Renewable Resources, Capital Accumulation, and Economic Growth

This paper proposes a dynamic economic model with physical capital and renewable resources. Different from most of the neoclassical growth models with renewable resources which are based on microeconomic foundation and neglect physical capital accumulation, this study proposes a growth model with dynamics of renewable resources and physical capital accumulation. The model is a synthesis of the neoclassical growth theory and the traditional dynamic models of renewable resources with an alternative approach to household behavior. The model describes a dynamic interdependence among physical accumulation, resource change, and division of labor under perfect competition.Because of its refined economic structure, our study enables some interactions among economic variables which are not found in the existing literature on economic growth with renewable resources. We simulate the model to demonstrate the existence of equilibrium points and motion of the dynamic system. Our comparative dynamic analysis shows, for instance, that a rise in the propensity to consume the renewable resource increases the interest rate and reduces the national and production sector’s capital stocks, wage rate and level of the consumption good. Moreover,it initially reduces and then increases the capital stocks of the resource sector and the consumption and price of the renewable resource. The stock of the renewable resource is initially increased and then reduced. Finally, labor is redistributed from the production to the resource sector.renewable resource, harvesting, capital accumulation, economic growth

The "amplitude" parameter of Gamma-Ray Bursts and its implications for GRB classification

Traditionally gamma-ray bursts (GRBs) are classified in the $T_{90}$-hardness ratio two-dimensional plane into long/soft and short/hard GRBs. In this paper, we suggest to add the "amplitude" of GRB prompt emission as the third dimension as a complementary criterion to classify GRBs, especially those of short durations. We define three new parameters $f$, $f_{\rm eff}$ and $f_{\rm eff,z}$ as ratios between the measured/simulated peak flux of a GRB/pseudo-GRB and the flux background, and discuss the applications of these parameters to GRB classification. We systematically derive these parameters to find that most short GRBs are likely not "tip-of-iceberg" of long GRBs. However, one needs to be cautious if a short GRB has a relatively small $f$ (e.g. $f<1.5$), since the chance for an intrinsically long GRB to appear as a "disguised" short GRB is higher. Based on avaialble data, we quantify the probability of a disguised short GRB below a certain $f$ value is as $P (<f)\sim 0.78^{+0.71}_{-0.4} f^{-4.33\pm 1.84}$. By progressively "moving" a long GRB to higher redshifts through simulations, we also find that most long GRBs would show up as rest-frame short GRBs above a certain redshift.Comment: 11 pages, 14 figures. Accepted by MNRA

A comprehensive analysis of Swift/XRT data: I. Apparent spectral evolution of GRB X-ray tails

An early steep decay component following the prompt GRBs is commonly observed in {\em Swift} XRT light curves, which is regarded as the tail emission of the prompt gamma-rays. Prompted by the observed strong spectral evolution in the tails of GRBs 060218 and 060614, we present a systematic time-resolved spectral analysis for the {\em Swift} GRB tails detected between 2005 February and 2007 January. We select a sample of 44 tails that are bright enough to perform time-resolved spectral analyses. Among them 11 tails are smooth and without superimposing significant flares, and their spectra have no significant temporal evolution. We suggest that these tails are dominated by the curvature effect of the prompt gamma-rays due to delay of propagation of photons from large angles with respect to the line of sight . More interestingly, 33 tails show clear hard-to-soft spectral evolution, with 16 of them being smooth tails directly following the prompt GRBs,while the others being superimposed with large flares. We focus on the 16 clean, smooth tails and consider three toy models to interpret the spectral evolution. The curvature effect of a structured jet and a model invoking superposition of the curvature effect tail and a putative underlying soft emission component cannot explain all the data. The third model, which invokes an evolving exponential spectrum, seems to reproduce both the lightcurve and the spectral evolution of all the bursts, including GRBs 060218 and 060614. More detailed physical models are called for to understand the apparent evolution effect.Comment: 13 pages in emulateapj style,6 figures, 1 table, expanded version, matched to published version, ApJ, 2007, in press. This is the first paper of a series. Paper II see arXiv:0705.1373 (ApJ,2007, in press

Renewable Resources, Capital Accumulation, and Economic Growth

This paper proposes a dynamic economic model with physical capital and renewable resources. Different from most of the neoclassical growth models with renewable resources which are based on microeconomic foundation and neglect physical capital accumulation, this study proposes a growth model with dynamics of renewable resources and physical capital accumulation. The model is a synthesis of the neoclassical growth theory and the traditional dynamic models of renewable resources with an alternative approach to household behavior. The model describes a dynamic interdependence among physical accumulation, resource change, and division of labor under perfect competition. Because of its refined economic structure, our study enables some interactions among economic variables which are not found in the existing literature on economic growth with renewable resources. We simulate the model to demonstrate the existence of equilibrium points and motion of the dynamic system. Our comparative dynamic analysis shows, for instance, that a rise in the propensity to consume the renewable resource increases the interest rate and reduces the national and production sector’s capital stocks, wage rate and level of the consumption good. Moreover, it initially reduces and then increases the capital stocks of the resource sector and the consumption and price of the renewable resource. The stock of the renewable resource is initially increased and then reduced. Finally, labor is redistributed from the production to the resource sector

Human Capital, Wealth, and Renewable Resources

This paper studies dynamic interdependence among physical capital, resource and human capital. We integrate the Solow one-sector growth, Uzawa-Lucas two-sector and some neoclassical growth models with renewable resource models. The economic system consists of the households, production sector, resource sector and education sector. We take account of three ways of improving human capital: Arrow’s learning by producing (Arrow, 1962), Uzawa’s learning by education (Uzawa, 1965), and Zhang’s learning by consuming (Zhang, 2007). The model describes a dynamic interdependence among wealth accumulation, human capital accumulation, resource change, and division of labor under perfect competition. We simulate the model to demonstrate existence of equilibrium points and motion of the dynamic system. We also examine effects of changes in the productivity of the resource sector, the utilization efficiency of human capital, the propensity to receive education, and the propensity to save upon dynamic paths of the system

Oscillations in a Growth Model with Capital, Technology and Environment with Exogenous Shocks

This paper generalizes the dynamic growth model with wealth accumulation, technological change and environmental change by Zhang (2012) by making all the parameters as time-dependent parameters. The model treats physical capital accumulation, knowledge creation and utilization, and environmental change as endogenous variables. It synthesizes the basic ideas of the neoclassical growth theory, Arrow’s learning-by-doing model and the traditional dynamic models of environmental change within a comprehensive framework. The behavior of the household is described with an alternative approach to household behavior. We simulated the model to demonstrate existence of equilibrium points, motion of the dynamic system, and oscillations due to different exogenous shocks

How Do the Richest 1% Owns 50% of Wealth in a Small-Open Growth Model with Endogenous Wealth and Human Capital

This paper extends the growth model for a closed national economy by Zhang (2015) to a small-open economy. We attempt to explain some economic mechanisms of how the richest one per cent of the population own 50% of national wealth. We consider endogenous wealth and human capital accumulation by heterogeneous households with different preferences and learning abilities as the main determinants of growth and inequality. We describe the production technologies and economic structure on the basis of the Uzawa two-sector model. By applying Zhang’s concept of disposable income and approach to household behavior, we describe consumers’ wealth accumulation and consumption behavior. We model human capital accumulation on the basis of Arrow’s learning by doing and Zhang’s creativity with leisure. We simulate the model with three groups of the population, the rich 1 %, the middle 69%, and the poor 20%. We demonstrate the existence of an equilibrium point at which the rich 1% own more than half of the national wealth and the poor 20% less than 10% of the national wealth. We show how the system moves to the equilibrium from an initial state and confirm that the equilibrium point is stable. We also conduct comparative dynamic analysis