0000000000147206
AUTHOR
José Ramón Ruiz-tamarit
Environmental pollution, sustained growth, and sufficient conditions for sustainable development
Abstract Sustainability and optimality are the two main issues discussed in environmental economics and economic growth theory. This paper studies economic growth in the presence of two environmental externalities. The first one is local and gives account of the marginal damage from the emissions flow. The second one is aggregate, or global, and relates to the extreme damage which may happen if the accumulated stock of pollutants is on the threshold of a worldwide catastrophe. In this context, the decentralized equilibrium is inefficient and economic growth unsustainable. However, we find and completely characterize the socially optimal equilibrium, which shows that sustained growth is feas…
Endogenous Growth, Capital Utilization and Depreciation
We study the one sector model of growth when a linear production technology is combined with adjustment costs and a technology for capital maintenance. Agents are allowed to under-use the installed capital and to vary the depreciation rate. This economy decides endogenously how much resources devotes to the accumulation of new capital and how much to maintenance and repair activities. We find as striking results that the long-run depreciation and capital utilization rates are positively related to the population growth rate, and that both depend negatively on the intial conditions. The long-run growth rate appears positively correlated with the depreciation rate.
Sustainable growth and environmental catastrophes
Abstract In the standard AK growth model we introduce the threat of an ecological catastrophe and study the consequences for the economic variables in the long-run. We extend the basic framework by considering two environmental externalities: the first one is local and gives account of the marginal damage from emissions flow; the second one is aggregate, or global, and relates to the extreme damage which may happen if the accumulated stock of pollutants is on the threshold of a worldwide catastrophe. In this context dominated by market failures, we focus on the socially optimal solution and the search of conditions for sustainability. We identify the efficient balanced growth path, which ma…
Solution to nonlinear MHDS arising from optimal growth problems
Abstract In this paper we propose a method for solving in closed form a general class of nonlinear modified Hamiltonian dynamic systems (MHDS). This method is used to analyze the intertemporal optimization problem from endogenous growth theory, especially the cases with two controls and one state variable. We use the exact solutions to study both uniqueness and indeterminacy of the optimal path when the dynamic system has not a well-defined isolated steady state. With this approach we avoid the linearization process, as well as the reduction of dimension technique usually applied when the dynamic system offers a continuum of steady states or no steady state at all.
The closed-form solution for a family of four-dimension nonlinear MHDS
In this article we propose a method for solving a general class of four-dimension nonlinear modified Hamiltonian dynamic systems in closed form. This method may be used to study several intertemporal optimization problems sharing a common structure, which involves unbounded technological constraints as well as multiple controls and state variables. The method is developed by solving the first-order conditions associated with the planner's problem corresponding to the Lucas [1988. On the mechanics of economic development. Journal of Monetary Economics 22, 3-42] two-sector model of endogenous growth, and allows for explicitly showing the transitional dynamics of the model. Despite the externa…
Global Dynamics and Imbalance Effects in the Lucas-Uzawa Model: Further Results
In this paper we use a new analytical approach to the Lucas-Uzawa model (Boucekkine and Ruiz Tamarit, 2007) to extend the existing results on the dynamics, and notably on the imbalance effects arising in the model. The approach does not only allow to extend the traditional analysis to any initial conditions and for all variables in level, but it also permits a more general investigation of imbalance effects.
Economic and statistical measurement of physical capital: From theory to practice
Abstract The standard measurements of capital and depreciation are statistical measures based on assumptions about the average service life of capital goods, which are accumulated according to the perpetual inventory method. The purpose of this paper is to obtain a true economic measure of capital stock according to the prescriptions of the neoclassical theory. In this way, we develop an alternative method based on the equations that solve the dynamic optimization problem of the firm, yielding an economic estimation based on indicators of profitability, such as the distributed profits and the Tobin's q ratio. Thus, this method enables us to endogenously calculate the variables' rate of depr…
Optimal Sustainable Policies Under Pollution Ceiling: the Demographic Side
AD; International audience; We study optimal sustainable policies in a benchmark logistic world (where both population and technological progress follow logistic laws of motion) subject to a pollution ceiling. The main policy in the hands of the benevolent planner is pollution abatement, ultimately leading to the control of a dirtiness index as in the early literature of the limits to growth literature. Besides inclusion of demographic dynamics, we also hypothesize that population size affects negatively the natural regeneration or assimilation rate, as a side product of human activities (like increasing pollution, deforestation, ...). We first characterize optimal sustainable policies. Und…
A Closer Look at the Comparative Statics in Competitive Markets
In this paper we revisit the dual approach to comparative statics in competitive markets, allowing for the essential results to arise from a comprehensive and unified framework. We study, for both the long-run and the short-run, the response of all the endogenous variables to price factor changes in a way that captures the outputprice effects arising from market-firm interactions. We show that it is necessary a richer characterization of the nature of factors with respect to output, connected with marginal cost and output demand elasticities, for completely determining such responses.
Multiplicity, Overtaking and Convergence in the Lucas Two-Sector Growth Model
This paper provides the complete closed-form solution to the Lucas two-sector model of endogenous growth. We study the issues of existence, unique-ness, multiplicity, positivity, transitional dynamics and long-run growth, re-lated to the competitive equilibrium paths. We identify the parameter range where the different results hold and deduce the entire trajectories for the original variables. We revise the results on convergence and overtaking which arise from this model, and prove that the parameterization currently used as the background for an explanation of economic miracles and disasters, is not satisfactory because of its counterintuitive implications.
Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model
The special functions are intensively used in mathematical physics to solve differential systems. We argue that they should be most useful in economic dynamics, notably in the assessment of the transition dynamics of endogenous economic growth models. We illustrate our argument on the famous Lucas-Uzawa model, which we solve by the means of Gaussian hypergeometric functions. We show how the use of Gaussian hypergeometric functions allows for an explicit representation of the equilibrium dynamics of all variables in level. The parameters of the involved hypergeometric functions are identified using the Pontryagin conditions arising from the underlying optimization problems. In contrast to th…
Growth vs. level effect of population change on economic development: An inspection into human-capital-related mechanisms
ACL-1; International audience; This paper studies the different mechanisms and the dynamics through which demography is channeled 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…