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There are many puzzles and unresolved problems in empirical economics that depend on the reliability of the productive capital series. Some macroeconomic topics and questions cannot be addressed correctly or answered with the available standard statistical measures of capital stock. We make an innovative contribution to the theory of capital together with an exercise that quantifies the depreciation rate and the capital stock for the U.S. economy. An intertemporal optimization model with adjustment and maintenance costs, gives us the algorithm and the corresponding economic estimation of capital deterioration and obsolescence. Our measures are based on profitability and the Tobin’s q ratio.

The reader will find in this paper a simple theoretical framework where to analyze the usual issues from environmental and economic growth literature, including the problem of global warming, the corresponding climate change, and the impact on economic system. This paper considers 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, the decentralized equilibrium path is inefficient and unsustainable, while the socially optimal balanced growth path shows a singularity with trajectories truncating and changing of course. With respect to the economy's long-run performance we s how environment matters in different ways and at different stages, and give conditions for sustainability of sustained growth.tudy

When there are pollution externalities the competitive equilibrium is not Pareto-optimal nor environmentally sustainable even if abatment activities are endogenously decided. In this paper we introduce the possibility of an ecological catastrophe like the one predicted by the global climate change, imposing the constraint of an upper-limit to the pollutants stock. We characterize this socially optimal soclution and study conditions for the sustainability of the balanced growth path. We find a trade-off between environmental quality and growth. The rate of growth depends negatively on the weight of environmental care in the utility function and positively on the population growth rate. We show that the emissions reduction recommended in the Kioto protocol is an appropriate policy to avoid the ecological catastrophe and ensure global efficiency and positive long-run growth.

In an endogenous growth model with pollution and abatement we characterize the socially optimal solution. We find that the rate of growth depends negatively on the weight of environmental care in utility and positively on the population growth rate. We also find a trade-off between growth and environmental quality beyond which an environmental Kuznets curve is derived in the long term. This one emerges from the implications of the demographic transition for the rate of population growth, and the accompanying variation in the willingness to pay for environmental quality as the economy develops.

In this note, we extend Xie (JET, 1994) to solve analytically the Lucas model with a weak externality in a specific parametric case. In particular, we characterize the shape of imbalance effects in this model. Our results are mostly consistent with the findings of the related computational literature. Among other analytical findings, we prove that, while U-shaped imbalance effects are not apparent in the Lucas model for the growth rate of output per capita, the level of such a variable may exhibit this shape.

In this note, we use a technique analogous to Xie's method (1994) to solve analytically the Lucas model with externality in a specific parametric case. In particular, we characterize the shape of imbalance effects in this model. Our results are entirely consistent with the findings of the related computational literature. Moreover, our analytical investigation tends to show that these findings are robust to the presence of the Lucas externality as long as a unique equilibrium path exist.

This paper is concerned with the theoretical properties of demand for capital maintenance services. To this end, we consider two investment problems incorporating maintenance services and we analyse their steady state equilibria. At first, we shwo that if no variable capital utilization rate is allowed, investment and maintenance expenditures have the same qualitative properties, and so cannot be regarded as gross substitutes. If a variable rate of capital utilization is allowed, the occurence of substitution Vs complementarity features and the comparative statics properties depend on the sensitivity of the postulated capital depreciation function with respect to both the rate of capital utilization and the maintenance expenditures ratio. We prove that the case where the elasticity with respect to maintenance expenditures is lower, gives much better shaped demand functions and fits definitely better the recent real business cycles studies.