This paper introduces endogenous and directed technical change in a growth model with environmental constraints. The final good is produced from "dirty" and "clean" inputs. We show that: (i) when inputs are sufficiently substitutable, sustainable growth can be achieved with temporary taxes/subsidies that redirect innovation toward clean inputs; (ii) optimal policy involves both "carbon taxes" a...

This note offers a general proof of the converse of Hartwick’s rule, namely that — in an economy with stationary instantaneous preferences and a stationary technology — an efficient constant utility path is characterized by the value of net investments being zero at each point in time. In a one consumption economy with two stocks — a stock of a natural resource and a stock of man-made capital —...

I investigate two versions of a differential Cournot oligopoly game with nonrenewable resource exploitation, in which each firm may either exploit its own private pool or exploit a common pool jointly with the rivals. Firms use a deterministic technology to invest in exploration activities. In both models, there emerges that (i) the individual exploration effort is higher when each firms has ex...

We study transitions between nonrenewable and renewable energy forms at di!erent development stages of an economy. It is shown that in the historical context the emphasis on energy production may evolve from renewables to nonrenewables and back to renewables. Typically both energy forms are used simultaneously. Along the equilibrium path, nonrenewable resource consumption may increase and their...

In this short paper, uncertainties on resource stock and on technical progress are introduced into an intertemporal equilibrium model of optimal extraction of a non-renewable resource. The representative consumer maximizes a recursive utility function which disentangles between intertemporal elasticity of substitution and risk aversion. A closed-form solution is derived for both the optimal ext...

I examine the long-run behavior of oil, coal, and natural gas prices, using up to 127 years of data, and address the following questions: What does over a century of data tell us about the stochastic dynamics of price evolution, and how it should be modeled? Can models of reversion to stochastically fluctuating trend lines help us forecast prices over horizons of 20 years or more? And what do t...

We consider a simple model of energy saving investments under uncertainty of energy costs. Adjustment delays in replacing energy-intensive capital follow from two natural elements: uncertainty and heterogeneity of the existing capital structure. They imply a simple dichotomy where short-run output contracts, but the long-run output recovers and increases above the initial output, despite the in...

Most research on the effects of endurance training has focused on endurance training's health-related benefits and metabolic effects in both children and adults. The purpose of this study was to examine the neuromuscular effects of endurance training and to investigate whether they differ in children (9.0-12.9 years) and adults (18.4-35.6 years). Maximal isometric torque, rate of torque develop...