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 —...

We consider an environment of a fixed size that can be converted to another use. This conversion can be made in steps, but it is irreversible. The future benefits (per unit) from the original use, and from the alternative use, follow a diffusion process. For a fairly general case, we show that the value function must be the unique (viscosity) solution to the associated Hamilton-Jacobi-Bellman e...

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...

Paired end Illumina Mi-Seq sequencing of 16S rRNA gene amplicon was carried out to study the bacterial community in the soil of Murlen National Park located in Indo-Burman Biodiversity hotspot region. Metagenome consisted of 302,416 reads with 151.81 Mb data and G + C content of 56.48%. More than 85% sequence was having a Phred score >=Q30 and individual sequence length was 251 bp. Metagenome s...