On Technical Change in the Elasticities of Resource Inputs

Abstract

This article considers an economy whose production function takes both renewable and non-renewable resources as inputs. We extend the current literature by allowing for exogenous technical change in the elasticity of substitution between these two types of resources. In addition, we study the consequences of biased technical change which alters the resources' relative productivities. We derive long-run asymptotic results, which we use to compare several cases. In the benchmark case of no technical change, our results are close to those obtained by Dasgupta and Heal (1974). In the case of technical change in the elasticity of substitution, we observe that this kind of technical change helps obtain positive long-run production despite the depletion of non-renewable resources. In the biased technical change case, long-run production is only possible either if non-renewable resources are non-essential or if biased technical change is quick enough to compensate for the decreasing flow of non-renewable resources. We embed our production function in an optimal growth model and study its dynamics. As a steady state (or a balanced growth path) is only attainable as time goes to infinity, we resort to numerical simulations to convey what is happening during the short and medium run. Our results provide new considerations for the debate on natural resources. We suggest that technical change should be directed to the resource which is most important for production.