Capital Resource Substitution, Overshooting, and Sustainable Development

Abstract

We study an optimal control problem with a man-made capital stock, and a stock of renewable natural resource. They are substitutable inputs in the production of the final good. Starting from low levels of both stocks, the optimal policy consists of three phases. In phase I, the planner builds up the stock of resource above its steady state level, while the man-made capital stock is kept below its steady state level. In phase II, the resource stock declines steadily, while the man-made capital stock continues to grow, until the steady state is reached, and the economy stays thereafter. The model exhibits “overshooting” property.