Resources as an Input of Production in a Two-Sector Economy

This paper extends models of renewable resources to an economy with two sectors, resource extraction and production. In contrast to one sector models, we show that the optimal strategies in the single-firm model are essentially different from those in the two-player model. In the single-player model, the optimal strategy is to keep the resource extraction a constant multiple of production labor. In the two-player model, the optimal strategy for each player is to keep extracting labor a constant multiple of production labor. It is also shown that the extraction-to-production labor ratio is increasing with the wage and the interest rate and is decreasing with the production TFP, the extraction TFP, and the stock level in the single-player model, but not in the two-player model. Finally, I show that another way for each firm to maximize profit is to raise its zero-profit stock level by maximizing its geometric average TFP.