Simple taxation schemes on non–renewable resources extraction

Traditional economic theory, up to the middle of the twentieth century, builds up the production functions regardless of the inputs’ scarcity. In the last few decades it has become clear that in many cases inputs are depletable quantities and at the same time a lot of constraints are imposed in their usage in order to ensure economic sustainability. Furthermore, the management of exploitation and use of natural resources (either exhaustible or renewable) has been discussed by analyzing dynamic models applying methods of Optimal Control Theory. This theory provides solutions that are concerned with a single decision maker who can control the model’s dynamics facing a certain performance index to be optimized. In this paper we consider some simple taxation schemes based both on price charged and on the stock size as well. As the feedback taxation rules are more efficient than the other (non feedback) rules we have constructed the simple taxation scheme and found the analytical expression of the tax function