Do Optimal Non-Renewable Resource Tariffs Suffer From Dynamic Inconsistency?

In this paper we have examined optimal tariffs for non-renewable natural resources in the setting of imperfect competition. We do this because Larry Karp (1984, p. 74) states that, If the buyer attempts to exert market power, he is constrained by the dynamic optimization behavior of the seller and does not face a standard control problem. We show that when extraction costs are a function of the remaining stock of the resource, the costate variable can be separated into a scarcity effect and a cost effect. Karp concludes that the cost effect must be left with the producer; thereby, restricting the actions of the buyer. We, however, prove that it is not necessary to pay this cost effect to the producer; hence, we conclude that the monopsonist can extract all of the rent from the seller. The optimal tariff is neither dynamically time inconsistent, nor is it Karp\u27s consistent tariff