A Stackelberg Game Model of Trade in Renewable Resources with Competitive Sellers

Abstract

We model international trade in renewable resources between a single buyer and competitive sellers as a Stackelberg differential game. The buyer uses unit and ad valorem tariffs to indirectly encourage conservation of the renewable resource under study. First, we show that the efficacy of these trade policy instruments in promoting conservation depends fundamentally on whether harvesting costs are stock dependent or independent. When harvesting costs are stock independent, the optimal open loop tariffs are dynamically consistent. In contrast, when harvesting costs are stock dependent, the optimal open loop tariffs are dynamically inconsistent. Second, we point out that whether the terminal value of the resource stock is higher with the stock independent or the stock dependent cost function cannot be resolved unambiguously. Third, we show that it does not make sense for the buyer to use both tariffs simultaneously. Finally, we discuss the implications of these and other findings for renewable resource conservation in general.