A Differential Game Analysis of Timber Trade, Optimal Tariffs, and the Seller s Rent

The analysis of import tariffs on natural resources has been undertaken on the establishment of two modeling approach for both non-renewable resources and renewable resources. However, it is too hard to find the literature that analyzed the optimal tariffs on timber trade by modeling the biological characteristics of forest explicitly. This paper, hence, is designed to examine the dynamic structure of optimal unit tariffs on timber by specifying both the dynamic change of forest stock and the quantity of timber production in a realistic sense. For this purpose, we establish a Stackelberg differential game of timber trade where the buying country has a market power, and analyze the dynamic structure of optimal unit tariffs on timber imported. We perform this procedure for two cases of the cost for timber production. In addition, we show that the shadow value for the stock of forest can be partitioned into the scarcity effect and the cost effect. On the basis of this, we identify that the selling country only takes the cost effect of the shadow value for the stock of forest as a rent.