The Dynamic Structure of Optimal Tariff on Timber Trade: a Differential Game Approach

The analysis of import tariffs on natural resource has been undertaken on the establishment of two modeling approaches for both nonrenewable 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 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 tariff on imported timber. We perform this procedure for two forms of cost function for timber production. One form is dependent on the stock of forest and the other is independent of it. In addition, we show that the costate variable for the stock of forest can be partitioned into the scarcity effect and the cost effect. On the basis of this result, we identified that the selling country takes the cost effect of the shadow value for the stock of forest as a rent. Key words; Optimal tariff on timber, Stackelberg differential game, Dynamic inconsistency, Scarcity effect and cost effect JEL Code: F12, H21, Q23