Optimal Tariffs on Exhaustible Resources: The Case of a Quantity Setting Cartel

We formulate a dynamic game model of trade in an exhaustible resource with a quantity-setting cartel. We compute the feedback Nash equilibrium and two Stackelberg equilibria under two different leadership scenarios: leadership by the strategic importing country, and leadership by the exporting cartel. We numerically show that as compared to the Nash equilibrium, both players are better off if the importing country is the leader. The follower is worse off if the exporting cartel is the leader. Among the three game-theoretic outcomes, the world welfare is highest under the importing country's leadership and lowest under the exporting country’s leadership.