The non-equivalence of import tariffs and export taxes in trade wars : ad valorem vs specific trade taxes

Using perfectly competitive, general equilibrium models of international trade, specific import tariffs, specific export taxes, and ad valorem trade taxes are compared in a trade war. A trade war is modelled as a NE in trade policies, where each country can choose to use ad valorem trade taxes (import tariffs or export taxes, which are equivalent), or specific import tariffs, or specific export taxes. In the two-country case, where there is a negative terms of trade externality a specific export tax dominates a specific import tariff or ad valorem trade taxes. Hence, the Lerner Symmetry Theorem does not hold for specific trade taxes in a trade war. This result continues to hold when the model is extended to the case of many countries assuming that there is a negative terms of trade externality. In a trade policy game where two countries export the same good so there is a positive terms of trade externality in the trade policy game between these two countries, the results are reversed with a specific import tariff dominating a specific export tax or ad valorem trade taxes. Hence, again the Lerner Symmetry Theorem does not hold for specific trade taxes in a trade war.