Import tariff upstream versus export tax downstream: are they welfare equivalent?

Along the lines of the strategic trade policy inquiry under vertical structures we show that two rival governments may select different rates of export subsidies and import tariffs respectively upon their own industries even if their marginal costs are identical. Moreover, regardless of any combination of these policy instruments optimally introduced, we show that each nation's welfare level will remain the same and higher than that under free trade with no trade policy at all.