This paper examines the equivalence among price-modifying and quantity fixing international trade policies in a differential game. We employ two well known capital accumulation dynamics for firms, due to Nerlove and Arrow and to Ramsey, respectively. We show that, in both cases, open-loop and closed-loop Nash equilibria coincide. Under the former accumulation the tariff-quota equivalence holds, but it does not under the latter. Moreover, in the Ramsey model, the country setting the trade policy prefers a quantityequivalent import quota to the adoption of the tariff.