We visit the non-equivalence of tariff and quota in higher dimensional finite change trade models when goods outnumber factors of production. Under competitive conditions, exogenous shocks (e.g., exposure to international trade) support the production of only a subset of commodities. If we try to protect some of the vanishing goods, tariff and quota will have different results when a tariff turns out to be a more restrictive policy than a quota, contrary to the conventional wisdom. © 2016 John Wiley & Sons Ltd.