How large are optimal tariffs? What tariffs would prevail in a world-wide trade war? How costly would a breakdown of international trade policy cooperation be? And what is the scope for future multilateral trade negotiations? I address these and other questions using a unified framework which nests traditional, new trade, and political economy motives for protection. I find that optimal tariffs average 62 percent, world trade war tariffs average 63 percent, the government welfare losses from a breakdown of international trade policy cooperation average 2.9 percent, and the possible government welfare gains from future multilateral trade negotiations average 0.5 percent.