Never in history has there been a black market defeated from the supply side. From prohibition to prostitution, from gambling to recreational drugs, the story is the same. Supply-side controls act, much like price supports in agriculture, to encourage production and increase profits. At best a few intermediaries get knocked out of business. But as long as demand persists, the market is served more or less as before.
That is from his 2004 book, Wages of Crime, an attack on the notion that the world is being taken over by underground criminal networks worth billions of dollars - the biggest profits in fraudulent activity is being made, he argues, by banks, speculators and big corporations. Not always thoroughly argued or backed up with convincing proof, but a suggestive take on the world of transnational crime.
As for the eastern Congo, I would probably say he is right: We are not going to get far by banning tin exports. But if we can adjust the incentive structure in the international markets to promote more accountability, then the mineral trade could become a foot in the door of institutional reform in the Kivus. In the best case scenario.