The markets for drugs such as cocaine are characterized by much ignorance about the nature of trading relationships, in particular the volumes and prices exhibited by overlapping national and international networks of buyers and sellers (i.e. markets), and by severe regulation by the State. The regulation of illegal markets is expensive; for example, in 1988 in the UK, over 5000 Customs officers and 1800 CID and uniformed policemen were involved in enforcing the law at a cost of about 140 million pounds. The size of the markets can be only 'guesstimated': in 1989 just over 520 kg of cocaine was seized. If this is assumed to be 10% of the market, the total size of the cocaine market was somewhere in excess of 5000 kg. The 'cost-effectiveness' of both Customs and the police in enforcing the law may have declined in the late 1980s. What economic arguments are there for sustaining illegality and an expensive enforcement effort? Some arguments for State regulation are explored; for example, the drug user harms 'innocent' third parties, the drug user is less productive and reduces national income, the drug user will impose costs on the National Health Service, the drug user's behaviour is offensive, and the drug user should be protected from his own stupidity. Where do these arguments leave the case for maintaining public policy towards illicit drugs? Would it be cost effective to move towards the liberalization of these markets?