The government already levies duties on alcohol. This law is in part designed to prevent supermarkets from selling at a deliberate loss.

The justification for levying punitive duties on drink and fags is that these are things which cannot / should not be banned, but are in the public interest to mildly dissuade. The justification for applying minimum pricing would be that it is unscrupulous to override this nanny state policy with loss making discounts.

It's odd that we use these mildly punitive taxes for some social health ills like booze and smokes while applying blanket prohibition to others like marijuana and ecstasy. If this is a successful policy, then similar situations must surely invite similar treatment.