I want to take a different angle, of relevance to my ECON100 students. What would be the effects of alcohol minimum pricing, if it was introduced. For simplicity, I'm going to ignore the existing excise tax on alcohol, and any externalities, and just concentrate on the minimum price.
The effect is shown in the diagram below. Without minimum pricing, the market equilibrium price is P0, and the quantity of alcohol sold (and presumably consumed) is Q0. But with a binding minimum price (above the equilibrium price) of P1, the quantity of alcohol demanded falls to Q1. In other words, alcohol consumption falls.
Now consider the economic welfare effects. The consumer surplus is the difference between the price the consumers are willing to pay, and the price they actually pay. Without the minimum price, consumer surplus is AEP0, but with the minimum price this falls to ABP1 (which makes sense - consumers consume less alcohol with the minimum price than without it, and pay a higher price for that alcohol). The producer surplus is the difference between the price the alcohol retailers receive, and their costs (which are shown by the supply curve). Without the minimum price, producer surplus is P0EF, but with the minimum price producer surplus is P1BCF. However, we can't easily tell if producer surplus has increased or decreased - retailers are selling less alcohol, but they are receiving a higher price for it.
Whether producer surplus increases or decreases when minimum pricing is introduced depends mainly on the price elasticity of demand for alcohol. If alcohol is price elastic, then alcohol consumers are relatively sensitive to price changes. That means that if price increases by x%, then the quantity of alcohol demanded will decrease by more than x%, and the firm's revenue (price multiplied by quantity sold) will decrease. Whether that results in decreased profit depends on whether the loss of revenue is larger than the costs saved by selling fewer units (which in most cases it will be).
On the other hand if alcohol is price inelastic, then alcohol consumers are relatively insensitive to price changes. That means that if price increases by x%, then the quantity of alcohol demanded will decrease by less than x%, and the firm's revenue (price multiplied by quantity sold) will increase. Given that costs will likely decrease (because the firm is selling fewer units), then profits will necessarily rise.
So, is demand for alcohol price elastic or price inelastic? There is a fair amount of debate on this point, and Eric Crampton has some of the latest evidence here. However, we need not go too far to determine whether the sellers themselves believe that demand is price elastic - if they think that is the case, they will argue against any minimum pricing (because if demand was price inelastic, minimum pricing would increase their profits!). And indeed, supermarkets (who have the largest market share of the retail alcohol market) are arguing against this policy. That suggests alcohol demand is price elastic. [*]
As an addendum I recently had a student, who worked for a large brewer, estimating the price elasticity of demand for products (note: not for alcohol as a whole). This student (who I can't name given their position in the industry) found that demand for specific products was highly elastic. This shouldn't be too surprising - there are many substitutes for a specific brand of beer. However, the student's results also suggests that consumers are very willing to shift to cheaper options (within the beer category).
Overall then, it appears that alcohol minimum pricing would reduce profits (else the retailers would be less likely to argue strongly against it), suggesting that alcohol is price elastic.
[*] The supermarkets might also argue against the policy if they believed that it would increase their costs, such as if they had to change their pricing policies. The costs of complying with minimum pricing don't seem to me to be large, so this seems unlikely as an explanation.