Inelastic demand

Gorbachev's crackdown on alcoholism reduced heavy drinking in the former Soviet Union. He combined some measures directly targeting heavy drinkers with price increases and supply reductions. Bhattacharya and coauthors wrote:

The results suggest little evidence that our summary measure of campaign intensity operates either through differential supply shifts or through differential price increases. However, we are hesitant to draw conclusions given the limitations of the state vodka production and alcohol price index data noted earlier. We emphasize that this is an important area for further research.

I wasn't surprised that Bhattacharya wasn't able to find price effects on heavy drinking; I expected that the Soviet campaign's effectiveness came rather from bans on workplace drunkenness and mandatory treatment for alcoholism. Why? It's hard to target heavy drinkers with price measures.

I've previously cited Wagenaar's metastudy showing that heavy drinkers are only about 60% as responsive to prices as are moderate drinkers. Jon Nelson adds to this literature looking in particular at the differential price responsiveness of heavy and moderate drinkers. He concludes that Wagenaar was too optimistic about the degree to which heavy drinkers respond to price measures. After an extensive literature review, Nelson concludes:

The review found only two of nineteen empirical studies where there was a significant and substantial price/tax response by heavy-drinking adults (ages > 26 years), and even these two studies present mixed results. On the other hand, many studies show that moderate-drinking adults have significant and substantial price/tax elasticities, including both studies for Australia (Brynes et al., 2012; Harris et al., 2006) and several of the US studies. The review of cirrhosis mortality found only two of nine studies obtained significant negative price/tax effects, but prices in these studies might be proxies for other (omitted) alcohol policies or drinking sentiment generally. The other cirrhosis studies contain mixed results or are sensitive to econometric specifications. Several limitations of the studies should be kept in mind, which also provide a basis for future research in this area.

...
In summary, a review of two sets of related studies casts doubt on public policies that rely extensively on price controls or higher alcohol taxes as a means to reduce abusive drinking by adults, adverse health outcomes, and related social costs. The price/tax elasticity for heavy drinkers appears to approach zero in most instances. This result is robust across countries, time periods, drinking measures, and model specifications. Improvements in price data in empirical studies might remove some uncertainty associated with this evidence. 

Nelson cites one new piece the I'd missed: Ayyagari et al, newly out in Health Economics. They used finite mixture models on individual-level data on heavy drinking incidence from the HRS (older adults, large sample) and found that their dataset effectively consisted of two groups of people. The largest group didn't drink very much, averaging 0.13 drinks per day, but was very responsive to prices. The smaller group averaged 1.86 drinks per day and really didn't seem to vary consumption with prices. The neat trick in Ayyagari et al is that when they pooled the two groups, they got about the same estimate that everybody tends to get: aggregate elasticity of around -0.4. Studies that pool results from heavy and moderate drinkers make a bit of a hash of things if we're trying to assess whether price measures curb the harms from heavy drinking. They conclude:

There is growing political support for increased alcohol taxes; however, we are cautious about predicting welfare gains to alcohol tax hikes with regard to older individuals.25 Revenue may be raised at the cost of welfare loss for many older individuals but with little reduction in externalities. Heavier drinkers are more likely to impose negative externalities than the lighter drinkers. However, our results indicate that the heavier drinking group is insensitive to price; thus, higher taxes would be unlikely to reduce negative externalities for older drinkers.26 In contrast, for the largest group of individuals, composed of moderate-to-low drinkers, the higher tax will reduce their alcohol consumption, resulting in a utility loss and loss of potential health benefits of alcohol (Thun et al., 199727), yet it is unlikely to reduce externalities.

Especially sensitive to price increases were lower income moderate drinkers.

At least Gorbachev had some idea that curbing harms from heavy drinking required something other than price and supply controls, though I do not endorse his methods.

Be very wary of policy recommendations that cite aggregate effects of prices on quantities consumed when harms are non-linear in consumption and when the heaviest consumers are least responsive to price measures.