Taxation on alcohol is considered ineffective (but a great way to collect high tax revenues which can also be used to finance other policies aimed at decreasing consumption of these 'demerit' goods). Why won't even a high an indirect tax be effective in lowering consumption of alcohol? Because taxes on alcohol lead to a "chain of substitutions". There are very many different types of alcohol (vodka, whisky, wine, beer, tequila, rum, cider, ouzo, you name it...) and each type has zillions of brands and qualities and thus prices range from very low to extremely high. A high tax on alcohol (say 50%) would induce this "chain of substitutions": many consumers, especially individuals in lower socio-economic status (SES) groups where greater prevalence of harmful alcohol consumption (binge drinking) is documented will simply switch to equally strong but cheaper and often lower quality alcohol or brands. Note though that the minimum unit price (MYP) policy implemented in Scotland and Wales (for which, BTW, you can not use a typical demand and supply diagram that we use to illustrate a minimum price on, say, corn, because the markets for vodka, whisky etc. are not perfectly competitive and there is no supply curve in markets where firms are price setters) is considered most effective especially if complemented by other policies, such as increased education and awareness in the population (note that also some techniques -nudges- associated with behavioral economics have also produced promising results).
Cigarettes are a different story. Why? Because even though there are again many brands of cigarettes, they are typically sold at roughly the same price. An indirect tax can thus prove effective but only if it is high enough (very high) so that the post-tax price rises to the elastic section of the demand for cigarettes curve. Remember that PED is affected by the number and closeness of available substitutes, whether the good is addictive (tobacco is very addictive) but also, and most importantly, by the proportion of income spent on the good. So a low indirect tax will not lead to a significant decrease in smoking (but it will fill the state's coffers with a lot of tax revenues) and will thus prove ineffective. But a very high tax has a greater chance of proving effective because if smokers continue to smoke as much, their monthly expenditure on cigarettes will become a much too high proportion of their monthly income and many will be forced to cut back and even kick the habit as all are aware of the fact that smoking is a killer.
But what about 'close substitutes'? That's a big one these days. In order for a tobacco tax to prove effective it must be imposed on all tobacco-related products and this will have to include heat-not-burn nicotine delivery systems (like IQOS, devised and marketed by -take a guess- Philip Morris International, one of the biggest 'big tobacco' companies) and e-cigarettes (like JUULs). In addition, the state must make sure that no illegal markets arise (relatively easy if there is the political will).
So, assume that with the high taxes that many countries have imposed and with the impact other necessary complementary policies sales of cigarettes do go down in many advanced economies
Well, unfortunately this would not be the end of the story for the huge tobacco multinationals.
Watch this (very short): Big Tobacco Goes South
In the search for new consumers, Big Tobacco is setting its sights on markets in the Global South, using the same tactics that hooked smokers in rich countries decades ago. But with weak health-care systems and low regulatory capacity, the developing world will have a harder time fending off the industry’s marketing blitz.
Remember though that in many countries in the South, the State needs high tax revenues to be able to finance pro-development projects: so they are caught between a rock and a hard place...
PS: I've quit very many years now but the first couple of years of my graduate work in the States I was, unfortunately, a smoker. I still remember when, late one night, I ran out of cigarettes and, not having a car during my 1st year, I called a cab to get to the nearest ‘Store 24’ and buy me a pack. The driver took me there and when he saw what I bought, he remarked “Oh, you went to buy coffin nails, I see’. Still, haven’t forgotten his comment.