It's worth noting that this is at least a debatable assumption. Imagine a world with two goods—beer and bourbon—such that beer is cheaper per unit of alcohol than bourbon, but bourbon is tastier. Drinkers arrive at some kind of beer/bourbon mix based on their desires to (a) get drunk, (b) drink something tasty, and (c) have money left over for other activities. Now the price of beer falls. One possibility is that people shift consumption from bourbon to beer, holding total alcohol consumption constant and freeing up expenditures for non-booze purchases. Another possibility is that people hold spending and bourbon consumption constant and drink more beer. Yet another possibility is that people hold total spending and total alcohol consumption and use the budgetary headroom opened up by cheaper beer to buy less beer and extra bourbon.
It all sort of depends on what people want to do and what constraints they're operating under. If you're a lush or a cheapskate then, yes, cheaper beer means you'll drink more beer. But there are other possibilities.