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Whiskey is the product of fermenting a barley mash, then distilling it and aging it in oak barrels. That is just as true now as in the 20th and 19th and 18th centuries. Yes, the scale of production is eased by modern automation and technology, but the scarcity of modern quality oak is as great a factor in the price of oak barrels as the reduced craftsmanship required in making them.
The reason aged whiskey is so much more expensive than younger has to do with the cost of the long storage. The cost of the barrels is much less even considering that the barrels must be refilled regularly as some of the whiskey evaporates through the oak and is replaced by oxygen. It is the very gradual exposure to trace amounts of oxygen that causes the oxygen (thus why product in screw-top bottles ceases aging), but the process must be kept very gradual for optimum effect.
Also, barrels can be reused, and previously used barrels are actually preferred for the longest malt Scotch whiskeys:
It didn’t take long for distillers to realize that the original cask contents - the dark, sweet, fortified wines - could beneficially mellow maturing whisky. Badly distilled whisky could be disguised, young whisky made to seem older. These prized casks were hand-coopered from European oak, Quercus robar, found across the mid latitudes of Europe. And the French used it too, for wine, but also for warships.
Update (World's Most Expensive Scotch Whiskies - my emphasis):
Yet another product of the Dalmore Distillery, Trinitas is so named because only three bottles of this expensive whisky have been made. The whisky is a blend of rare stocks, including some that have been maturing at the distillery for more than 140 years. Two bottles were sold in Glasgow in 2010, one to a US-based collector and one to a UK-based investor. It is the first Scotch to sell for six figures.
Note that there is a natural limit to how long a whiskey can be barrel-aged, depending on the initially available. There is a slow evaporation through the oak barrel, requiring regularly refilling of some barrels from others. Once the level in the last barrel drops below the refill threshold it must be decanted into successively smaller barrels, with any remainder consumed (I volunteer for barrel refilling!), until the volume drops below that of the smallest practical barrel.
... Bourbon, for example, is aged in brand-new barrels in relatively dry conditions. By comparison, scotch is aged in previously used barrels in a relatively humid climate.
What distinguishes these two approaches is what Pickerell refers to as “the tea-bag effect”: The first time a tea bag (or barrel) is used, there’s more flavor to draw out. Resting in brand-new barrels, bourbon needs less time to extract what Pickerell calls “wood goodies”—it sucks vanilla and caramel flavors, as well as spice-like notes, out of the wood with ease. Many of those same bourbon barrels, once emptied, make their way to Scotland, where they are used to age Scotch whisky. At this point, most of the “wood goodies” have been depleted, so scotch often needs a longer aging time to suck out the remainders. Evaporation plays a role, too: In the dry climate favored by bourbon distillers, liquid evaporates more quickly, and the product becomes concentrated more quickly.