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Immediately after a disaster that knocks out the power, most people and businesses will still accept cash. But people nowadays don’t have much cash on hand, and the banks only keep a fraction of their balance sheets in their vaults.
If power isn’t quickly restored, it will soon become apparent that there isn’t enough paper money to facilitate a local economy. On the other end of the spectrum, there could be too much money due to hyperinflation. If that happens, money (both paper and digital) will become worthless.
If either of these things happens, people will have to resort to bartering for what they need. Tin Hat Ranch recently published a list of 20 SHTF barter items. Most of these items are things you should have on hand anyway, but you might want to stock extra items in case you need to trade with others.