How is 2% inflation different from 3% or 4%?

In his dedication to educating the public about the zero bound, Paul Krugman has asked several times (most recently today):

. . . what calculation leads to the notion that a target of “close to but less than 2%” is appropriate, as opposed to, say, 3 or 4 percent.

I think I know the answer: An inflation rate of 2% is small enough that price changes due to inflation are unnoticeable in the noise of other price changes, even over periods of a few years.

Among the costs of inflation are those that come from uncertainty about not only future prices, but also about current prices.

When inflation is under 2%, the price of a cookie at the local bakery might remain unchanged for years at a time. I can stop by the bakery with exact change, and be reasonably confident that I’ll be able to buy one. The costs of flour, sugar, and chocolate will vary over time—but some will rise and others will fall, and the bakery will be able to hold the line on the price of a cookie. This is a convenience for me. It’s also good for the bakery, because people who are confident that they have enough cash in their pocket to buy a cookie are more likely to stop and get one. If they had to make a stop at the ATM first to get cash—or worse, be sent away to visit an ATM mid-transaction—they might not.

At some point—and I assert that the point turns out to be slightly above a 2% inflation rate—stores find that it’s necessary to raise prices at least annually, just to keep up with inflation.

Even if the inflation rate is known and not a surprise, there’s still the threshold effect of one day the price is $x and the next day it’s $x+3%.

When the inflation rate is below 2%, prices can remain stable for years at a time—long enough for people to learn what they are. And that knowledge can make their day run more smoothly. They can be sure they have appropriate cash on hand. They don’t need to check prices ahead of each transaction.

When the inflation rate is above 3%, stores might need to raise prices twice a year, to avoid falling behind. When the prices of a hundred things are all being raised more often than annually, it becomes impossible to learn what prices are, and impossible for that knowledge to make the day run more smoothly. All of a sudden, you have to pay attention to price changes, because they’re happening all the time. In advance of every transaction, you need to allow for the fact that maybe today is the day that prices went up several percent.

Some prices change all the time anyway, especially where the item being sold is a single commodity, such as milk or gasoline. For exactly this reason, prices of those items are often prominently displayed—to reduce the transaction effort of the consumer who wants to know what the price is going to be.

I think that’s why 2% inflation is different from 3–4% inflation: Because price changes due to inflation begin to stand out from changes in relative prices, adding another whole layer of informational costs on every purchaser, on every purchase.