Though the behavior of central bankers suggests the answer is obvious, it is, in fact, not.  If you pick up your standard textbook on macroeconomic theory, you will get answers like those provided by Greg Mankiw a couple of months back: "shoe leather"costs (associated with the opportunity costs of holding money instead of other financial assets), the regressivity of the so-called inflation tax, and the empirical relationship between the level of the inflation rate and the volatility (and presumed uncertainty) of average changes in prices.  The problem is that shoe leather costs (and related distortions) are usually found to be tiny, it is not so clear whether the inflation tax is regressive or progressive, and theoretical explanations (i.e. good stories) for why uncertainty is related to high inflation are few.

To put it another way, standard macroeconomic theory does not provide a ready answer to the question "Why we should we strongly prefer a steady, predictable rate of inflation in the low single digits to a steady, predictable rate of inflation in the range of, say, 10-15%?".  In a recent Cleveland Fed Economic Commentary, John Boyd and Bruce Champ suggest an answer.

First, some theory:

There is good reason to believe that inflation is harmful even at what one might consider relatively moderate rates—annual rates of perhaps 5 to 10 percent...

... theories suggest that inflation may damage financial markets or impede their smooth operation...

One way inflation might affect economic growth through the banking sector is by reducing the overall amount of credit that is available to businesses. The story goes something like this. Higher inflation can decrease the real rate of return on assets. Lower real rates of return discourage saving but encourage borrowing. At this point, new borrowers entering the market are likely to be of lesser quality and are more likely to default on their loans. Banks may react to the combined effects of lower real returns on their loans and the influx of riskier borrowers by rationing credit. That is, if banks find it difficult to differentiate between good and bad borrowers, they may refuse to make loans, or they may at least restrict the quantity of loans made...

But there is something peculiar about the effect of inflation on the financial sector: It appears to have important thresholds. Only when inflation rises above some critical level does rationing occur. At very low rates of inflation, inflation does not cause credit rationing.

And the evidence:

... the theories have several testable hypotheses. We consider two of them. First, as inflation increases beyond some point, bank lending should decrease. Second, inflation should lower real returns on assets...

Our empirical work lends support to the theories. We find that the size and profitability of the banking sector both are negatively associated with inflation. Further support comes from survey data, which seem consistent with the notion that banks may ration credit as inflation rises...

For countries with inflation rates above 5 percent or 10 percent, the results here are strongly suggestive. A reduction in inflation should have a favorable impact on the country’s financial system. By stimulating investment activity, such a reduction in inflation should have a beneficial impact on real economic activity.

Boyd and Champ also discuss how the same theory and evidence helps support the evident desire of central bankers to avoid deflation.  In discussing related research several years ago, I offered this conclusion:

On the basis of observing central bank decisionmaking today, the dominant definition among monetary policymakers of the “right” inflation goal seems to be somewhere between 1 percent and 4 percent. To be sure, the book on this subject is far from closed. But as we confront this conclusion with economic theory and real-world evidence, the sense of today’s central bankers looks more and more like wisdom.

I stand by that sentiment.