Dear Ask the Economist:
Could governments simply fight inflation by destroying (shredding, burning, melting) their currency? Why don't they?
First, we must be careful to operate from the best definition of inflation. Though it is commonly thought of as "rising prices," I am among the many economists who prefer the more traditional (and ultimately, more meaningful) definition: "an increase in the quantity of money and credit." Rising prices are simply one of the effects of inflation; first you have the inflation in the form of an increase in money and credit and then as an aftereffect we experience rising prices.
Having defined inflation that way, the answers to your questions become clearer. Since government increases the supply of money directly and increases the credit supply indirectly through the banking system, then yes, government can certainly decrease inflation by destroying some of the very currency it first created. If such destruction is not offset by increases in new currency or credit, and all other things remaining equal, then one of the effects of the destruction of currency would be for prices to rise at a slower pace or even decline.
The government does indeed destroy some of its currency now, but that activity is confined to the destruction of old bank notes that have become excessively soiled or torn. The average life of a dollar bill, for instance, is less than two years. This currency destruction probably has no impact on prices in the marketplace because it's not a significant quantity at any one time and is usually if not always offset by new, replacement notes.
Could the government actually cause prices to stop rising or even decline by a larger, net decrease in currency through the methods of destruction you suggest? Theoretically, yes. But even then, it is important to understand that paper currency is a relatively small portion of the total monetary base. Bank reserves and credit are much larger and the government can greatly affect those elements through Federal Reserve policy: raising or lowering its discount rate, buying or selling government bonds, and regulating reserve requirements. These methods are actually the primary tools the monetary authorities of the government employ to raise or lower the money supply and thereby affect prices.
Why doesn't the government destroy more currency to deal with the problem of rising prices? As explained above, paper currency is a small component of our total purchasing power. Burning paper money as a way to affect prices would be a very inefficient way to deal with the problem and would have minor impact in any event. The Federal Reserve prefers to use its more powerful tools that I outlined in the previous paragraph. Personally, I think these tools represent excessive government control over the money supply and the economy, but that's another matter altogether.