I want to contrast inflation to the cost of living. In casual language, we often interpret a rise in the cost of living as inflation. They are not the same thing. Cost-of-living increases are a result of increases in individual prices relative to other prices and especially relative to income. These relative price movements reflect supply and demand conditions and idiosyncratic influences in the various markets for goods and services. If some component of a household's cost-of-living basket goes up in price, the higher cost of living is not ipso facto inflation.
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The Fed, like every other central bank, is powerless to prevent fluctuations in the cost of living and increases of individual prices. We do not produce oil. Nor do we grow food or provide health care. We cannot prevent the next oil shock, or drought, or a strike somewhere —events that cause prices of certain goods to rise and change your cost of living.