Short-run trade-off between unemployment and inflation

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What really is the Philips Curve as explained in this chapter 28 and why is it important to Economics?

Although today the short-run trade-off between unemployment and inflation plays a role in the Fed's monetary policy decisions, this trade-off was not widely recognized until the late 1950s. In 1957, New Zealand economist A. W. Phillips plotted data on the unemployment rate and the inflation rate in Great Britain and drew a curve showing their average relationship. Since that time, a graph showing the short-run relationship between the unemployment rate and the inflation rate has been called a Phillips curve. (Phillips actually measured inflation by the percentage change in wages rather than by the percentage change in prices. Because wages and prices usually move together, this difference is not important to our discussion.)

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