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Please explain this step by step, how was the graph obtained? thats all you need to explain In 1993, the American economist John Taylor showed

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Please explain this step by step, how was the graph obtained? thats all you need to explain

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In 1993, the American economist John Taylor showed that US monetary policy in the period 1982-1991 could be described reasonably well by the following simple decision rule: i=r+x +0.5 (1 - x) +0.5Y, where i is an estimate of the normal real rate of interest and 7 is the inflation tar- get of the central bank. If we assume that expected inflation is equal to observed inflation, the implication is that the expected real rate is equal to r=i-1 =r+0.5 (1 - x) + 0.5Y. The real interest rate is higher if inflation is above target. Taylor assumed that the normal real interest rate and the inflation target were both 2 percent, i = 1 = 0.02, leading to the decision rule i= 0.02 + 7 + 0.5 (x - 0.02) + 0.5Y = 0.01 + 1.5x + 0.5Y. Fig. 10.6 illustrates how the interest rate responds to inflation if the output gap is zero. If expected inflation is equal to past inflation, the expected real rate is the difference between the interest rate and inflation. If inflation is on target - 2 percent - the nominal interest rate is 4 percent and the real interest rate is 2 percent, which is assumed to be the normal real rate. If inflation is 4 percent, the central bank sets the interest rate at 7 percent, making the expected real interest rate equal to 3 percent. For every percentage unit that inflation rises above the target, the real rate increases 0.5 percentage units.Fig. 10.6 The Taylor Rule Inflation 2 8 5 6 Inflation Interest rate Note: Interest rate and inflation are shown in percentage units

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