Let the Symbol $\pi$ Stand for the Rate of Inflation, with E

Essay

Let the symbol $\pi$ stand for the rate of inflation, with E $\pi$ the expected inflation rate, both measured in percent. The letter u is the unemployment rate and uⁿ is the natural rate of unemployment. Suppose the short-run Phillips curve is u = uⁿ - $\alpha$ ( $\pi$ - E $\pi$ ) applies in a certain economy. The Fed's loss function is L(u, $\pi$ ) = u + $\gamma$ $\pi$ ². The analysis in the appendix to textbook Chapter 18 shows that if the Fed minimizes its loss function under the assumption that E $\pi$ is fixed and "rational" private agents know this, the expected inflation rate will be E $\pi$ = $\alpha$ /2 $\gamma$ , and this will also be the inflation rate the government chooses. a. Suppose that $\alpha = 0.5$ and $y = 0.05$ . What are the expected and actual inflation rates?
b. Suppose $\alpha = 0.5$ and $y = 0.50$ . In this case, does the Fed have greater or lesser relative distaste for inflation than in part a? What are the expected and actual inflation rates with $\gamma =$ $0.50$ ? Why do they differ from the inflation rates in part a?