In the 1970s in the United States, the inflation rate and the natural rate of unemployment both rose. Let's use this model of time inconsistency to examine this phenomenon. Assume that policy is discretionary.

a) In the model as developed so far, what happens to the inflation rate when the natural rate of unemployment rises?

b) Let's now change the model slightly by supposing that the Fed's loss function is quadratic in both inflation and unemployment. That is, . Follow steps similar to those in the text to solve for the inflation rate under discretionary policy.

c) Now what happens to the inflation rate when the natural rate of unemployment rises?

d) In 1979, President Jimmy Carter appointed the central banker Paul Volcker to head the Federal Reserve. Volcker had a strong distaste for inflation. According to this model, what should have happened to inflation and unemployment? Compare the model's prediction to what actually happened.