Take a look at panel (b) of Figure 17-4, and suppose that the economy initially operates at point $A$, at which the inflation rate is $0$ percent and the unemployment rate is $6$ percent, which is the natural rate of unemployment. Then the inflation rate increases to $3$ percent. Does reduced cyclical, frictional, or structural unemployment account for the resulting decrease in the unemployment rate at point $B$ ? Explain briefly.

Suppose that the greater availability of online job placement services generates a reduction in frictional unemployment during an interval in which the inflation rate remains unchanged. Would the result be a movement along or a shift of the short-run Phillips curve? Explain your reasoning.

Suppose that economists were able to use U.S. economic data to demonstrate that the rational expectations hypothesis is true. Would this be sufficient to demonstrate the validity of the policy irrelevance proposition?

Explain whether the cyclical unemployment rate is positive, zero, or negative at the point $E_2$, after the shift in the aggregate demand curve from $A{D}_1$ to $A{D}_2$. In addition, explain whether the cyclical unemployment rate is positive, zero, or negative at a point $E_3$, following the shift in the short-run aggregate supply curve from $SRAS$, to $SRAS$.

Consider the diagram below, which is drawn under the assumption that the new Keynesian sticky-price theory of aggregate supply applies. Assume that at present, the economy is in long-run equilibrium at point A. Answer the following questions.

a. Suppose that there is a sudden increase in desired investment expenditures. Which of the alternative aggregate demand curves- $A{D}_2$ or $A{D}_3$-will apply after this event occurs? Other things being equal, what will happen to the equilibrium price level and to equilibrium real GDP in the short ran? Explain.

b. Other things being equal, after the event and adjustments discussed in part (a) have taken place, what will happen to the equilibrium price level and to equilibrium real GDP in the long run? Explain.

Evaluate the following statement: "In an important sense, the term policy irrelevance proposition is misleading because even if the rational expectations hypothesis is valid, economic policy actions can have significant effects on real $GDP$ and the unemployment rate."