Use the dynamic AD-AS model to solve for inflation as a function of only lagged

Question

Use the dynamic AD-AS model to solve for inflation as a function of only lagged inflation and supply and demand shocks. (Assume target inflation is constant.) According to the equation you have derived, does inflation return to its target after a shock? Explain. Suppose the central bank does not respond to changes in output hut only to changes in inflation, so that theta_y = 0. How, if at all, would this fact change your answer to part (a)? Suppose the central bank does not respond to changes in inflation but only to changes in output, so that theta_pi = 0. How, if at all, would this fact change your answer to part (a)? Suppose the central bank does not follow the Taylor principle but instead raises the nominal interest rate only 0.8 percentage point for each percentage-point increase in inflation. In this ease, what is theta_pi? How does a shock to demand or supply influence the path of inflation?

Explanation / Answer

a. A supply or demand shock will lead to an increase in current inflation. As the economy adjusts and returns to long-run equilibrium, the inflation rate will return to its target level. Note that the coefficient on the lagged inflation variable in the equation above is positive but less than 1. This means that inflation in time t + 1 will be less than inflation in time t, and that inflation will eventually return to its target rate.

b. If the central bank does not respond to changes in output so that Y is zero, then the economy will still return to its target inflation rate after a supply or demand shock because the coefficient on the lagged inflation variable in the equation above is still positive but less than 1. In this case, inflation should return more quickly to its target rate. This is because the coefficient on lagged inflation has become smaller (the change in the numerator is large in comparison to the change in the denominator). The dynamic aggregate demand curve is relatively flat when the central bank only cares about inflation.

c. If the central bank does not respond to changes in inflation so that is zero, then the coefficient on lagged inflation in the above inflation equation equals 1. In this case, the economy will not return to its target inflation rate after a demand or supply shock. The demand or supply shock will increase inflation in time t. When is zero, inflation in time t + 1 is equal to inflation in time t

d. The Taylor rule says that a one-percentage-point increase in inflation will increase the nominal interest rate by 1 + percentage points. If the central bank increases the nominal interest rate by only 0.8 percentage points for each one-percentage-point increase in the nominal interest rate, then this means is equal to –0.2. When is negative, the dynamic aggregate demand curve is upward sloping. A shock to demand or supply will set the economy on a path of ever-increasing inflation. This path of ever-increasing inflation will occur because real interest rates will continue to fall and output will remain above the natural level. You can see this phenomenon in the above equation for inflation: If is negative, the coefficient on lagged inflation is greater than 1. That larger than-one coefficient is the mathematical manifestation of explosive inflation.

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.