We have assumed that the coefficients in the Taylor rule, ay and aπ, are both positive. Under this assumption, the rule guides the economy back to long-run equilibrium after a shock. The output gap eventually returns to zero, and inflation returns to its long-run level πT.
a. Suppose the inflation coefficient aπ is positive but the output coefficient ay is zero. Does the economy still return to equilibrium with 0 and π - πT after a shock? Explain.
b. How is the answer to the previous question different if ay is positive and aπ is zero? Explain.