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