Suppose that natural real GDP (YN) equals $12,000, the Federal Reserve’s desired real federal funds rate (rFF*) equals 2.5 percent, and its desired inflation rate (P*) equals 2 percent. Initially, an asset bubble collapses, which results in a negative demand shock. It is then followed by an upsurge in government spending those results in a positive demand shock. You are given the following combinations of actual inflation and real GDP: (1.0, $11,400); (1.5, $11,700); (2.0, $12,000); (2.8, $12,480); (2.4, $12,240).
(a) For each level of real GDP, compute YN = 100(log(Y/YN)).
(b) Explain what each of the following pairs of values for the parameters a and b in equation (14.1), the equation for the Taylor Rule, means in terms of how the Fed weighs inflation against output: (0.5, 0.5); (1/3, 2/3), if real GDP is less than natural real GDP, and (2/3, 1/3), if real GDP exceeds natural real GDP; (0.0, 1.0); (1.0, 0.0). In particular, which combination might be referred to as unemployment targeting and which combination might be referred to as inflation targeting?
(c) Use the Taylor Rule as given by equation (14.1) to calculate the real federal funds rate for the given combinations of inflation and real GDP when a = b = 0.5.
(d) Use the Taylor Rule as given by equation (14.1) to calculate the real federal funds rate (rFF) for the given combinations of inflation and real GDP when a = 1/3 and b = 2/3 if real GDP is less than natural real GDP, and when a = 2/3 and b = 1/3 if real GDP exceeds natural real GDP.
(e) Use the Taylor Rule as given by equation (14.1) to calculate the real federal funds rate for the given combinations of inflation and real GDP, when a = 0 and b = 1.
(f) Use the Taylor Rule as given by equation (14.1) to calculate the real federal funds rate for the given combinations of inflation and real GDP, when a = 1 and b = 0
(g) Use your answers to parts c–f to explain why the greater the weight the Fed places on output, the greater the variation in the real federal funds rate.
(h) Use your answers to part g and your knowledge of the monetary policy effectiveness lag to discuss how the weight the Fed places on inflation relative to output affects how long it takes for the economy’s output to return to natural GDP after a demand shock, all other things being equal.