Question

Suppose that the Fed's inflation target is 2%, potential output growth is 3.5%, and velocity is a function of how much the interest rate differs from 5%: %^V= 0.5 X (i-5). Suppose that a model of the economy suggests that the real interest rate is determined by the equation r= 8.35-%^Y where Y is the level of output, so %^Y is the growth rate of output. Suppose that people expect the Fed to hit its inflation target.

Calculate the optimal money growth rate needed for the Fed to hit its inflation target in the long run.