Suppose the relationship between H/P and p is given by H/P = 8 - 0.8p

Here, H/P is real high-powered money, in billions of dollars, and p is the rate of inflation, in percent. Define the inflation elasticity of real high-powered money, η, as η = -%∆(H>P)>% ∆p = -(p/[H/P])(∆[H/P]/∆p)

(a) If the current rate of inflation is 5 percent, what are H/P, pH/P, and η?

(b) If p falls to 4 percent, what are H/P, pH/P, and η?

(c) If p rises to 6 percent, what are H/P, pH/P, and η?

(d) On the basis of these calculations, can you formulate a relationship between pH/P and η?