An economy has the following money demand function: (M/P)^d = .2Y/i^(1/2).
a) Derive an expression for the velocity of money. What does velocity depend on? Explain why this dependency may occur.
b) Calculate velocity if the nominal interest rate i is 4%.
c) If output Y is 1,000 units and the money supply M is $1,200, what is the price level P?
d) Suppose the announcement of a new head of the central bank, with a reputation of being soft on inflation, increases expected inflation by 5 percentage points. According to the Fisher Effect, what is the new nominal interest rate?
e) Calculate the new velocity of money.
f) If, in the aftermath of the announcement, both the economy's output and the current money supply are unchanged, what happens to the price level? Explain why this occurs.
g) If the new central banker wants to keep the price level the same after the announcement, at what level should she set the money supply?