An economy has the following money demand function: (/)^d = 0.5Y / i^0.5 .

(a) Derive the function of velocity and explain the intuition. (please explain the intuition behind the function in detail)

(b) Calculate velocity if the nominal interest rate i is 1 percent (i.e., 0.01).

(c) If output Y is 1,000 units and the money supply M is $1,200, then what is the price level (the nominal interest rate is still 1 percent)?

(d) Suppose the appointment of a new central bank governor increases the expected inflation rate by five percentage points. What is the new nominal interest rate according to the Fisher effect?