Fisher’s Equation of Exchange
MV_T = PT
T =  # transactions in a year
V_T = “transactions velocity”
M = any measure of the money supply,
e.g. M1
P = $ amount of an average transaction

Fisher’s Equation of Exchange: Income version
MV_Q = PQ
Q = real GDP = income (sometimes Y)
V_Q = “income velocity”
M = any measure of the money supply,
e.g. M1
P = price level

Note
T > Q
So, transactions velocity is greater than income velocity

M3 > M2 > M1
So, M3 velocity is greater than M2 velocity or M1 velocity

Money Demand Equation
Solve MV = PY for M
M = (1/V) PY
define k = (1/V)
M = kPY

k = (1/V) = M/PY
V = 1/k = PY/M

Motives for holding money
Transactions demand
Precautionary demand
Speculative demand

Each increase as income increases
Each decrease as r increases (opportunity cost of holding money)

Estimating money demand functions
M/P = f(Y,r,Z)
Z = financial technology scale variable
M/P = Z(Ya)(rb)

Put in logartithms:
ln(M/P) = [ln(M) – ln(P)]
= ln(Z) + a[ln(Y)] + b[ln(r)]