How to Calculate the Monetary Base
The monetary base equals currency in circulation plus bank reserves, the money the central bank controls directly.
The Monetary Base formula
Calculator
Enter currency in circulation, bank reserves and the reserve ratio to get the base and the money supply it supports.
Cash and coin held by the public. Notes sitting in bank vaults belong with reserves instead.
Vault cash plus deposits banks hold at the central bank, required and excess together.
Enter 20 for 20%, which the calculator reads as 0.20.
Bonds the central bank buys. It adds to the base dollar for dollar, and a negative figure is a sale.
Currency in circulation plus bank reserves comes to $1,000 billion, the quantity the central bank sets directly.
- Deposit multiplier
- 5
- Maximum checkable deposits
- $1,000 billion
- Money supply the base supports
- $1,800 billion
- Currency share of the base
- 80%
- Base after the open market purchase
- $1,050 billion
- Change in the money supply
- $250 billion
One divided by a reserve ratio of 20% gives 5, the most each dollar of RESERVES can support in deposits.
Multiplier times reserves gives $1,000 billion, the ceiling on deposits once banks lend out every spare reserve. Currency in the public's hands is not lent out, so it plays no part here.
M1 is currency plus checkable deposits, so $800 billion of cash plus $1,000 billion of deposits gives $1,800 billion.
80% of the base is cash in the public's hands, and the rest sits as reserves that back deposits.
Paying for the bonds credits banks with new reserves, so the base moves to $1,050 billion.
The purchase works through the multiplier to shift the money supply by $250 billion, which is why base dollars are called high-powered.
How to calculate Monetary Base, step by step
- 1Add up currency in circulation. Count cash and coin held by the public. Notes sitting in bank vaults are reserves instead, so nothing gets counted twice.
- 2Add bank reserves. Reserves are vault cash plus the deposits banks hold at the central bank, required and excess together.
- 3Sum the two. Monetary base = currency in circulation + bank reserves. This is the quantity the central bank sets directly.
- 4Build the deposit multiplier. Deposit multiplier = 1 divided by the required reserve ratio written as a decimal, so a 20% ratio gives 5.
- 5Scale reserves up to deposits. Multiply the multiplier by RESERVES, not by the whole base. Currency the public is holding never reaches a bank, so no bank can lend against it.
- 6Add the currency back for M1. Maximum money supply = currency in circulation + maximum checkable deposits. The cash is already money; the reserves are what gets multiplied.
Worked example: Monetary Base
Suppose currency in circulation is $800 billion and bank reserves are $200 billion, so the monetary base = 800 + 200 = $1,000 billion. With an illustrative required reserve ratio of 20% (0.20), the deposit multiplier = 1 ÷ 0.20 = 5, so $200 billion of reserves can back at most 5 × $200 billion = $1,000 billion of checkable deposits. Adding the cash the public already holds gives a money supply of 800 + 1,000 = $1,800 billion. Currency is 800 ÷ 1,000 = 80% of the base. If the central bank then buys $50 billion of bonds, the base rises to $1,050 billion, and because that new money lands in the banking system as reserves, the deposits it supports rise by 5 × $50 billion = $250 billion.
Monetary Base questions
What is the difference between the monetary base and M1?
The base is currency in circulation plus bank reserves, while M1 is currency plus checkable deposits. Reserves count in the base but not in M1, and the deposits those reserves support count in M1 but not in the base.
Why is the monetary base called high-powered money?
Each dollar added to the base can support several dollars of deposits once banks lend it out, so the money supply moves by the multiplier times the change in the base rather than by the change alone.
How does a central bank change the monetary base?
Mainly through open market operations. Buying bonds pays the sellers' banks in new reserves and raises the base dollar for dollar, while selling bonds drains reserves and lowers it.
Can you multiply the whole monetary base by the money multiplier?
No, and it is the most common error on this calculation. The multiplier applies to reserves, because only reserves sit in banks that can lend them out. Multiply the whole base and you lend out the cash in people's pockets, which produces a deposit total far larger than the reserve ratio allows.
Why is the actual money supply smaller than the multiplier predicts?
Banks that hold excess reserves and households that keep cash outside banks are both leakages, so the real expansion stops short of the maximum the reserve ratio allows.
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