The Multiplier, Growth and Money and Banking: Question 4

Worked solution

Part (a): Two functions of a commercial bank

Besides accepting deposits, commercial banks:

• Lend money to households and firms, through loans and overdrafts, earning interest income.
• Provide a payments system, allowing customers to transfer money to one another (e.g. by electronic transfer, cheque or debit card) without needing to use cash.

(Other valid answers include holding or dealing in foreign currency and securities, or providing other financial services such as safe-keeping of valuables.)

Part (b): The bank credit multiplier

The bank (credit) multiplier is the reciprocal of the reserve ratio:

$\text{Bank credit multiplier} = \frac{1}{\text{reserve ratio}} = \frac{1}{0.08} = 12.5$

Part (c): Maximum increase in the money supply

Multiplying the initial deposit by the bank credit multiplier gives the maximum eventual increase in the money supply:

$\Delta \text{Money supply} = 12.5 \times 5{,}000{,}000 = 62{,}500{,}000$

So the money supply could rise by up to $62.5 million as a result of the initial $5 million deposit.

Part (d): How the credit creation process works

Bank Celoria is required to keep only 8% of the new $5 million deposit as reserves, that is $0.08 \times 5{,}000{,}000 = 400{,}000$ dollars, and is free to lend out the remaining 92%, which is $5{,}000{,}000 - 400{,}000 = 4{,}600{,}000$ dollars, to borrowers.

When these borrowers spend this $4.6 million, it becomes income for someone else, who is likely to redeposit at least part of it somewhere in the banking system, creating a new deposit. That bank, in turn, keeps 8% of this new deposit as reserves and lends out the remaining 92%, and the process repeats. Each round creating a smaller new deposit than the last, since 8% is withheld from reserves at every stage.

Crucially, both the original $5 million deposit and every new deposit created along the way count as part of the money supply (since bank deposits are money). Summing the initial deposit and every subsequent round of new deposits created gives a total increase in deposits, and therefore in the money supply, equal to the initial deposit multiplied by the bank credit multiplier, $\dfrac{1}{\text{reserve ratio}}$, which is exactly the $62.5 million found in part (c).

Part (e): A reason the actual increase might be smaller

Commercial banks are not obliged to lend out the maximum amount permitted by the required reserve ratio. If Bank Celoria and other banks in Larenta choose, for prudential or liquidity reasons, to hold excess reserves, reserves above the required 8%, then less than the full 92% of each deposit is actually re-lent at every stage of the process. This means fewer new loans (and so fewer new deposits) are created at each round than the theoretical maximum assumes, so the actual eventual increase in the money supply is smaller than $62.5 million.

(Other acceptable reasons include a “cash drain”, some of each loan being withdrawn and held as cash by the public rather than redeposited in the banking system, or a lack of demand from creditworthy borrowers, meaning banks are unable to lend out the full amount even if they wished to.)

Final answers

• (a) Any two of: lending money (loans/overdrafts); providing payment services; holding/dealing in foreign currency or securities
• (b) Bank credit multiplier $=$ 12.5
• (c) Maximum increase in the money supply $=$ $62.5 million
• (d) Only 8% of each deposit is held as reserves; the other 92% is re-lent, redeposited, and re-lent again in progressively smaller rounds, and the sum of all these new deposits equals the initial deposit times the bank credit multiplier
• (e) Banks may hold excess reserves above the required 8% (or a cash drain / weak loan demand may occur), so the actual increase in the money supply is smaller than the theoretical maximum