Explain the multiplier effect with example

Deposits and loans in banks give rise to an important multiplier effect. We use a simple example to illustrate this effect. Consider the bank K-bank with total deposits of 10,000 (millions or whatever). K-bank is aiming for a reserve ratio of 10% of deposits. At the moment it has lent 9,000 and has 1,000 in reserve - exactly meeting their desired reserve ratio.

Emma makes a deposit:       

Emma has 1,000 in her mattress and decides to deposit it in K-bank. The deposit will not affect the money supply but K-bank now has 11,000 in deposits, 9,000 in loans and 2,000 in reserves.

K-bank lends money:           

With deposits equal to 11,000, K-bank wants reserves to be 1,100, not 2,000. The bank therefore wants to lend 900, that is, 90% of the amount Emma deposited. The bank now lends 900 to Ashton.

Ashton borrows money:      

At the same moment K-bank lends 900 to Ashton, the money supply increases by 900. Emma's decision to transfer 1,000 from the mattress to the bank has the effect of increasing the money supply by 900. There are three ways Ashton can use the funds borrowed from K-bank. He can withdraw the funds in cash and keep the cash, he can keep them in his account at K-bank or he can spend them (or a combination of all three).

Ashton withdraws the money:        

If Ashton withdraws the funds in cash, K-bank will have 11,000 in deposits, 9,900 in loans and 1,100 in reserves. Thus, it will prefer not to lend any money until deposits increase.

Ashton keeps the funds in his account:

If Ashton decides to keep his funds with K-bank the deposits will increase by 900 the same instant it lends Ashton the money. K-bank will now have 11,900 in deposits, 9,900 in loans and 2,000 in reserves.

K-bank lends money again:

In the case where Ashton keeps his funds in his account at K-bank, the bank will want to increase lending further. In the next step, it will want to lend 90% of 900 or 810. When it lends 810, money supply will increase by 900 + 810 = 1,710 because of the deposit made by Emma. If the second borrower also decides to keep the funds in the bank, the bank can lend money a third time. In the third step it will lend 90% of 810 or 729. Note that the amount in each step will be smaller and smaller and if you add them, you will always end up with a finite amount.

...and we have a multiplier effect:

If all or some of the borrowers keep the borrowed funds in the bank, a deposit will generate an increase in the money supply which is larger than the initial deposit and this is what we call the multiplier effect. Remember that this effect is not guaranteed - had Ashton withdrawn the borrowed funds in cash, he would have broken the chain and the increase in money supply would have been equal to the deposit.

Ashton spends the money:

We had a third possibility: Ashton may spend the borrowed funds. Let's say that Ashton buys a stamp collection from Brittney for 900. If Brittney uses the same bank as Ashton, the funds will simply be transferred to Brittney's account. However, to K-bank, this makes no difference. K-bank will still want to increase its lending.

...will not disturb the multiplier effect:

If Brittney has a different bank, funds will be transferred from K-bank to Brittney's bank. In this case, K-bank will not be interested in lending any more money. However, in this case, deposits have increased in Brittney's bank and the multiplier effect continues in her bank. The only way the chain of the multiplier effect may be broken is if someone withdraws funds in cash and keeps the cash (if the cash is spent and it goes into an account - the multiplier effect will take off again). If some of the funds are withdrawn, the multiplier effect is weakened but not broken.