Question

Assume that no banks hold excess reserves and the public holds no currency (which implies that ER = C = 0). If a bank sells a $100,000 security to the FED, explain what happens to this bank (Bank A) and two additional steps (or two additional banks, Bank B and Bank C) in the deposit expansion process assuming a 10% reserve requirement. Put differently, what will be the change in deposits for the first bank (ΔDA), the second bank (ΔDB), and the third bank (ΔDC)?

Answer 1

To answer this question let's understand what it means to say that no bank holds excess reserve and public hold no currency. It means that apart from reserve requirement banks don't hold nay cash and lends all the money to public and then public don't hold any cash which means public keeps all its money with bank.

So let's see what happens when bank A sells security to FED worth $100,000. It means the bank A will get $100,000 from the FED. After it receives the money the bank A needs to keep 10% of it as reserve requirement with itself and then it can lend rest of the money to public. 10% of $100,000 is equal to $10,000. So, bank A keeps $10,000 and lends rest of the money that is $90,000 to public. Now suppose person A borrows $90,000 from bank A for some reason.

Let's assume person A uses the money to buy a car worth $90,000 and he pays for it with the money he borrowed. Now the seller of the car has a bank account with bank B.

Let's see second step of deposit and lending. The car seller puts his entire money that is $90,000 since public doesn't hold any cash into bank B. And now bank B will keep 10% of this money which is $9,000 keeps as a reserve requirement. The bank will then lend the rest of the money that is 90,000-9,000= $81,000 to public again. Now suppose some person B wants to borrow the money.

The bank B will lend to person B the entire amount which is $81,000 since the bank doesn't keep any excess reserve. Let's assume person B uses the money to buy some capital asset from person C and pays for it with the borrowed money. Now person C has $81,000 with him and given that public doesn't hold any cash it means he will deposit his entire money with his bank.

Now let's understand the third step of deposit in Bank C and lending. The person C has a bank account with Bank C. The person C puts his entire money which is $81,000 with bank C. Then bank C will keep 10% of $81,000 with itself as a reserve requirement and lend rest of the money as banks don't keep any excess reserve according to the question. 10% of $81,000 is $8,100 which means bank keeps $8,100 as reserve requirement and lends rest of it $81,000-$8,100 = $72,900.

So this is the three steps of deposit expansion and lending. ​​​​​​

The change in the deposits of bank A will be DA=​​​​ $100,000 and change in the deposits of bank will be DB= $90,000 and change in deposits of bank C will beDC= $81,000.

We can also calculate the deposit multiplier for the initial deposit of $100,000 in bank A. The deposit multiplier is nothing but the total money that will be created through continous process of lending and borrowing with 10% reserve requirement.

Deposit multiplier = 1/RR where RR= reserve requirement which is equal to 0.1or 10%

In this case deposit multiplier will be equal to,

DM = 1/0.1 = 10.

So if we keep following the process that we have followed for the first three banks namely, A, B and C the total money deposited and created in the economy will be 10 times of the initial deposit in bank A. And we know the initial deposit was $100,000 thus total money created will be = 10×100,000 = $10,000,00.

I hope I was able to help you. Feedback will be appreciated.