Change in money supply

Question

Suppose a bank makes a loan of $1M to someone taking out a mortgage to buy a house by crediting that person's bank account with a deposit equal to the size of the mortgage. Suppose the required reserve ratio is 10%.

a)How much has the money supply increased by?

b)Does reserve or high powered money change? Why or why not?

What I did: $\frac{$1M}{0.10}$ = $10M (this will be the increase in money supply)

Because the reserve ratio is 10%, the reserve money changes by 10% of 10,00,000 = 1,00,000

Is this correct?

Answer 1

The person taking out the 1 million dollar mortgage will take the funds and use them towards buying a 1 million dollar home. If the home is sold by Joe who keeps his money under the pillow then in this scenario money supply does not increase at all. If, on the other hand, the party selling the home will deposit the 1 million dollars in his/her bank account with bank A, assuming a 10% reserve ratio, bank A will keep 100,000 dollars as reserves and lend out the remaining 900,000. Bank A lends these 900,000 to Bob, who will take them and deposit them with Bank B. As long as Bank B will again keep 10%, 90,000 in this case, and lend out the remainder - 810,000 to some other customer and if this chain continues in this fashion with no one keeping money under the pillow, then the overall money supply will increase by 1,000,000 + 900,000 + 810,000 + ... = 1,000,000/0.1 = 10,000,000. The banks will end up increasing their reserves by 100,000 + 90,000 + 81,000 + ... = 100,000/0.1= 1,000,000.

Answer 2

A) The money supply only increased by $1 million, since that is the increase in deposits.

B) Reserves are deposits at the central bank. A private bank extending a loan to a customer does not create a deposit at the central bank (or government-issued notes and coins). The bank would have to either have \$100,000 in excess reserves before making the loan, or borrow the reserves.