How does the money multiplier differ when currecy holdings are zero, compares to if then are greater then zero

Question

How does the money multiplier differ when currecy holdings are zero, compares to if then are greater then zero

Answer 1

Money multiplier is smaller.  A bank lends out all of its excess reserves, and if no extra currency is held by the nonbank public, all of the loan proceeds will get deposited in other banks, which will gain deposits and reserves, and be able to lend out more, depending on the size of the required reserve ratio (which determines the simple money multiplier (1/r) in your textbook). But if some of the loan proceeds are held as currency and not redeposited, some of the new loans won't be made and the money multiplier will be smaller.  Same is true if banks hold some excess reserves.