1. Assume that total reserves are equal to $200 and total checkable bank deposits are equal to $1,000. Also assume that the public does not hold any currency. Now suppose that the required reserve ratio falls from 20% to 10%. Trace out how this leads to an expansion in bank deposits.
Since they only have to hold $100 in reserves, instead of $200, banks now lend out $100 of their reserves. Whoever borrows the $100 will deposit it in a bank, which will lend out $100 × (1 − rr) = $100 × 0.9 = $90. Whoever borrows the $90 will put it into a bank, which will lend out $90 × 0.9 = $81, and so on. Overall, deposits will increase by $100/0.1 = $1,000.