The banking system currently has $10 billion of reserves, none of which are excess. people hold deposits and no currency and the reserve requirement is 10%. if the fed raises the reserve requirement to 20% and as the same time buys $1 billion of bonds, then by how much does the money supply change?

money supply will decrease by $45 billion

Explanation:

the current money multiplier = 1 / reserve ratio = 1 / 10% = 10, but the new money multiplier will be = 1 / 20% = 5

if the banks' total reserves are $10 billion, then the total deposits are $100 billion

the new reserve ratio will decrease the money supply by $50 billion ( = $10 billion in extra reserves x 5). At the same time, the money injected by the Fed with the purchase of $1 billion in bonds will increase the money supply by $1 billion x 5 = $5 billion.

The net effect will be - $50 billion + $5 billion = - $45 billion