The FOMC has instructed the FRBNY Trading Desk to purchase $$510$ million in U$.$S$.$ Treasury securities$.$ The Federal Reserve has currently set the reserve requirement at $10$ percent of transaction deposits. Assume U$.$S$.$ banks withdraw all excess reserves and give out loans.

a$.$ Assume also that borrowers eventually return all of these funds to their banks in the form of transaction deposits. What is the full effect of this purchase on bank deposits and the money supply?

b$.$ What is the full effect of this purchase on bank deposits and the money supply if borrowers return only $90$ percent of these funds to their banks in the form of transaction deposits?