$6.$Suppose that Bob withdraws $$100$ of cash from his checking account at Security Bank and uses it to buy a camera from Joe, who deposits the $$100$ in his checking account in Serenity Bank. Assuming a reserve ratio of $10$ percent and no initial excess reserves, determine the extent to which $($a$)$ Security Bank must reduce its loans and demand deposits because of the cash withdrawal and $($b$)$ Serenity Bank can safely increase its loans as demand deposits because of the cash deposit. Have the cash withdrawal and deposit changed the money supply?