In the simple deposit expansion model,a decline in checkable deposits of $500 when the required reserve ratio is equal to 10 percent implies that the Fed

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In the simple deposit expansion model, the required reserve ratio is the percentage of deposits that banks are required to hold in reserves. If there is a decline in checkable deposits, it means that banks are holding fewer reserves than required. To restore the required reserve ratio, banks need to reduce their lending activities, which will decrease deposits. This reduction in lending ultimately leads to a contraction in the money supply. To achieve this contraction, the Fed sells government bonds to banks, and in return, banks pay the Fed with a fraction of their deposits. The decrease in deposits implies that banks need to pay the Fed less, so they hold fewer reserves, which means they can lend even less. Therefore, a decline in checkable deposits of $500 when the required reserve ratio is equal to 10 percent implies that the Fed sold government bonds worth $50 (10% of $500) to banks.

In the Simple Deposit Expansion Model,a Decline in Checkable Deposits