If banks wish to hold excess reserves equal to 3% of deposits and the public withdraws 10% of every deposit in cash, how will a $1 million open market purchase by the Fed affect banking system deposits?

To understand why the correct answer is that the impact on banking system deposits will be more than $1 million but less than $10 million, we must consider the effects of the open market purchase and the reserve requirements.

When the Federal Reserve purchases $1 million in securities, it injects that amount into the banking system. This action increases the reserves of banks by $1 million. In a typical banking system, banks can create money through the process of fractional reserve banking, which involves lending out a portion of their deposits while keeping a fraction as reserves.

In this scenario, banks wish to hold excess reserves equal to 3% of deposits. That means if banks hold $X in deposits, they want to keep 0.03X as excess reserves. Additionally, the public withdraws 10% of every deposit in cash. This means that for every dollar deposited, banks will need to ensure they have enough reserves not only to cover the required reserves but also to account for the public's tendency to withdraw a portion of those deposits.

First, let's look at the reserve requirement: banks need to keep enough reserves to cover the cash withdrawals. If the public withdraws 10% of every deposit, for each $1 in deposits, banks need to