Final answer:
The money supply increases as the Fed's purchase of a government bond from Gilberto leads to a deposit in Gilberto’s checking account, which can then be loaned out and multiplied throughout the banking system.
Step-by-step explanation:
that the money supply increases when the Fed buys government bonds and the funds are deposited into Gilberto’s checking account. Given that the required reserve ratio (r) is 20%, the bank must hold $300,000 ($1,500,000 x 0.20) in reserves. However, the remaining $1,200,000 can be loaned out, potentially increasing the money supply as those funds circulate through the economy. This is because, in a fractional reserve banking system, banks can lend out a portion of their deposits, creating new money in the process.
When the Fed conducts an open market operation like purchasing bonds, it injects liquidity into the banking system, which can then be multiplied through the lending process. The initial deposit of $1,500,000 will have a money multiplier effect, where a single dollar of reserves can ultimately support several dollars of money supply through successive rounds of banking transactions and lending.