In the early stages of the $2008$ economic contraction, the Federal Reserve $($central bank$)$ responded with aggressive easing of monetary policy. However, the economy continued to contract in spite of the policy.

a$.$ Fully explain the process of money creation by the Federal Reserve and how it works via the fractional reserve banking system.

b$.$ Explain how the economy's money supply can remain rather unchanged in spite of large increases in the monetary base.

c$.$ Are there other tools the Fed can use in these situations to stimulate the economy and how were they used in $2008-2010$ and $2020$ during the covid response?