Question Unconventional Monetary Policy case study

spread between the three$-$month US dollar London Interbank Offered Rate $($LIBOR$),$ a survey interest rate at which large, internationally active banks report they can obtain three$-$month US dollar loans from each other, and the interest rate on three$-$month US Treasury Bills $($T$-$Bills$)$ was approximately $15$ basis points. By late March $2020,$ the spread between the $3-$month LIBOR and the $3-$month US T$-$Bill was $140$ basis points.

$1.$ Assuming that the T$-$Bill market is always highly liquid, what do you conjecture would happen to the availability of credit to firms and households from February to March $2020?$ What does it mean for a market to be liquid? What does this mean in reference to equation $(4)$ in the notes above?

$2.$ What is the intuition for equation $(4)?$ The expectations theory suggests that the long$-$term rate is equal to a weighted average of the current and expected future short$-$term spot rates. What does equation $(4)$ suggest about the relationship between the long$-$term rate and the weighted average of the current and expected future short$-$term spot rates?

$3.$ What is to make of the assumption that the T$-$Bill market is always highly liquid? What are the main drivers of the $3-$month T$-$Bill rate?

$4.$ If $0$i$0,$N is taken to be the $3-$month LIBOR and the $3-$month T$-$Bill is taken to be a good approximation of the $$average of short rates,$$ then what is $\backslash$sigma N $($that is$,$ what is its value$)?$

$5.$ What does this spread imply for the real economy? In particular, what does this imply for the availability of credit to businesses and consumers?

$6.$ What would you recommend the Fed to do$?$ How should the Fed go about doing it$?$

$7.$ Fast forward a few years $($today$,$ February $19,2022).$ The economy has recovered and output is above its full$-$employment level. What would you recommend the Fed do$?$ How should the Fed go about doing it$?$ Show graphically.