Why is the prime rate typically 3% higher than the fed funds rate? What is the right framework to think about the prime rate in relation to the fed funds rate?
Idea 1: A bank is safer to lend to than even trustworthy institutions so there's a premium on prime rates. Why is this true though? I could imagine several institutions with great credit could be safer than some banks. Is there something that makes a loan to a bank safer?
Idea 2: A bank can borrow at the fed funds rate. So banks could borrow at fed funds and lend to customers at higher rates. If their borrowing rate changes, their lending rate changes with it to reflect their cost. Perhaps though this is uncommon because lending on borrowed capital would inherently have a smaller margin than lending on unborrowed capital, so it would be hard to compete with borrowed capital.
Basically the causality can come from the fact they can lend at the fed funds rate or borrow.
The Prime Rate in the US is supposed to represent the rate at which banks make loans to customers.  For many years is has been set at Fed Funds+300bp, whereas the rate at which banks actually make loans varies a lot depending on the creditworthiness of the borrower.