Exercise 3: What Real Option Runs Out at Zero Interest Rates — Possible Solution
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The central bank's standard, everyday tool for stimulating a weak
economy is cutting its own benchmark interest rate further, making
borrowing cheaper and saving less attractive, exactly as Exercise 1's
own mechanism describes. That tool works by moving the rate DOWNWARD
from wherever it currently sits.

An interest rate has a real, practical floor near zero (or, in some
cases, only slightly below it) - you can't meaningfully keep cutting a
rate that's already sitting at 0.10%, the real historic low the Bank
of England actually reached in March 2020, by anywhere near the same
kind of magnitude a normal rate cut involves. There's simply very
little room left to move the number down any further as a way of
making borrowing cheaper still.

Once that standard downward lever has essentially run out of usable
room, quantitative easing becomes necessary specifically because it
achieves a similar underlying goal (lowering borrowing costs and
encouraging economic activity) through a genuinely different real
mechanism - directly creating new reserves to buy assets like
government bonds, which pushes those assets' prices up and their
yields (effectively, longer-term borrowing costs) down, without
requiring the short-term interest rate itself to move any further.

ANSWER: Quantitative easing became necessary once the interest rate
had already been cut close to its real practical floor near zero (the
actual 0.10% low reached in March 2020) - at that point, the standard
tool of cutting rates further to stimulate the economy had essentially
run out of usable room, so QE provided an alternative real mechanism
(directly buying assets to lower longer-term borrowing costs) to
achieve a similar stimulating effect.

WHY THIS WORKS AS AN ANSWER
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This identifies the real practical constraint (a rate near zero has
little room left to fall) that makes the standard tool unusable, and
explains why QE's own different mechanism becomes the real remaining
option once that constraint is reached.