Exercise 2: Why £110,000 Isn't Just a 40% Marginal Rate — Possible Solution
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This assumption only counts the direct 40% Higher-rate income tax and
misses the chapter's own real Personal Allowance taper. At £110,000,
this person is already £10,000 into the £100,000-£125,140 taper band,
where the £12,570 Personal Allowance is being reduced by £1 for every
£2 of income above £100,000 - meaning it hasn't reached £0 yet, and
every additional £1,000 earned continues shrinking it further.

Earning an extra £1,000 in this band has two real, simultaneous
effects: the £1,000 itself is taxed at 40%, AND it causes £500 of
previously tax-free Personal Allowance to become taxable at 40% as
well (since the allowance shrinks by £1 for every £2 earned - £1,000
of extra income shrinks the allowance by £500). That extra £500 of
newly-taxable income, taxed at 40%, adds a further real £200 in tax
on top of the direct £400 from the £1,000 itself - £600 total tax on
£1,000 of extra income, a real effective marginal rate of 60%, not
40%.

ANSWER: This assumption understates the real rate because it ignores
the Personal Allowance taper - between £100,000 and £125,140, each
extra £1 earned is taxed at 40% AND shrinks the Personal Allowance by
50p, which itself then becomes taxable at 40%. Combined, this produces
a real effective marginal rate of approximately 60% in this band, not
the 40% the person is assuming.

WHY THIS WORKS AS AN ANSWER
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This correctly identifies that £110,000 falls inside the real taper
band and works through the combined mechanism (direct tax plus the
taper's own knock-on effect) to arrive at the real ~60% figure, rather
than treating the headline Higher-rate percentage as the complete
picture.