Progressive income tax is widely misunderstood as applying a single rate to the whole of an income. In practice each rate applies only to the slice of income within its own band. Rules differ by jurisdiction and change over time.
Income is divided into bands, not classified
Earnings are taken in order from the bottom. The first portion is taxed at the lowest rate, the next portion at the following rate, and so on.
A taxpayer whose income reaches into a higher band pays that higher rate only on the amount above the threshold, not on everything earned.
The average rate paid across the whole income is therefore always lower than the rate on the top slice, and the two are often confused.
Crossing a threshold does not reduce net pay
Because only the excess is taxed at the higher rate, an extra unit of earnings always leaves the taxpayer with more after tax than before, under a purely banded system.
The belief that a pay rise can leave someone worse off comes from applying the top rate to the entire income, which no banded system does.
What does change is the value of each additional unit earned, and that is the figure relevant to decisions about additional work or a bonus.
Withdrawn allowances create steeper effective bands
Systems frequently taper allowances, credits or benefits as income rises. The withdrawal acts like additional tax over the range in which it happens.
The effective marginal rate across that range can exceed the headline rate of the band it sits in, sometimes considerably, which is where genuine cliff effects arise.
These interactions rather than the published bands are what produce awkward income ranges, and they vary widely between jurisdictions.
Different income types run through different rules
Employment earnings, investment income, dividends and capital gains are often taxed under separate schedules with their own rates and allowances.
Where that is the case, the order in which income types are stacked against the bands matters, and it is set by statute rather than chosen by the taxpayer.
This is why two people with identical total incomes can owe materially different amounts depending on the composition of what they received.
The marginal rate is the figure for decisions
Questions about the effect of extra income, a deduction or a pension contribution turn on the marginal rate, since they concern the top slice.
Questions about overall burden turn on the average rate, which is the total tax divided by total income and is a different number entirely.
Because thresholds, tapers and definitions change and differ by jurisdiction, anyone acting on these interactions should confirm the current position with a qualified adviser.