The catch here that the author was trying to tease out is that marginal utility is not always a smooth curve. Sometimes it is a step function, which changes the rules around the step.
Tax brackets are another classic example. Sometimes you get much more by being paid a little less.
Edit: The tax thing was a brain glitch and not true IRL. Check Matt's comment below. There may be true life examples where you come out ahead but they are likely to be scholarships or insurance policies or something with similar hard cutoffs that form step functions.
No you don't. Earning more never causes you to take hom eless after taxes (at least in any country I know of). That's a common fallacy about them amongst people who don't understand the tax code.
Tax rates are marginal. So for instance if the tax rate was 20% up to $100k, then 30% afterward, you'd pay 20% on your first $100k, then 30% from $100,001 and up.
Income tax is probably always marginal, but in the UK at least this kind of thinking does apply to selling houses - when a house is sold in the UK the buyer must pay "stamp duty", which is a percentage of the value of the house, with the percentage changing at certain thresholds. For example at £250,000 the stamp duty changes from 1% to 3% - but the percentage applies to the entire value of the house. So if you sell for 250,000 the buyer pays 250000 * 0.03=£7500, compared to 249999 * 0.01=£2,499.
That introduces some distortions into house pricing, making it very difficult to sell a house in the £250,000 to £265,000 range - because you are competing with houses just under the threshold which work out significantly cheaper for the buyer. As someone selling a house which falls into that price range, you might be better off asking for slightly less from the sale (versus asking for just over the threshold and waiting much longer to find a buyer).
Hmm. You are right. All of the examples I was taught with used fictional examples of magical taxes. I though surely there must be somewhere... but no, just a clever fiction, repeated ad absurdum to make word problems for 5th graders and then glossed over by time until I took it for reality. Ouch. Harder still because with a moments reflection I should have seen its absurdity(1).
But the step function thing was the point, not the taxes. I'll put in an edit and get that last bit ignored.
(1) Be careful what you take as truth when young and don't rethink later.
You only pay the higher rate for income within that bracket.
Making an extra dollar pushing your taxable income to $34,001 as a single American in 2010 does not raise your Federal taxes from $5100.00 to $8500.25 by naïvely applying the higher rate — it actually raises your taxes by 25¢ from $4681.10 to $4681.35.
Tax brackets are another classic example. Sometimes you get much more by being paid a little less.
Edit: The tax thing was a brain glitch and not true IRL. Check Matt's comment below. There may be true life examples where you come out ahead but they are likely to be scholarships or insurance policies or something with similar hard cutoffs that form step functions.