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Diminishing returns

mental model · origin: study · evidence: supported

In short

Diminishing returns means that, past a certain point, each extra unit of something (money, time, effort, another slice of cake) brings a smaller and smaller gain. It does not mean the benefit disappears, only that each additional step counts for less than the one before. The best-studied example in psychology is the link between income and well-being: the same amount matters a lot to someone on a low income and little to someone on a high one.

What it says

The old idea. In 1738, the mathematician Daniel Bernoulli proposed that any increase in wealth brings a gain in utility “inversely proportionate to the quantity of goods already possessed”. His example: a gain of a thousand ducats matters more to a pauper than to a rich man, although both gain the same amount. Mathematically, his hypothesis leads to utility that grows with the logarithm of wealth: each doubling brings the same gain.

What the data show about income and happiness. Three large studies, all published in PNAS, contradicted each other and then made peace:

Where the diminishing returns are. “Linear in log income” means exactly diminishing returns per dollar. Going from $25,000 to $50,000 brings roughly the same gain in well-being as going from $100,000 to $200,000, although the second takes four times as much money.

Illustration: well-being rises linearly with log income. From $25,000 to $50,000, from $50,000 to $100,000 and from $100,000 to $200,000, each doubling brings the same step, even though the amount added doubles each time. The same step for every doubling the shape Killingsworth (2021) found; illustration, not data well-being 0 50,000 100,000 200,000 annual income ($) +25,000 +50,000 +100,000 Each step costs twice as much money
An illustration of the "linear in log income" relationship in Killingsworth (2021). The vertical axis has no units: it shows only the shape, not measured values.

Example

An example built for this text: a raise of 500 a month. For someone earning 3,000, it is a one-sixth increase and is felt every month. For someone earning 30,000, it barely registers. The studies above suggest that the two would need very different amounts (proportional to their incomes) for a comparable gain in well-being.

The same pattern appears, as an analogy, outside money too: the first hours of studying for an exam bring a lot, the last ones less. The tenth review read before a purchase rarely changes the decision.

How to apply it

The steps below are a practical approach we propose. The studies cited measure the link between income and well-being; they don’t test this advice.

  1. Think in proportions, not amounts. When weighing a gain or an expense, ask what share it is of what you already have, not just how much it is.
  2. Look for the point where one more step brings little. In projects, in preparation, in the search for the “perfect option”: if the last effort changed the result only a little, the next one will probably change it even less. See the entry on maximizing and satisficing.
  3. Move the resource to where it is still scarce. If more of one thing brings less and less, the same resource may bring more elsewhere. It is the same logic behind the Pareto principle.
  4. Don’t confuse “diminishing” with “zero”. In Killingsworth’s data, for most people more money still goes with more happiness. It’s just that each doubling brings the same step, not each extra amount.

Limits and nuances

Sources

See also: Maximizing vs satisficing, Pareto principle, Via negativa