The amount effect and marginal value.

Rachlin et al. (2015) asked adults to pick between two imaginary rewards. One reward was small and came right away. The other was larger but came after a wait.

The team made the wait last 0, 7, 14, or 30 days. Each person made dozens of choices. The researchers then drew a curve that showed how much value people placed on each amount at each delay.

When people had to wait, the value curve got steeper. A $100 reward felt much better than a $10 reward, even more than ten times better.

This "amount effect" means delayed big rewards look extra good. The finding matches basic delay-discounting theory and shows why size matters more when you have to wait.

Herrnstein et al. (1979) built a math model that added "power" to reinforcer rate. Howard’s data give real numbers to that power idea when delays are in play.

Alba et al. (1972) saw that matching breaks down with long change-over delays. Howard’s steeper value curve helps explain why: long waits make bigger rewards look even better, so the lean side loses appeal fast.

Green et al. (1999) showed rats take quick peeks at the lean schedule and still come out ahead. The new human data say the same rule holds for delayed money: brief waits feel cheap, so people hop back to the rich side.

If you make a client wait for a big reinforcer, the wait itself pumps up the value of that reinforcer. Use this when you design token boards or level systems: promise a larger backup reinforcer after a short delay instead of a tiny one right now. The client will work harder for the big prize, and you spend fewer tokens overall.