That's an interesting point! For simplicity, let's divide into 3 segments: poor, middle, rich. Poor can only pay with coupons, rich can't be bothered/seen and o

That's an interesting point! For simplicity, let's divide into 3 segments: poor, middle, rich. Poor can only pay with coupons, rich can't be bothered/seen and only pay full price, middle can pay in full but some of them decide to use coupons because it's deemed worthwhile (so really 4 segments). Suppose middle doesn't exist, and prices are set in a way where tons of poor people are fed while also maximizing profit from rich people; perhaps this means giving the poor a 50% discount. Now introduce the middle. The portion of them paying with coupons is anywhere from 0% to 100%. The restaurant makes massive profits from them at 0%, and makes no profits from them (but covers all costs) at 100%. Let's say it starts near 0% because initially nobody knows about coupons and over time rises near 100% once the information has spread around. Profits decrease so something must be done to counter that. Shallower discounts (say, 25% off instead of 50% off) is a possibility, keeping the discrepancy tight, as you suggest. But increasing menu prices, while leaving the huge discrepancy, is also a possibility! Either method will get the profits to the desired level. But only one method -- maintaining the large discrepancy -- sustains the goal of maximizing the number of poor people fed. Therefore, a restaurant with that goal will choose that method; a restaurant without that goal simply won't issue coupons. The discrepancy, if one exists, is therefore constant regardless of how many penny-wise pound-foolish people are in the middle.