How can credit card companies offer a cash back program? [duplicate]

Question

Many credit cards offer cash rewards or similar programs which effectively amount to a small % discount (at the CC company's expense) for various purchases.

For instance, American Express has a card that returns 6% of the first $6000 spent in supermarkets per year.

Granted the card has an annual fee ($75) but it is very small in comparison: A reasonable person might spend $300 a month, hence $3600 a year, on groceries, which they are buying anyway. From this they get $216 back, and they have already covered the fee and ended up $141 "in the green".

If one were to use this bonus to its fullest, spending $6000 at supermarkets, that would be $360 cash back, $285 after fees. On top of this there is still a 1% cash back after the first $6000.

This seems like a lot of money! If someone gets this card and only uses it at supermarkets (and why not, since the supermarket cash back is the biggest reason to get this card) then they end up with Amex basically paying them a few hundred every year just to use their card, almost like a negative annual fee. Doesn't Amex lose money on this?

I know that CC companies charge a transaction fee but if you spend to the $6000 bound you end up getting 4.75% of your spending paid back after the annual fee. Surely no merchant would agree to a 5% transaction fee, so the company is still losing some money on rewards even after the annual card fee and transaction fee.

Obviously, some people will underutilize the card and solve the problem:

• Maybe they go to an ineligible merchant and get only the lower 1% cash back (but even if you shop only at the 1% stores, if you spend at least $625 a month you still break even on the annual fee)
• Maybe they spend too little on groceries and don't even make back their annual fee (but, as pointed out in the previous item, you would have to be spending hardly any money for this to happen)
• Maybe they don't pay their balance in full and end up paying the hefty interest and late fees (but the card requires a good credit score which this sort of person is unlikely to have)

But from the company's point of view, why even have the optimal users, like the $6000 in supermarkets and nothing else guy (not actually that unlikely, since the card requires good credit in the first place, members will be people who manage their personal finances well), who are just a money sink? For instance, they could say the cash back can only be redeemed for interest/late fee payment.

How are high cash-back programs like this a good idea for the company? I can think of some possibilities:

• The promise of driving more customers through the rewards allows Amex to negotiate an even higher transaction fee with the merchants (but then you'd think they would expand the program to other merchants such as electronics retailers or online stores)
• They are losing money but gaining market share
• The "optimal users" who break even are a necessary evil, the profit comes from people who hope to get the rewards but instead end up losing money on the annual fee or late payments, and it makes up for the money lost on people who really do save money with the card

But which one is it?

Answer 1

1) Every credit card company charges vendors a fee. That's sufficient to make an acceptable profit per charge even if some of that money goes into marketing expenses -- and the cash-back offer is a marketing expense.

2) Many if not most consumers pay interest; probably everyone does so occasionally when we get distracted and miss a payment.

3) The offer encourages you to put more payments on the card -- and in particular on their card -- than you might otherwise. See #1; that increases net income.