You know that those credit card rewards aren't free, but who's really paying for them? Most of the people I know have credit cards or other payment cards with some kind of reward or point program. For every dollar charged to the card, the card carrier is credited with points or some other reward measure. Often, people try to pay as many of their expenses as they can through the cards to maximize their points. Who pays for the benefits received by accumulating points? Are the card issuers taking lower profits per transaction to increase the use of their cards? Are merchants paying the price through higher fees? Or are the card holders paying in some way? A new study by some economists answers the question. The economists are from the National University of Singapore, the International Monetary Fund, and the U.S. Federal Reserve. The study concludes that the costs are borne by some of the card holders. Some card holders benefit while others pay for those benefits. The difference depends on how carriers manage their card purchases and balances. The points systems induce more spending. Sophisticated consumers pay off the card balances regularly and capture the rewards at little or no cost. Naive consumers don't pay down their balances as often. The interest and fees they pay for carrying balances more than offset the reward benefits. The card issuers also profit several ways. Cards with rewards generally carry lower interest rates than cards without rewards. But since the rewards stimulate more spending, the naive consumers pay more total interest because they carry higher balances than they would without the rewards. The card issuers also profit, even from sophisticated consumers, from the fees charged to merchants because more spending is put on the cards. There's a free lunch for the card owner who pays down the balances each month, avoiding interest charges and fees. That lunch is paid by other card owners and merchants.