THE SOURCE: “Life-­Cycle Prices and Production” by Mark Aguiar and Erik Hurst, in The American Economic Review, Dec. ­2007.

It’s no secret that ­penny-­pinching older people seem to get more for their money. Now two economists have combed through 950,000 grocery receipts to pro­duce mathematical proof and to show how seniors do it: They spend more than an hour and a half trundling their carts along the grocery aisles every week, compared with 58 minutes for the under-30 crowd; those 65 and older shop nearly eight times a month, com­pared with 6.5 times for young folks, and more than ­two-­thirds take advantage of discounts, compared with about half of the younger ­group.

The result: Seniors save 3.4 percent on groceries compared with the average 25-to-29-year-old, according to Mark Aguiar of the Univer­sity of Rochester and Erik Hurst of the University of Chi­cago’s business school.

The economists wondered whether the mature shoppers were producing their bargain loaves and fishes by going to more discount stores, buying cheaper products, stocking up during sales, or cutting back on eating. Their answers: no, no, no, and no.

The older shoppers’ secret is clear: They shop slightly more often and considerably more intensively, cruising familiar stores, and they spend more time at home in meal preparation.

At age 49, the prices people pay for food turn down. By the time their Social Security checks tumble through the mail slot, they’re saving real money. If they shop twice as often as younger people, they can cut their grocery bills by as much as seven to 10 percent. They’re making an econ­omic substitution: time for money.