The price of eating out jumped 0.7% last month — a staggering pace not seen since 1981, inflation data out Tuesday shows.

Why it matters: Demand is soaring, but so are the costs restaurants and other food providers face — for ingredients, supplies and staff, which are all in short supply. The dynamic is playing out on the menu in the form of pricier meals.

One big factor: Restaurants are paying up to lure employees to staff the comeback. The data is a sign they are passing on the costs.

• "I am a little surprised that food away from home has not accelerated more given the issues around finding staff," says ING economist James Knightley.
• "With reports of rising wages, I suspect that restaurants would be looking to raise their prices more rapidly."

It's not just restaurants. Here's a stat for the history books: Food from vending machines saw the biggest single-month cost jump on record.

• One theory: The machines are "more common in offices and break rooms where workers are finally returning," Diane Swonk, an economist at Grant Thornton, wrote Tuesday.
• "Many restaurants and fast-food establishments in urban centers, where offices are located, shut down during the crisis."

The big picture: All six major grocery store food categories saw prices increase — with meat, fresh fruit and vegetables seeing the steepest hikes.

What to watch: Executives at some of the biggest packaged food companies — brands you see down the grocery aisle — see steeper price hikes ahead.

• PepsiCo CFO Hugh Johnston said today ... “Is there somewhat more inflationary out there? There is. Are we going to be pricing to deal with it? We certainly are."
• Conagra, the maker of Slim Jim and Duncan Hines, already jacked up costs —and more will be coming. Why? "[C]ontinued increases in the cost of edible fats and oils, proteins, packaging and transportation," CFO David Marberger told analysts today.

The bottom line: Whether you're eating out or at home, it costs more.