I would like to see the statistics. I eat a high carb low protein low calorie diet because I like to fit my grocery bill in $15 a week. I would wager the opposite is true actually; if you're eating 1000 to 1400 calories a day and they're not mostly carbs, you're probably feeling terrible hunger pangs.

Most vegetables are carbs, milk and yogourt have tons of carbs (in the form of lactose), lentils are carbs, beans? still carbs, etc. I'm not sure how you can have a cheap low-carb diet (lots of eggs and ham? dissolving multivitamin and whey protein into avocado puree?).