It’s unfortunate that the OP was phrased toward people in actual poverty as opposed to whether it’s cheaper for the average person to eat crap food. I think that detail’s inclusion skews the discussion too far away from the general population, which makes it harder to bust the perception that healthy eating is expensive.
If an average-person anecdote will do:
I began a diet change in December. I loved carbs, and ate lots of high-calorie quickie pastas and rice mixes and salty potato or corn snacks. I often ate fried, cheesy, buttery foods, and I ate all my lunches and 3-4 dinners a week out. My diet changes consisted of a daily calorie limit, reduced portions, adding breakfast, more frequent meals, cooking everything at home, and, integrating as much as I could stand it, whole grains, fruits, vegetables, and lean meats. No foods were forbidden, but I eliminated things that weren’t worth the calories.
As a result of these changes, I’m down 25lbs in 14 weeks.
As a supplement to my weight loss progress, I tracked my food-related expenses. I’ve long been a receipt saver/shredder, so I was able to chart all my grocery spending from June 2009, with per-week and per-month spending averages.
It’s been consistent over the last four months that although I’m spending more at grocery stores these days, overall, I am spending about the same amount of money on food. This is because I’m no longer buying food from restaurants, which greatly inflates cost-per-meal spending. The $30 per week I used to spend for 5 lunches buys me 10-15 meals instead. I’m actually getting more food for my money now, since my grocery spending includes breakfast, a meal I didn’t eat before.
The trade-offs of time-investment, planning, learning about diet and cooking, etc., have all been minimal and worthwhile. It all sounds more daunting than it is.