You know what I think is a myth? That it's cheaper to live off unhealthy food than it is healthy food. Buying, for example, loose potatoes is cheaper than buying chips (fries, if you're American), and you don't have to cover them in grease and fat when you cook them. I think it's unquestionably true that going to McDonald's is more expensive than cooking for yourself.
It seems that research which looks at how expensive various foods are in comparison to how healthy they are tend to assess price per calorie (like
this study, which found that healthy food is 3x as expensive as non-healthy food). But part of what classifies a foodstuff as more healthy is that it has a lower energy density than the less healthy foodstuff. This is especially true if what you're looking at is weight loss.
So, to go back to potatoes and chips.
Potatoes have 75 KCal per 100g
McCain Chunky Oven Chips* have 544 KCal per 100g, uncooked (more if cooked, with how much more depending on the method of cooking).
From the link above, you can see that in Sainsbury's 1kg of McCain Chunky Oven Chips costs £2.20. From the same supermarket,
loose potatoes are £1.20/kg.
But those are randomly selected - what are the cheapest options? Okay, sticking with the same supermarket:
Own brand budget oven chips are 194kCal per 100g, and cost 72p per kg
Own brand budget salad potatoes are 79kCal per 100g and cost 70p per kg
The chips have more than twice the calories for roughly the same price. This means that they will be counted as more than twice as cheap by studies such as the one linked above, yet if you're trying to reduce your calorific intake, then the potatoes would be the better option, would they not?
If you want to go really cheap:
Own brand tinned potatoes are 54kCal per 100g and cost 58p per kg
So, no, I don't believe that it's cheaper to eat unhealthily than it is to eat healthily. I think that the usual method of assessing the expense of food is unsuited for this purpose, as it necessarily means that foods which are lower in calories are deemed more expensive than those which are full of calories. It's front-loading the results into the testing method.
I think that eating healthily is as cheap as, if not more cheap than, eating unhealthily. I know from experience that it's entirely possible to have a wide, balanced, nutritious and downright delicious diet for not a great deal of money.
*Brand and supermarket chosen as the first in a google search for oven chips, and oven chips chosen as it obviates the need to take into account additional calories and cost of oil inherent in deep frying.