The truth of the matter is, as a percentage of the population, very few people live in 600 square foot homes. This is particularly true in the case of families. That's where you really have to start talking about double that space.
Anyhow, all-up home construction via traditional means is not cheap. These days transportation costs likely add a non-trivial amount of money to the total. Costs do vary across the country, and so does median income.
It would be interesting to find a comparison of construction costs of the kind of home the average family is looking for to the median family income for the area in question.
I don't even know if many people are building 1 bedroom houses anymore; those only seem to show up as condos now and then.
Everything is built as a three bedroom and so all you have as an option is three bedroom.
Low-cost building is something like $85 a square, so 50k gets you about 600 square. It is totally doable and that's with "current" setups (these are often built as "cabins" etc.
But the permits and other things destroy them (which is why so many "tiny homes" are technically mobile homes because then you just deal with the DMV).
And you can buy brand new homes including land around here for $300k so I suspect that they didn't cost $200k in labor. But maybe they do?