There are places where people don't have enough mobility to be able to do this.
EDIT: One of the interns at the non-profit I volunteer at landed a job, but had to give it up because he didn't have transportation that could reliably get him to his job. (Late shift.) He lives in Oakland.
That's where Internet shopping comes in. Ideally you want to support local businesses to keep jobs in the area, but if you need to fight against price hikes and can't do so locally then the best thing to do is shop online until the price hikes are reduced.
Sounds like a good project to benefit those lower on the socioeconomic ladder.
Why would you need BI if that existed in the first place? Then people would have the discipline to not work shitty jobs and strong competition would provide them the work they want! What has BI solved, then?
The desire to eat trumps the desire for a better job. If you tie people's choices to their need to survive, you are going to interfere with what people would choose that serves their best interests. Amongst other things, UBI tackles this issue.
Ideally you'd want UBI to increase with inflation. However, as the initial study is over 5 years the decrease in purchasing power by the end of the study is likely to be minimal.
There is a risk that companies that service low-income people will increase their prices faster than inflation, negating some of the benefits of UBI. The only guard I know of for this is strong competition and disciplined consumers, people have to be willing to express their dislike of price hikes by shopping elsewhere otherwise the system won't work. I'm guessing that monitoring price rises will be part of this YC-backed study.