I think the cost of a lot of basic goods and services would fall. Employers would only need to offer relatively modest wages because the marginal value of those wages would be so much higher. This could drive down labour costs without driving down net pay for low wage workers. Basically a worker on $1,000/Mo now might be on $600/mo basic income and $600 wage after (fantasy numbers). This could make low wage workers much more affordable for employers leading to more employment and cheaper goods and services, leading to lower cost of living. A win for employees, won for employers and win for customers. Of course this is an idealised scenario, it would all need to be funded from higher overall taxation.