It is hard to put arbitrary number on minimum wage, but there labor cost are much less percentage of doing business than was 20-30 years ago. Even in retail where majority of these people are employed. However, low minimum wage ties to low productivity. Higher wages increases productivity, because businesses would replace them with automation and robotization. For example in Czech Republic, the minimum wage were kept frozen under right-wing pro business government for seven years and productivity barely grew. Slovakia on the other hands continued to increase minimum wage on yearly basis, and enjoys today not only higher wages, but also productivity. Similar trend was observed in Slovenia, Estonia, where labor productivity continued to increase with minimum wages. Countries that have stagnant or depressed minimum wage, there was just little push for investment and technology, because it could be supplemented by cheap labor.
This is not a new. Roman Empire had cheap labor, which prevented increase of productivity, innovation, and technology. Europe until 1350 had similar issue, cheap, plentiful labor, and low productivity. Once Black Death decimated labor, productivity had to increase so did wages. Europeans in 1450 enjoyed much higher living standard, lower cost of production, cheaper goods than did generations before. The sudden rise of living standard at the end of the Medieval era was so profound that government in Europe attempted to regulate wages and spending, but they were not successful.