Doesn't really matter if prices go up. If minimum wage goes up, then what is considered a 'descent enough' wage will also go up.
This wont affect people who are living paycheck to paycheck.
It is inflationary to the currency (which the wage is paid in). So anyone that has saved, or wants to save that currency will see the buying power of it go down. So if you want to save up for something, don't use that currency that is getting inflated.