Since the UK first introduced the minimum wage there has been no significant rise in inflation as a result of it but a dramatic hike might raise inflation. My solution wouldn't be a dramatic hike to 15 dollars an hour as has been proposed in some areas of the US, I would propose a steady rise in the minimum wage which is above inflation year on year.

One reason I support the minimum wage is due to benefits. Here in the UK we had something called tax credits where those considered in need of in work benefits could have the government top up their pay packets. This had three bad effects, the first was that the system was badly managed and prone to overpaying, those in the lowest income quartiles who received tax credits would then receive a letter demanding that the amount by which they were overpaid be paid back. This was often in the thousands. The second problem was that people were so afraid of being overpaid that they stopped claiming meaning that billions were wasted. The third was that if the government subsidised pay then companies could get away with keeping wages low. Tax credits were ended in the last budget and were replaced with a promise of a minimum wage of 9 pounds an hour by 2020. This solved all three issues.