inflation isn't a primary driver for prices.
labor costs, however, are.
Inflation is a reflection of prices. If the CPI isn't going up, then overall prices are not going up. Just because a latte goes from $4.00 to $4.25, does not mean that over all consumer prices on goods and services have increased. Its a all wash unless you see an uptick in the inflation rate.
If a company sees an increase in labor costs they can address that by numerous means:
1. They can increase prices on their products and services, but it is still a competitive environment that they are operating in, thus often they cannot do that.
Thus, they usually opt for one or more of the following:
1. They could pursue productivity improvements.
2. The owner or upper management could take a little less money home or see a reduction in their raises year over year (not always a bad thing considering wealth and income concentration - perhaps the CEO ends up with just 380 times his average employees salary rather than 420 times.).
3. They could absorb it with a slightly smaller profit margin (at home care agencies have huge margins for example).
4. They could reduce hours. In this case those earning the minimum wage may well still end up ahead because the increase in wages could very well more than offset the reduction in hours.
5. They could do a combination of any of these things.
However, what we do know is that the low wage job market is pretty stable. Even in the height of a recession you still see plenty of minimum wage jobs in the want ads.
Now, that all said, that is assuming typical increases in the minimum wage. An increase all the way up to 15 dollars an hour is uncharted territory so who knows what will happen.