Sure, it'd increase the cost of living. But let's not pretend it's a 1:1 increase. I mean let's say you double the minimum wage. The prices of everything isn't suddenly going to...double. Why the fuck would it? The cost of labor in production isn't 100%. If it was, companies wouldn't make a profit.
On the other hand not raising the minimum wage leaves many people in poverty. Buying power for those people decreases as inflation goes up. Their $7.25/hour buys less and less every year.
On the other hand not raising the minimum wage leaves many people in poverty. Buying power for those people decreases as inflation goes up. Their $7.25/hour buys less and less every year.