I'll just copy and paste a perfect explanation to a question raised by an OP on Reddit and the response to it.
The question was "ELI5: People seem to support raising the minimum wage to $15.00, but if everyone is now making at least fifteen bucks an hour, won't that just drive the prices for things up and also drive the buying power of a dollar down, effectively making the new minimum wage the same as the old minimum wage?"
The response credited to /r/don_truss_tahoe :
"The best short answer to this question is "maybe, but probably not." The more appropriate answer is "there are people who have dedicated their lives to studying the impact of wages on inflation and they still have a ways to go."
Depending on the basic set of assumptions you would like to use to start, wages, prices, and inflation can all be expressed as linear functions of eachother. However, the actually impact of adjusting wages like this would be a litte weird. As an economist, it's almost impossible to tell what would happen if we suddenly changed minimum wage to $15. we aren't good at predict that. What we are good at doing is predicting what will happen given a unit-change in wages. This distinction is vital. We can (approximately) tell you how much prices and inflation will adjust if you increase wages by one monetary unit, but after that adjustment the world is a different place so trying to estimate the effect of this kind of wage hike is really really tough.
What is for sure: the labor market would respond, price levels would change, inflation would change, and there would be large-scale adjustments to individuals' preference structures with respect to certain types of goods as well as their incentives to work.
Personally, the last point is the most interesting to me as it plays on the inherent short-sightedness in people. Let's take a closer look at what I mean. When an individual sets his or her choice of optimal labor supply, price levels, wages, and expectations for future discount of savings/investment/Yada Yada come into play. The effect of an increase in wages like this is almost certainly nonlinear as the rational person would realize that inflation would likely catch up to them in the future vis-a-vis prices and interest rates. But, right now they are ahead of the curve so they adjust consumption and savings in the current period to maximize utility based on a belief about the distribution of effects from the wage hike. In every period after that, using Bayesian updating to adjust preferences and expectations based on the outcome of the last period, rational individuals would continue to adjust their labor supply, consumption and savings decisions all the way until the nth period. It's quite possible that, when we expand this our to infinity, we actually see no change in the individual's utility stemming from this wage hike, because the shock was isolated and the effects drowned out in time.
I'm just rambling on my phone at this point. Suffice it to say that the answer to your question is impossibly difficult to answer. But the odds of the increase resulting in things returning to equilibrium is very small. After all, things have never returned to their original stead states after any major economic event. The economy simply finds a new direction, pattern, and speed with which to baffle economists and torment graduate students."