Businesses would generally charge the price that would result in the most profit (revenue - expenses). Businesses can't just raise prices and get more revenue. If they could, they would do that already.
Minimum wage has to do with marginal cost of producing an extra product. Marginal cost generally increases after a while. So producing that last additional unit usually costs more than the one before. When you increase cost in the form of the price of human capital, the marginal cost of producing a unit will increase and the intersection with the marginal revenue (price of the unit) will drop to a lower quantity supplied and higher price.
So yes, prices will go up but the business will also sell less units. Since less units are sold, there will be less capital that will need to be utilized.
Prices aren't arbitrarily set and increase in price will result in less units being sold and less employment. This isn't as controversial as journalists make it out to be.
Pre-political Paul Krugman does a great job explaining it:
> So what are the effects of increasing minimum wages? Any Econ 101 student can tell you the answer: The higher wage reduces the quantity of labor demanded, and hence leads to unemployment. This theoretical prediction has, however, been hard to confirm with actual data. Indeed, much-cited studies by two well-regarded labor economists, David Card and Alan Krueger, find that where there have been more or less controlled experiments, for example when New Jersey raised minimum wages but Pennsylvania did not, the effects of the increase on employment have been negligible or even positive. Exactly what to make of this result is a source of great dispute. Card and Krueger offered some complex theoretical rationales, but most of their colleagues are unconvinced; the centrist view is probably that minimum wages “do,” in fact, reduce employment, but that the effects are small and swamped by other forces.
> What is remarkable, however, is how this rather iffy result has been seized upon by some liberals as a rationale for making large minimum wage increases a core component of the liberal agenda–for arguing that living wages “can play an important role in reversing the 25-year decline in wages experienced by most working people in America” (as this book’s back cover has it). Clearly these advocates very much want to believe that the price of labor–unlike that of gasoline, or Manhattan apartments–can be set based on considerations of justice, not supply and demand, without unpleasant side effects.[0]
[0] http://www.forbes.com/sites/timworstall/2015/03/02/paul-krug...