commented on The Earned Income Tax Credit Subsidizes Low-Wage Employers, While the Minimum Wage Boosts Incomes for Everyone
Also, even if prices raise the same way, the rich still become a little less rich as the inflation hits, and narrowing the gap between rich and poor still has big benefits. Whether you're pulling the rich down or pushing the poor up is largely a matter of perspective. Even in capitalism, concentrating money at the top isn't productive.
Even without worrying about inflationary effects, raising the minimum wage is a great way to tax the rich. And most of the 'entitlement spending' that the rich hate is there to subsidize business models that are hostile to the underclass employees they require.
(Remember, giving money to the poor (minorities) makes them lazy; giving money to the rich (whites) makes them more productive).