Many lower income individuals struggle to see their income increase faster than inflation. By contrast when you have immense wealth, it's pretty easy to achieve extremely stable returns on that immense wealth well beyond inflation. In cases where this is true it means the net effect is that the poor effectively pay more while the rich effectively pay less.
There's also an issue of debt differences. One of the big 'benefits' of inflation is that it makes old debts worth less. This is a major incentive for pursuing investments on debt. Not only can you see investments on money beyond what you presently have, but the debt that you took on becomes worth less - meaning it takes a smaller share of your profits each year assuming the principle is not growing. For instance during the government auto bailouts Ford took on a loan for billions of dollars of debt from the government. The interest rate on that loan is sub-inflation. Unsurprisingly, they aren't paying it back since each year it becomes worth less, and given enough time, it will become worthless.
By contrast when a lower income individual takes on debt, it's often 'consumed' such as in the case of education. And the debt becoming worth less over time is not true if an individual's income is not keeping pace with inflation. And another big issue is that lower income individuals are also often going to be seeing rather high interest rates on their loans further diminishing any theoretic benefit of inflation.
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This is not to say inflation is bad. You can create a comparably negative argument against deflation. I don't really have much of an opinion one way or the other. We've seen how depressive systems can end. And while our current inflation and debt driven system has not yet collapsed, it's not looking as stable as it once did to put it very mildly. I think in 20 or so years (and especially once the petro dollar is 100% dead) we'll have a much better idea of the pros and cons of each system.