Class based inflation rates?

So here's my question. I know, from Cowen's Second Law that the answer must be yes.

Is there any research on class-based inflation rates.

What I am thinking is that the Middle Class, the Lower Class, and Upper Class (or whatever nomenclature is preferred) have distinctively different consumption patterns. They buy different things in different amounts.

All consumption gets dumped into one big pot of data to derive a single inflationary index such as the Consumer Price Index.

But what if, based on the difference in consumption patterns, there are material differences in perceived inflation rates.

More specifically, I would speculate that the lower class of consumers probably face a lower inflation rate. They consume basic commodity items that are exposed to the most extreme competition which in general ought to keep inflation low.

I would guess that the upper class face the second lowest inflation rate owing to consumption opportunism. A much higher proportion of your consumption is purely optional so you can more easily choose to switch between categories of consumption based on market signals. Maybe exotic vacations are especially expensive this year and so instead you upgrade your car because the industry is in a downturn and offering great deals.

In this hypothesis, the middle class are the ones who take it in the neck. They are buying more than commodities but are also more financially constrained to patterns of established purchasing. They don't switch between categories of purchases, at best they postpone them. There is also an element of keeping up with the Joneses which likely makes them less responsive to adjusting spending patterns even if there are inflationary pressures.

Over the past few years, there seems to me from anecdotal conversations that there is a much higher perceived inflation rate than is reflected in the actual averaged data and there is certainly little apparent concern about inflation from the policy elite. But the policy elite are in the upper class. Perhaps they experience a materially lower effective inflation rate than do the much larger middle class?

I don't know, but it seems perhaps plausible.