The sum of a percentage of all items should be the same as a percentage of the sum, no?

Suppose you buy two items costing x and y, and there's a constant sales tax of t (say 10%, or 0.1). You'd pay t * x + t * y, or t * (x + y). You can even generalize this to Σ(t * x) = t * Σx (for x ∈ X, where X is the set of prices you're paying).

In other words, yes.

In case you want the math name for this property, it's the distributive property.

I think the issue they were bringing up though is that tax is not applied equally to all items, and that tax may be determined by number of items sold. I don't actually know if this is true or not, but if it is, the distributive property doesn't apply anymore. Edit: I re-read the comment, that doesn't look like what they were saying actually. Either way, if tax is weird like this, distributive property may not apply anymore.

Hopefully someone can. Me no math good either.
!SeaJ@Lemm.ee shared this:

https://www.taxjar.com/blog/retail/can-retailer-include-sales-tax-in-the-price

Check out the article linked below. I'm interested in what you think after that. Especially with the states that forbid including tax in displayed prices (and why they don't).

I didn't know about that until I just read it.

In Ontario Canada there is no provincial tax component on meals costing less than $4. This dates from the time you could get a simple lunch for < $4. Unfortunately it's never been adjusted for inflation.

No reason not to show amount with tax and give people a pleasant surprise though

You're a hero. I hope your customers notice what your doing for them.

The problem is at the advertising level.

Could your local Safeway put tax-inclusive prices in the circular? Sure, although there are actually laws that prohibit such local pricing (YMMV; I've lived in a lot of states) specifically so that people in the sticks aren't shouldering the entire transportation bill to their IGA. This is why grocery circulars are regional, but that's an aside. Still, different cities in the region will have different tax rates, so they can't do tax-inclusive, and they certainly can't have a different price on the shelf than in the circular, and here we are.

But these are small potatoes.

Now, can Tim Cook release a new iPhone and list the price in every municipality in the U.S. in the keynote? The patchwork of devolved taxing authority makes the U.S. a poor candidate for tax-inclusive pricing.

States universally abandoning income tax for VAT (ain't never gonna happen, since VAT inconveniently hits even billionaires' consumption [and even less likely would be pushing through VAT while retaining income tax]) could get things closer to what Europeans have come to expect, where each state would have a universal rate and consistently applied carveouts and then distribute that to lower tiers of government as some states currently do with sales tax, but the closest advertising could get to that would be "state VAT excluded," at which point nothing has been fixed in terms of walking out the door paying the advertised price at the cost of unpopular economic upheaval.