They're not the same pens though (extra fine v. ultra fine).

I can understand why the FTC is concerned. This has the potential to be worse for competition than MFN agreements, because it forces any supplier whose products might end up on Amazon to police its entire distribution network for minimum pricing. It also forces suppliers to crack down on (legal, authentic) grey market imports, even if those are never sold on Amazon, or risk losing the ability to effectively sell on Amazon.

I was offering the comparison because those two pens should be priced within a few cents of eachother (the difference is the tip width and ironically "extra fine" is more expensive). If the products were the same then there would only be one product page and the $9.99 offer would be the highlighted deal.

The fact that one product has the buy box at $9.99 and 1-day shipping and the other product does not have the buy box at $14.28 and 8-day shipping lets us infer that $14.28 is not a competitive price for these pens and there may be a cheaper price elsewhere (likely closer to $9.99).

You seem to be thinking that manufacturing costs alone dictate the product cost. Demand and volume in circulation are also part of what determines costs, though. That is, your first assertion that they should be within cents of each other is clearly wrong.

It doesn't let us infer that there is a cheaper cost somewhere, it lets us infer that Amazon has a low confidence that someone will buy it. That or they have such a low inventory of it that they are not confident showing it on the buy box without more engagement from the users.

To be clear, I'm ok with the idea that this is getting investigated. I have low confidence of finding smoking gun reasons to punish sellers on this. I am far more confident that Amazon is optimizing to convert sales.

Actually, in this case I am cheating because I already know that this SKU is offered for a lower price with faster shipping from Walmart. I suspect that listing is what triggered the loss of the buy box.

But that is a non-sequitur. Literally, in that that doesn't necessarily follow. We literally don't know why the buy box doesn't have it here and I could guess at a few other reasons. Most likely, I'd guess that the cheapest option not being Prime factors in to it more so than external offers being cheaper.

You're right, shipping speed likely also factors into it in addition to cost (that's why I also mentioned the shipping speed). If Amazon can't deliver within its 2-day Prime guarantee it is less likely to promote the offer.

Of course, without access to Amazon's systems I can't say for sure why any individual listing is or is not promoted. I'm just making an educated guess based on what the FTC put in its complaint.

Totally fair, and I think this is the kind of thing they could/should make rules around having a good audit mechanism for regulators to check.