Who should own pricing? Product management or product marketing? And what role should each play?

It’s a joint decision between product management and product marketing at Square. In general our PMMs tend to have more ownership here. They will lead competitive analysis and commission qual/ quant research to inform pricing decisions.

That said, from what I observed, when you zoom into the specific PM/ PMM pair, it really comes down to whoever has the expertise and the respect from the team to make the right call.

Pricing and packaging is typically a PMM function.

1. P&P is typically a business decision. In general, PMMs own business and go-to-market decisions, while PMs own the user experience and the product roadmap. And P&P falls into the former. 
2. Product should have a perspective on which features to build. Pricing and packaging refreshes typically happen because the composition of your existing product has changed materially (i.e. a lot of new features have been launched, new acquisitions, etc). As such PMs will always have a role to play in determining how certain features and product should be packaged
3. P&P involves a lot of market research. P&P requires deep market and competitive knowledge. Many PMs will have that, but this is typically a PMM function. As such, PMMs will be best placed to turn those insights into a coherent pricing strategy.

I used to be very much on the side of "PMM should own pricing" but I will now caveat this with a couple considerations.

First off, though, I think at a smaller company, say a startup where you're the only PMM, PMM should still own pricing. That's because there's both a strategic ("how should we set our suggested retail prices and package the product?") and tactical ("how much should we allow our reps to discount the product and on what basis?") element to pricing. At smaller companies, I've seen more problems with the latter. Failure to set acceptable discount levels and enforce them with the sales team creates the wrong kind of working relationship with them and leads to a lot of "special" deals that you'll end up having to unwind later when your product is successful. ("What do you mean $EARLY_CUSTOMER from 5 years ago is only paying $5/seat/year? They have 80,000 seats now and we can't raise our prices that dramatically!")

At a larger company, my answer is "it depends who is capable of taking a rigorous approach to pricing and packaging" including conducting both quantitative and qualitative research on how products should be priced and packaged (P&P). If this sounds a lot like product management, it is. That doesn't necessarily mean I think P&P should sit under PM, however. P&P is such a specialized skillset that works in a domain so distinct from traditional PM that I've started to see companies start to create VP/Senior Director of Pricing roles. These roles often roll up to a Chief Product Officer (CPO), but not always; particularly with the rise of growth marketing and the renewed hype around product-led growth (PLG), sometimes it's more effective for these folks to sit in marketing.

My default choice would be to put P&P in product marketing, because experimenting with packaging and pricing is a job better left to the go-to-market side of the house.