Promotional prices for customers with "member" tag?

I could swear I read a tutorial or technique about something like this ages ago, or maybe I just imagined it?

Is it possible to show promotional pricing for products managed in Shop based on whether a customer has a tag associated with their account, e.g. "member," or not? Alternatively, is it possible to automatically apply a discount code to "member" purchases?

Part of the benefit of my client’s membership program is that members get discounts on retail products. I’m trying to figure out how best to approach that with Shop. Ideally, it doesn't require customer/members to enter a discount code manually.

Thanks!