$7 billion in profit would be about $15 per share, yielding a P/E around 24. That's on the high end, but not absurd, so I think your analysis is a good justification for the valuation.
A key question is whether that 10% price increase would be absorbed by customers with no change in sales. There's an argument it goes the other way: customers trade the immediacy of brick-and-mortar for Amazon's low prices. But if the online prices are no better, then Amazon provides no benefit, and a 10% price increase could result in a much larger drop in sales. This played out in my own household: we used to buy diapers exclusively through Amazon, but completely stopped following their diaper price increase.
> But if the online prices are no better, then Amazon provides no benefit
Speaking only for myself, the vast selection and stock is a huge factor for why I often prefer to buy things from Amazon.
For instance, there's a particular mustard that I like that is hard to find in stores nearby. I don't like it enough to justify going from store to store to find it, but I do like it enough to buy it from Amazon for the same price that I would pay by doing that, and just wait a day or two. Often stores are out of stock of the things that I want. Amazon tells me that without leaving the house. I live in a city where a trip to a store that isn't in walking distance can be a couple of hours or more to haul myself around on transit, but Amazon delivers to my office. I imagine that there are people in more rural areas that if the local store just doesn't have what you're after, you're out of luck. And so on.
My point is, there are plenty of reasons besides price to give up immediacy
Depends on how expensive your commute to the shop. I don't use Amazon because it's not available in my country. However, if it was, I'd probably use it even if it's expensive.
You spend lots of time in shopping + gas + car. Delivery is a nice thing.
A key question is whether that 10% price increase would be absorbed by customers with no change in sales. There's an argument it goes the other way: customers trade the immediacy of brick-and-mortar for Amazon's low prices. But if the online prices are no better, then Amazon provides no benefit, and a 10% price increase could result in a much larger drop in sales. This played out in my own household: we used to buy diapers exclusively through Amazon, but completely stopped following their diaper price increase.