$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.
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.