Surely prices would rise? There would be a limit on how far they could rise because Intel will always be competing against its own previously-sold (previous generation) products (and against any still-existent AMD products still out there). But prices will always be higher in a monopoly situation than in one with competitors.
If Intel's gross margins were depressed like AMD's then I'd expect them to raise prices over time just to get their gross margins up to the desired target value of 60%.
But they are already there, at +60%, because Intel has effectively had a monopoly for the past decade anyways. Even when AMD was king of the performance ladder they still weren't king of the gross margins ladder nor the marketshare ladder.
I suspect that at most, at the absolute top-end of greed that Intel could pursue without getting themselves busted up like RCA and AT&T, they could increase prices such that their gross margins hit ~80%, the same as microsoft managed to achieve without getting busted up as a monopoly.
A 20% increase in gross margins doesn't mean a 20% increase in ASP, because gross margin is the delta between ASP and cost (not exactly, but close enough), so a 20% increase in the delta would require an increase in the ASP that was less than 20%. Probably around 15%.
A 15% increase in the average selling price would not be catastrophic. We'd bitch about it, for sure, for maybe 15 minutes and then we'd move on with our lives by noting we pay more than that in taxes and shipping costs alone just to get the CPU into our hands from the reseller.
If Intel raises its ASPs such that its gross margins exceed 80% then you, and they, can expect the FTC to bust them apart. And that is not in the best interest of the shareholders, so Intel won't set upon themselves a path that involves >80% gross margins.
Instead they will pursue exactly what they have pursued in the past 10yrs of being an effective monopoly - make decisions which continue to enable and support a gross margin floor of 60% while at the same time expanding the annual revenue and profit of the company.
80% gross margin on $5B revenue is not as enticing as 60% gross margin on $10B revenue. Literally everyone in the business chain understands this, from shareholders to the BoD to the FTC to the decision makers at Intel.
They aren't about to do anything that would jeopardize their ability to continue making tens of billions of profit at 60% GM, and getting the company busted up would be something they have been, and will continue to be, keen to avoid.
This also speaks to the claims that Intel would slow-down their node-cadence. If they did that then their expenses would drop and their gross margins would rocket upwards, inviting the FTC and DOJ to come in and bust them up. Something pretty much everyone can agree Intel would do anything to avoid.
So their expenses will rise so as to keep the gross margins in check (but not for the false implied cause-and-effect of that ordering). They will keep on the Moore's law bandwagon because they can afford to and because they can't afford not too. (if they elected to reduce spending then they'd actually need to reduce ASP and reduce revenue to keep their gross margins below the 80% danger level)