Is one consequence of oligopolists’ pricing power is that they can give up some profits when they choose to?

Yes, according to Is ‘Greedflation’ Rewriting Economics, or Do Old Rules Still Apply?Economists and politicians are debating whether monopolistic companies are fueling inflation in ways that confound longstanding theory by Lydia DePillis of The New York Times. 

Here is an excerpt from the article:

"most research on how market concentration affects companies’ “pass through” of suddenly higher costs has found that fiercely competitive industries raise prices more than those that are dominated by only a few companies, because they have thin margins and would lose money if they didn’t. That’s one consequence of oligopolists’ pricing power: They can give up some profits when they choose to."

I am not sure why they say that, but I can offer a graphical explanation. See my post Is The Airline Industry An Oligopoly?

Here is part of that post

One theory of oligopoly is that each firm (an oligopolist) might face a "kinked demand" curve. All firms choose Q so that MR = MC. Once Q is found that allows us to get the price (go up from Q, hit the demand line and then go to the left to get P). But if MC falls (due to things like lower fuel costs or better technology) and we stay in the gap in MR, Q does not change and neither does price.



But if we reverse this, and say that costs are rising, the MC line will shift up. What if it went from MC2 to MC1 so that we stay in the gap (the other market structures, perfect competition, monopoly and monopolistic competition don't have a gap in their MR lines or kinked demand lines like in oligopoly)? Then price would not change. That is because once you know the Q (Q1 in this case), you go straight up until you hit the demand line and then go to the left to find the price. So if Q does not change then P does not change and we stay at P1.

That post I link above also shows how monopoly would lower their price when costs fall. But if costs rise, then price would go up. Just think about moving from MC2 to MC1 in that graph.

I also did a post on how firms in perfect competition react to an excise tax (which works just like an increase in costs). It shows how price will rise. See How Firms’ Reaction To An Excise Tax Determines The Market Outcome. I show rising MC lines and the result is a higher market price.