1. The Fed has never said how high they expect inflation to rise as the economy reopens. But I bet they are surprised by the Apr/May numbers, even though they'll play the "transitory" card next week.
2. The higher inflation rises, the higher expectations and wage demands will rise, other things equal. That means labor supply will have to increase further than previously expected in order to dampen 2nd-round effects. Participation back at pre-Covid levels might not be enough.
The Fed will stall on this question until the impact of the end of enhanced unemployment benefits is clear, and schools/childcare are fully reopened. They'll talk about tapering before the labor market outcome is clear, but the risk is that rate hikes have to be brought forward.
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