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The phrase "will provoke higher" is correct and usable in written English.
It can be used when discussing the potential for something to cause an increase in a particular outcome or effect. Example: "The new policy will provoke higher levels of employee engagement and productivity."
Exact(2)
But the resultant shortages will provoke higher inflation.
Under such circumstances, the Federal Reserve, fearing that a falling dollar will provoke higher inflation even as the economy is slowing, may keep interest rates higher than it otherwise would in order to attract dollar buyers.
Similar(58)
Shining the light high on a wall will provoke your cat to jump high in an attempt to "catch" the light.
Hopefully, the documented barriers that exist for women and minority entrepreneurs in the high-tech sector will provoke a greater urgency for change in these organizations.
It will provoke debate and experiment.
Using tear gas will provoke a riot".
This will provoke us even more.
This will provoke much heated debate.
"Even a heavy police presence will provoke a reaction".
Whatever he does will provoke hostility from some quarter.
The playwrights hope "The Exonerated" will provoke debate.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com