mid-14c., "swelling caused by gathering of 'wind' in the body; flatulence," also, figuratively, "outbursts of pride," from Latin inflationem (nominative inflatio) "a puffing up, a blowing into; flatulence," noun of action from past participle stem of inflare "blow into, puff up," figuratively "inspire, encourage," from in- "into" (from PIE root *en "in") + flare "to blow" (from PIE root *bhle- "to blow").
Meaning "action of inflating with air or gas" is from c. 1600. Monetary sense of "enlargement of prices" (originally by an increase in the amount of money in circulation) first recorded 1838 in American English.
<a href="https://www.etymonline.com/word/hyperinflation">Etymology of hyperinflation by etymonline</a>
Harper, D. (n.d.). Etymology of hyperinflation. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/hyperinflation