From Longman Dictionary of Contemporary Englishdrive something ↔ up phrasal verbBBTPEto make prices, costs etc rise quickly The oil shortage drove gas prices up by 20 cents a gallon. → drive→ See Verb table
Examples from the Corpus
drive up• People panicked when it was cold and it drove the market up.• There were a lot of cars parked in the drive and up and down the road.• I drove slowly up the road, not wishing to overtake the white police car.• His feet seemed hardly to touch the ground as the wind drove him up the slope.• S. policy drives the mullahs up the wall.• He drove her up to Fordham Road.• They told me to get in the squad car and we drove right up to it.• Depending on where your drive ends up you will face a tricky second shot to a long, narrow green.From Longman Business Dictionarydrive something → up phrasal verb [transitive] to force prices, costs etc to rise quicklyA shortage is all it would take to tighten supplies and drive up prices. → drive→ See Verb table 