To cost the earth is to be outrageously expensive. It will cost the earth.
It is exaggeration and is used most in the negative, to say something was cheaper than feared. It belongs to speech rather than to anything written down.
1phrasecost the earthTo be outrageously expensive.
“A new boiler will cost the earth and there is no way round it.”
cost the earth is a phrase.
Practised in Idioms