I understand that this particular question is hard to answer. However, do there exist any historical record to how much was the GDP of Rome at some period? If not, could you give me a speculation or a guess of how much it was during the height of the Empire?
Population-weighted average is probably somewhere around 700*. There were around 45.5 million people in the Roman Empire in the year 14 CE.
So 45,500,000 * $700 = $31,850,000,000.
* Note I'm not too concerned with the exact average because these are all imprecise estimates anyway. But you can choose your own number between 600-800 to multiply by the population if you disagree with mine.