Imagine walking into a modern Bureau de Change and handing over a one drachma coin from Classical Athens, and asking for US dollars. What's the exchange rate?

(For the purposes of the hypothetical, let's disregard the inherent value of an antique coin.)

Modern exchange rates are determined by the relative popularity of the currencies, which normally depends on factors like GDP, inflation rates, and central bank interest rates. We could try the same, except adjusting for inflation over 2,500 years and accounting for minor social influences such as the fall of the Roman Empire is clearly a loser.

So I'll try to do it by equating incomes.

There are plenty of sources from Classical Athens to say the average wage of an Athenian worker was a drachma a day. Athenians didn't work every day. They didn't have public holidays like we do, but they did have a lot of religious festivals. No one much except slaves did any work during the Great Dionysia, for example. I'll arbitrarily assign 330 working days.

I found a 2005 US census which says the average yearly income of people in full time emplyment was USD 49,069.

If we take the value of average wages to be equivalent, then the Bureau de Change should give us about USD 150 for our coin.

The exchange rate of the modern Greek drachma, as I write this, is GRD 1 = USD 0.0037.

So 1 Classical Athenian drachma has the purchase power of 40,540 modern drachmae, which looks bad until you realize this gives a notional inflation rate, year on year, over 2,500 years, of 0.0425%

That's pretty good inflation control!