What is the most efficient way of traveling South America for a month on a 2000 euro budget Starting somewhere in Europe?

Well i have no Idea about this

It will be very difficult to stay for a month with such a low budget which should include transportation also, but you might still be able to achieve so by using the following,

1) You can plan your trip during non season (since the period is not told), this will help you with cost cutting to a good extend.

2) There are lot of budget airlines operating, to start with you can travel to south america with any one of those.

3) You can stay in low budget hotels or paying guest where ever possible.

4)  Reduce food expenses by preparing at your place (if paying guest) or with local restaurants.

5) when travelling withing the country use busses/shared transport.

The above will help you to enjoy a stay at South America with Euro for a month.

its not easy but you can do it

in certain countries they have direct flights to south america like france spain and germany in certain times in the year you can get a ticket less than E and you can find some hotels with- E per room per night the rest of your many you can use normal transportation in these countries and you can have local food in small restaurant

thanks for invitation ..... have nothing to add