You have to be a subscriber, and then it's available on their website: http://www.economist.com/audio-edition

If you just want to read The World This Week it's available online for free: http://www.economist.com/printedition/

To be clear, since I can't see without being a subscriber, the "audio edition" is different from the "Economist radio" linked on Soundcloud?

Yes. Audio Edition is a word-for-word reading of the print edition. Economist Radio looks like it has the random other audio things they do (there's also a podcast on iTunes with those sorts of things)

FWIW, I think all soundcloud stuff have download options. http://i.imgur.com/DzaoYSK.png

Not all, I believe whoever uploads it can turn it on and off...

Here's a direct link: https://soundcloud.com/theeconomist

Scroll down to "recent" and you'll see that many, but not all, of them have a download button.

Love the fact that they put it on soundcloud since I already use it