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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)

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