Got to agree with Blackmesa8. To my knowledge the content publishers (e.g. MS, Apple, ATI etc.) are Akamai's customers and they are the ones paying. The value of the Akamai service to them is to provide their customers (the content downloader) a better quality of service.
ISPs hosting Akamai nodes are partners of Akamai, tho I'm not sure if Akamai pay the ISP to host or whether it's a barter agreement e.g. Akamai supply servers & ISPs provide hosting & bw.
The value for the ISP to partner is they give their customers a better quality of service as popular files are on their local network & they save their upstream bandwith, as each file is only transfered once (to the hosted Akamai server(s)).