The main purpose of a music video is to entertain their audience, might be to invoke a reaction keeping the artist and/or band in the public eye or having a storyline. It promotes the music visually and ensures the song will be remembered.
In this industry especially it's all about making money. Miley probably didn't choose to take her clothes off and start singing in front of a camera, may be her record label told her to because it'll make it in the public eye and it will make people remember it.
Example: Miley Cyrus - Wrecking Ball. In a response to her fans reaction, she replied in saying that striping naked was a symbol of having nothing after her fiance broke up with her. The music video simply symbolizes her feelings about the whole ordeal.
Other purposes could include a political or social message, to establish and/or deliver an artists image or personality and creating an image to follow like One Direction and Little Mix wearing certain outfits to make retailers like Newlook and Topman more popular. Also the band/artist makes a profit for the recording and company.
Example: Band Aid - Do They Know It's Christmas. It has a political message about children and families that live in a less fortunate country/society. Making money for a charity
How might an artist extend their income through having a music video?
Extending their income could be a perfume the artist/band have created, music sharing websites such as spotify and iTunes, video games, biographies/autobiographies, CD's, clothes/jewellery/merchandise and the ticketmaster promotion tool to direct fans to buy tickets/gigs to see their band/artist live.
Example: One Direction - Best Song Ever. The music video simply promotes their new movie 'This is us' about their journey so far from coming third in the Xfactor.
Describe how and why music videos have been used to fill in for bands on tour or when otherwise unavailable?
If for some reason the band or artist is late or there's some technical difficulty, sometimes they'd play a music video on the back screen of the stage. The reason for this is the organizers feel responsible for putting a show on for their audience who have paid money not to be delayed. Also, it's important to for a band/artist to have a youtube channel to post music videos whilst they're on tour because then those who haven't got their tickets don't miss out any new music for however long the artist is on tour.
Example: When seeing Mcfly live on tour in early 2013, their supporting act The Vamps were late. In order for the audience not to get agitated, they played a music video from their Youtube channel explaining who and what the new band are.
Thinking back through the story and presently; how have music videos enabled an 'extension of outlets' (opened up ways to get music to the masses?)
Music videos have enabled extension of outlets by having music channels such as MTV, 4Music and Top Of The Pops. Also iTunes and Spotify are music sharing websites that allow their fans to download their favourite band/artists songs or watch their music videos. These all enable the artists/bands to get their music global and accessable.