Touring doesn't make up a high amount as most people believe. Alot goes into a tour, and everything costs money. Limo rides aren't free and unless it's in a contract the artist will foot the bill. Everything from the promoter promoting the gig, renting the facility to put on the gig, the concession stands, security, the road crew, and that's just the starters for who is dipping their hands into the money pot. I won't even mention the budget to tour, travel expenses, packing any additional items needed for the tour, musicians for hire to play on the tour if needed, hotel accommodations etc. 8>)
Merchandising is another matter. Materials used to create the products, getting the proper licensing to use various images on the merchandise if it's needed, artists for hire to create images get their share of the pie as well unless the image was created as a "for hire" basis also cost money. Any leftover unsold merchandising that's still around at the end of the tour is in essence a loss of revenue unless another sales outlet can be utilized to move the remaining product.
For the performance income it's a requirement by law in the United States as well as most countries in the world that compensation be paid to the copyright owners for the public performance of their music. This is where ASCAP, BMI, and SESAC come into play, as these organizations are the ones that collect the public performance income and then distribute it in proportion based on the success for each song licensed by the organization. These three organizations are the ones responsible for "sampling" thousands of hours of radio airplay to generate a model of music broadcast on the radio. Both ASCAP as well as BMI "sample" but BMI also uses the playlist created by the program director of the radio station or "logs" to get a broader scope of what is played since songs that are no longer hits or never were hits are also in the airplay lists for rotation. This income is paid out in two varieties: the writer's share as well as the publisher's share.
Mechanical income is the revenue generated from the sale of the discs (album and CD), as well as cassettes etc. Rates are used to pay this income and the rates are set by the copyright royalty tribunal. These rates vary if stated in the contract. Everything costs money and if an artist gets a cash advance they won't see dime one until the advance is repaid. Plus studio time, disc artwork etc. all cost money.
I agree on the print income it's not very much as the publisher earns the most in this segment of revenue, and the synchronization income while it can be a good source of revenue is a shaky source of income, although these days soundtracks to albums sometimes do better than the movie the product is supporting.
Alot has to be taking into account for revenue. Touring will only generate money if the artist is successful. If the facility isn't filled with enough paying customers the losses could be deep red ink, and merchandising gets affected accordingly.
The copyright is where the most revenue comes in. From radio airplay, live performances, cover versions by various artists, sampling, licensing usage of performances is the best long term way to generate revenue. The longer the artist is successful the more revenue will be generated. This also is a disadvantage as the artist I collect Led Zeppelin just found out. The licenses on Zeppelin's first five albums were up for renewal and the royalty rate is now roughly four times what it was when Zeppelin released the albums. Zeppelin went to court to get a newer more modern royalty rate and lost as the court found the songs to be made for hire due to the copyright act of 1976. While still at the old royalty rate generating millions in revenue the surviving members also lost millions. There are rare occurrences where touring does generate big dollar income. Zeppelin with their manager Peter Grant pioneered the 90 / 10 split for revenue generated by a gig.
Let's just say music is a hobby. 8>)