Yes, you can invent your own applications for different operations like on Facebook or for phones. There is a guy who invented an application for iPhone and he made more than $800,000 profit in less than a year. The amount of money you will charge depends on the amount for time and money spent in the invention as well as the price worth of the application. For some applications, like those of iPhone, they are charged around $0.99 to $9.99. You can go to, http://www.howtomakeaapp.net/, to get ideas on how you can invent one.
There is also this website I heard about inventing apps that will pay like $1,000 for your App Idea if you do not want to produce it yourself or have the money to do so. Called Https://www.InventThatApp.com. Never done it myself but have heard about it.