Q: Can't install Mavericks after hard reset

If your MacBook Air came with Mavericks installed, you can reinstall by booting to the Apple servers via the internet by restarting and hold the Command+Option+R keys.  The boot will take longer but you can then install Mac OS X. 

A basic question is, why did you format the internal storage?  You should never do that without making a backup on another hard drive so you have a path to restore the system.

If you are not able to get an internet connection, try taking the MacBook Air to an Apple store genius bar and see if they can install Mac OS X from their system.

What OS came with your computer? If it wasn't Mavericks and you have access to another Mac, go to the App Store. Sign in with your Apple ID and download Mavericks. Then use this program to create a bootable USD stick.

Bootable USB Flash Drive – Diskmaker X