composer self-update error when deploying on a shared hosting server

I am using Laravel 5.2 and I am attempting to deploy app on a live server. I copied the git repo to the new location and ran composer self-update and received the following error:

[Composer\Downloader\FilesystemException]
Filesystem exception:
Composer update failed: the "/usr/local/bin/composer.phar" file could not be written

How can I update composer?

via Chebli Mohamed