Im a big fan of GitHub - asdf-vm/asdf: Extendable version manager with support for Ruby, Node.js, Elixir, Erlang & more · GitHub.
You can manage a multitude of language versions, including elixir and erlang and set up global or per project versions.

I know this is old but I’m here to not preach language version managers or anything and just offer the simplest most straightforward upgrade since you mentioned you are using homebrew?

Upgrading Elixir if it was installed with homebrew is pretty easy. Erlang is a dependency that will be installed or updated for you by homebrew as needed.

1. brew update
2. brew upgrade elixir
3. elixir --version

(I never do brew upgrade without a specfic formula, as that has caused me many headaches in the past)

Happy Elixiring!

As you seem to be using homebrew you can use $ brew list FORMULA:

$ brew list elixir
/usr/local/Cellar/elixir/1.7.2/bin/elixir
/usr/local/Cellar/elixir/1.7.2/bin/elixirc
/usr/local/Cellar/elixir/1.7.2/bin/iex
/usr/local/Cellar/elixir/1.7.2/bin/mix
/usr/local/Cellar/elixir/1.7.2/lib/eex/ (7 files)
/usr/local/Cellar/elixir/1.7.2/lib/elixir/ (231 files)
/usr/local/Cellar/elixir/1.7.2/lib/ex_unit/ (29 files)
/usr/local/Cellar/elixir/1.7.2/lib/iex/ (30 files)
/usr/local/Cellar/elixir/1.7.2/lib/logger/ (12 files)
/usr/local/Cellar/elixir/1.7.2/lib/mix/ (90 files)
/usr/local/Cellar/elixir/1.7.2/share/man/ (4 files)
$ brew list erlang
/usr/local/Cellar/erlang/21.0.5/bin/ct_run
/usr/local/Cellar/erlang/21.0.5/bin/dialyzer
/usr/local/Cellar/erlang/21.0.5/bin/epmd
/usr/local/Cellar/erlang/21.0.5/bin/erl
/usr/local/Cellar/erlang/21.0.5/bin/erlc
/usr/local/Cellar/erlang/21.0.5/bin/escript
/usr/local/Cellar/erlang/21.0.5/bin/run_erl
/usr/local/Cellar/erlang/21.0.5/bin/to_erl
/usr/local/Cellar/erlang/21.0.5/bin/typer
/usr/local/Cellar/erlang/21.0.5/lib/erlang/ (4393 files)
/usr/local/Cellar/erlang/21.0.5/share/doc/ (1261 files)
$

to upgrade simply follow the usual homebrew process:

$ brew update

and then

$ brew upgrade

$ elixir -v
Erlang/OTP 21 [erts-10.0.5] [source] [64-bit] [smp:8:8] [ds:8:8:10] [async-threads:1] [hipe] [dtrace]

Elixir 1.7.2 (compiled with Erlang/OTP 21)
$

For that command to work Erlang and Elixir have to be on the PATH. So in your ~/.bash_profile there should be something like:

export PATH=/usr/local/opt/openssl/bin:/usr/local/opt/erlang/bin:/usr/local/opt/elixir/bin:$PATH;

Cleanup:

$ brew list --versions erlang
erlang 21.0 20.3.6 21.0.5 21.0.4 20.3.4
$ brew list --versions elixir
elixir 1.7.1 1.6.5 1.6.4 1.7.2 1.6.6
$ brew cleanup elixir
Removing: /usr/local/Cellar/elixir/1.6.4... (411 files, 5.4MB)
Removing: /usr/local/Cellar/elixir/1.6.5... (411 files, 5.4MB)
Removing: /usr/local/Cellar/elixir/1.6.6... (412 files, 5.4MB)
Removing: /usr/local/Cellar/elixir/1.7.1... (413 files, 5.5MB)
==> This operation has freed approximately 21.7MB of disk space.
$ brew cleanup erlang
Removing: /usr/local/Cellar/erlang/20.3.4... (7,036 files, 277.4MB)
Removing: /usr/local/Cellar/erlang/20.3.6... (7,036 files, 277.3MB)
Removing: /usr/local/Cellar/erlang/21.0... (5,668 files, 271.8MB)
Removing: /usr/local/Cellar/erlang/21.0.4... (5,668 files, 271.7MB)
==> This operation has freed approximately 1GB of disk space.
$