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Is it possible to do something similar to iPhone hotspot, but instead of using the iPhone's cellular data connection, it uses it's Wi-Fi connection instead. Thus, allowing a MacBook Air to access the hotspot in order to use the internet through the iPhone's Wi-Fi connection instead of its cellular connection.
I would like to try this because my MacBook Air's Wi-Fi connection is flaky, but when connecting it to my iPhone's hotspot it seems to be fine.
As per http://support.apple.com/kb/ht4517, you cannot use your Wi-Fi connection on your iPhone while using Wi-Fi for Personal Hotspot.
If other devices have joined your Personal Hotspot using Wi-Fi, you can use only cellular data to connect to the Internet from the host device.
However, if you connect your computer to the iPhone using a USB cable or Bluetooth, it seems to be possible to utilise the Wi-Fi via the phone. In this case the blue statusbar informs the usage of Personal Hotspot connections and Wi-Fi icon is still visible on the iPhone.
Disable unless needed box in System Preferences > Network > iPhone USB. I don't remember having to initially set up anything in particular, but YMMV. (E.g. if you don't have iPhone USB you may need to add the connection, etc.)