Nobody knows... EU and UK will have do deal on many aspects. There are EU workers in UK and Britains living in EU . In the future, UK and EU will probably sign some deals like it's happened between EU and Switzerland. Of course, now, some amusement for short sellers, catastrophic gurus and Brexit fans :-)

Here at Edinburgh, we have been fast to reassure EU applicants that they will not face international fees: there will be no change for existing and future EU students arriving in 16/17 and 17/18 for the duration of their studies. That's an important reassurance, especially for people on four-year PhD and undergraduate MA degrees.

The most likely result will be a Norway/Swiss deal where the UK continues to have free movement of labour. However, many employers will be more cautious about hiring in the UK. The lower value of Sterling will stimulate the small amount of manufacturing here (whisky, biscuits etc) but generally there will be fewer opportunities.

There's a great deal of uncertainty that surrounds the terms of exit at this point. There's also a possibility of Scotland going for an independence referendum again.
As a non-EU student, scheduled to start my MBA in UK this fall, should I be greatly concerned over the expected reduced number of opportunities at the time of graduation ?
I've already had some suggestions to reconsider my decision.

Indeed it's a big risk. I suspect Scotland, as a country, would be doomed if it is to go independent. I honestly don't think it can survive on its own. Same applies to Northern Ireland, especially it does not even have a reputable business school in the country. The UK is better to be united and then do trade with countries globally without the barriers imposed by the EU.

Bearing in mind that disposable income in Scotland is higher than in England, why is it doomed? Will staying in the single market not be an advantage? Is anyone in the Nrexit camp suggetsing that Britain should leave the free trade zone? If we stay in the free trade zone, then of course the EU tariffs will still apply.