You may have misread. The elite are the leaders of the MNCs, not the MNCs themselves.
There will not be any need to work as all desires are provided. If they want to work then they will be able to. The technological capability we will reach in the near future as well as the control over AI will allow individuals to pursue great amounts of work.
As for as elite numbers, I would suggest that the top 0.1% to top 1% of the population will comprise that number. Plenty of population to not have inbreeding. That number of people will also allow for power structures to form so people may exert control over one another.
Remove the bias you may have on the limitations of technology. Look at history and how far we've come in just the past 150 years. We are continuing on that trajectory no matter the "unrest" you see on TV. There will come a time where machines can and will replace human labor in its entirety. The elite will be the owners of said machinery. At that point commoners will have no use.