>I think this is what Baumol’s cost disease is about (productivity growth on one sector drives up labor costs and ultimately prices in other sectors,
This is a clear and accurate description, but your explanation of the underlying reasons isn't really as clear.
>1. students go into new lucrative thing
Part of the Baumol effect is that the share of total employment in the sectors with high productivity growth decreases, while that of low productivity sector increases. This is sort of the opposite of what you are saying.
>2. supply of doctors goes down
The Baumol effect by itself has no effect on the number of Doctors. There are always more qualified people who want to be Doctors than are allowed to be Doctors for a great number of reasons. It isn't because not enough people want to be Doctors.
3, 4, 5
Yes those look like the Baumol effect.
6, 7
Not really what the Baumol effect is talking about.
Baumol illustrated his point in a simple manner. In the 1700's a string quartet required four musicians, and today a string quartet still requires four musicians (no productivity gain). However, those musicians today expect 21st-century salaries to match the rest of the economy, making the cost of hiring a quartet vastly more expensive relative to goods like mass-produced items.
The wikipedia entry looks pretty well done:
https://en.wikipedia.org/wiki/Baumol_effect#cite_note-:11-4
