I really liked the discussion of the Chamley-Judd model, especially in parable form.
Question though: I worry that some individuals have the ability to recharacterize their earnings as either income or gains by shifting their contracts and methods of compensation.[0] If so, then you end up with odd results. Scenario 2 (a 50% tax on wages) turns into Scenario 1 (no taxes) for that subset of the population.
Looks like a well studied topic, so I'm sure someone tackles this?
[0] Say I build machines that make widgets, and your new widget factory wants such a machine. You could hire me as an machine-building employee, I could own my own business and you could buy the machine from me, or you could give me shares of ownership in your factory. Each of these could result in the same actions and changes in wealth for all parties, but would be taxed under completely different systems. CEO compensation packages are the most transparent real world example of compensation structuring I can think of. On the other hand, Jon Ronson interviewed a woman making 1.5-3 million per year who claimed she paid 35%, that she wasn't rich enough to restructure to avoid income taxes. This was in a piece on income inequality, maybe for GQ. So maybe this is non-trivial until you start getting near the top...