Mirrlees' 1971 paper (An Exploration in the Theory of Optimum Income Taxation) on optimal taxation can sometimes be hard to follow. Does anybody know of (or could even provide here) a simple sketch of the derivations of the optimal nonlinear income tax schedule in his paper?
You can find a didactic exposition of Mirrlees (1971) -- including derivations of optimal tax schedule formulas for different social welfare and utility function -- in section 4.2 of "The Economics of Taxation" by Bernard Salanié (2003, First Edition).
I bet it is still somewhere in the second edition too, but I do not have a copy of it so I don't know in which section that would be.
There is also a good discussion in "Contract Theory" by Bolton and Dewatripont. It is discussed in terms of non-linear pricing in Chapter 2, "Hidden Information and Screening". However, Mirrlees optimal taxation is discussed explicitly in section 2.2.2, "Optimal Income Taxation." This treatment covers the case with only two types. The case with a continuum of types is discussed in section 2.3.3, again in the non-linear pricing context.