We analyze a nonlinear pricing model where the seller controls both product pricing (screening) and buyer information about their own values (persuasion).
We prove that the optimal mechanism always consists of finitely many signals and items, even with a continuum of buyer values. The seller optimally pools buyer values and reduces product variety to minimize informational rents.
We show that value pooling is optimal even for finite value distributions if their entropy exceeds a critical threshold. We also provide sufficient conditions under which the optimal menu restricts offering to a single item.
