Two part tariff-income effects I understand that a monopolist optimally sets a two-part tariff by pricing at marginal cost and then extracting CS as a lump sum fee.  However, wouldn't the lump sum fee induce a decrease in consumer demand?  Is the typical assumption made in two-part tariff problems that there is no income effect?
In the typical textbook treatment of the two-part tariff model, income effect is ignored/assumed to be negligible.
Goldman, Leland, and Sibley (1984) provided detailed comparison of optimal nonlinear pricing strategies (of which two-part tariff is a special case) with and without income effect. Their conclusion is

When [income effects] are absent, the aim of optimal pricing is to raise a given amount of profit with the least possible distortion to individual's consumption plans. Therefore increments of consumption are priced according to the  Ramsey rule. When income effects are present, the optimal pricing problem is equivalent to the optimal taxation problem, and the goal is optimal income redistribution.