  We analyze competition on nonlinear prices in homogeneous goods markets with
consumer search. In equilibrium firms offer two-part tariffs consisting of a
linear price and lump-sum fee. The equilibrium production is socially efficient
as the linear price of equilibrium two-part tariffs equals to the production
marginal cost. Firms thus compete in lump-sum fees, which are dispersed in
equilibrium. We show that sellers enjoy higher profit, whereas consumers are
worse-off with two-part tariffs than with linear prices. The competition
softens because with two-part tariffs firms can make effective per-consumer
demand less elastic than the actual demand.
