  We show that economic conclusions derived from Bulow and Roberts (1989) for
linear utility models approximately extend to non-linear utility models.
Specifically, we quantify the extent to which agents with non-linear utilities
resemble agents with linear utilities, and we show that the approximation of
mechanisms for agents with linear utilities approximately extend for agents
with non-linear utilities.
  We illustrate the framework for the objectives of revenue and welfare on
non-linear models that include agents with budget constraints, agents with risk
aversion, and agents with endogenous valuations. We derive bounds on how much
these models resemble the linear utility model and combine these bounds with
well-studied approximation results for linear utility models. We conclude that
simple mechanisms are approximately optimal for these non-linear agent models.
