Motivated by experimental literature and cognitive psychology studies, we consider optimal screening problem in which an agent incurs a fixed cost of lying when she misrepresents her private information. In this environment, local incentive constraints are not binding in the optimal mechanism, and standard techniques for solving screening problems  are not applicable.

Significantly, the problem can no longer be dichotomized into two parts solved sequentially: an implementability part which involves an envelope condition and the monotonicity of the allocation, and an optimization part. We develop a new methodology to tackle this problem,characterize the optimal mechanism and compute it in special cases.Our method involves a procedure that jointly solves for the bindingnon-local incentive constraints and the optimal allocation.The optimal mechanism has a number of novel qualitative properties, such as lack of exclusion and first-best efficient allocation at  high- and low- ends of the spectrum of types. Also, bunching never arises, as the optimal quantity allocation is always increasing in type irrespectively of type distribution.