# Binding constraints at second-best optimum

I am dealing with ex-ante asymmetric information problems, i.e. adverse selection and in particular I cannot understand what's the intuition behind the fact that only two out of four constraints imposed in the second-best maximization problem are binding.

To be precise, when there is asymmetric information with two types of agents, the optimum is found maximizing the utility under two individual rationality (or participation) constraints and two incentive compatibility constraints. In order to simplify the computations, it can be proven that the IC for the high type agent and the IR for the low type agent are binding, whereas the other two constraints are redundant.

I have seen the proof and it is pretty clear but what I cannot understand is the economic intuition behind the proof; Is there someone that has this kind of intuition?

• My interpretation is something like this: because of the individual rationality of the low type, ql>0, because of the incentive compatibility constraint qh>ql, this implies qh>0. So in other words the incentive compatibility constraint is a stricter condition than the individual rationality – Lex Apr 21 '16 at 20:25
• The statement you make is not true for all utility functions. (E.g.: sometimes signaling and screening problems only have pooling equilibria.) So unless you narrow down your question the answer would be "Any percieved intuition will be false as the claim is not true." Perhaps you can define a class of utility functions that permit an intuitive explanation but I suspect that you will need mathematical properties that do not allow for such a class. – Giskard Apr 22 '16 at 15:45