Hidden Information Modelling:

The discussion of  this  sub-section is based on  the lecture notes of Tian, G., (2005) prepared as a part of microeconomic theory. We have taken liberty of adopting the sequence and notation used in the note of the Sub-section 12 and borrowed freely the work. The information gap between the principal and the agent has some fundamental implications for  the design of  the contract they sign. For an efficient use of economic resources, some information rent must be  given  up  to the private agent holding information. Thus,  we  look  for second-best solutions in the contract. In  such a situation the principal  trades off his desire to  reach  allocative efficiency by  giving information rent  to the agent to induce information revelation.

The main objective  of  this section  is  to find the optimal  rent  extraction efficiency trade-off faced by  the principal. We  seek to find the mechanism of designing his contractual offer to the agent under the set of incentive feasible constraints: incentive  and  participation constraints.  In  general,  incentive constraints are binding at the optimum, showing that adverse selection clearly impedes  the efficiency of trade.

Consider a consumer or a firm (the principal) who wants  to delegate to  an agent the production of q units of a good. The value for the principal of these q units is S(q) where S' >  0, S" <  0 and S(0) =  0.  

The production cost of the agent  is unobservable to the principal,  but  it  is known that  there is a fixed cost  F  and  the  marginal cost belongs to the set . The agent can be either efficient  (θ) or inefficient  (θ') with respective probabilities v and 1  -  v. That is, she has the cost function

Denoted by the spread of uncertainty on the agent's marginal cost. This information structure is exogenously given to the players.