Implementation of the First-Best:

In  order that  the agent enters into a contract, the principal must  offer her a utility level that  is  at least  as  high  as  that  the  agent obtains outside the relationship.

These are called the agent's participation constraints. If we normalise to zero the agent's  outside opportunity utility level (sometimes called her quo utility level), the participation constraints are

In the assumption of complete information, the principal makes the following take-it-or-leave-it offers  to  the agent:  If ,  the  principal offers the  transfer  for  the  production level .

The agent accepts the offer and makes zero profit.

Therefore,  the  complete information optimal contracts  are  . You  can represent complete information optimal contract with the  help of a graph. See Figure for that purpose.

It can be  seen from Figure that the indifference curves for efficient and inefficient agents cross only once as shown in the above figure. This property is called the single-crossing or Spence-Mirrlees property. The complete information optimal contract (A*, B*) is given in Figure It can  be seen  that since the  iso-utility  curves of  the principal  correspond  to increasing  levels of  utility when  one moves  in  the  southeast direction, the principal reaches a higher profit when dealing with the agent of efficient type. We denote by  Y' the principal's  level of utility when he  faces the  type. When the principal has the complete information, he will design the contract, such  that