13.3.3 A Graphical Representation of the Complete Information
Optimal Contract
Since ¯θ > θ, the iso-utility curves for different types cross only once as shown in the above
figure. This important property is called the single-crossing or Spence-Mirrlees property.
The complete information optimal contract is finally represented Figure 13.3 by the
pair of points (A∗,B∗). Note 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 efficient type. We denote by ¯ V ∗ (resp.
V
∗
) the principal’s level of utility when he faces the ¯θ− (resp. θ−) type. Because the
principal’s has all the bargaining power in designing the contract, we have ¯ V ∗ = ¯W ∗ (resp.
V
∗
= W
∗
) under complete information.