Consider a context with unobservability of theworkers’ effort such
as that presented in Subsection 9.3.2 but with the following additional possibility.
Now, if a particular worker exerts no effort, the situation is detected by the firm
with some independent probability q, even if that worker turns out to be productive.
(Note that the model described in the text follows from the particularization q = 0.)
Assume the probability q is a costly control variable of the firm. Specifically,
suppose that, for any “chosen” q, the firm incurs a cost given by C(q) = q2. Fix the
values for the parameters of the model as follows: p = 0.1, y1 = 3, y2 = 2, ωˆ = 0,
δ = 0.5. Then, compute the optimal value of q that maximizes the discounted profits
of the firm at an equilibrium analogous to that considered in the text.