(resp. ©L) has a task level of t* (resp. t*), where ^ (t£, 0H) dc
-rr (t?, 0. ) = 0. . The wage for 0„ (resp. 0T } is given by w *
Proof of Claim 1: A worker of quality 8 performing a task level of t, produces 0 + 0t, and his wage will be equal to 0 + 0t, since firms are
competitive. Workers of type 0 will thus choose their task level to maximize their utility, given this wage level; max w - c(t, 0) » 0 + 0t - c(t, 0) , and the FOC is: (t*t 0)
Remark: The competitive equilibrium with perfect information is Pareto efficient.
As one may expect, the equilibrium looks similar as in the original model in which the task level is unproductive. That is:
• the equilibrium contracts provide the firms with zero profits. - there exists no pooling equilibrium
- the low productivity type will provide the optima1 task level in a separating equilibrium.
The good news is that the high productivity type may also obtain the optimal
task level, i.e the above competitive equilibrium with perfect information may emerge as a separating equilibrium. In Figure 13.D.l(a), the competitive equilibrium with perfect information is sustained as a separating equilibrium:
ie of the competitive t
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