Please explain part (d), why does the total surplus is (T Scert = 0.3(120 − 100) + 0.3(99 − 80) = $11.7k), I get 0.3(120-100) for the firm’s utility, but I don’t know how my professor gets 0.3(99-80) for the worker’s utility.
A firm wants to hire a project manager (PM) at a salary of $100,000. 30% of PMs have high ability, and 70% of PMs have low ability. High ability PMs generate $120,000 in revenue and low ability PMs generate $80,000 in revenue. In addition to differences in productivity, high and low ability PMs have different outside offers. If a high ability PM is not hired by the firm, she can work for another company at a salary of $80,000. If the low ability PM is not hired by the firm, she can work for another company for $70,000. High ability PMs are also able to get a Project Management Professional (PMP) certification at a cost of $1,000. Low ability PMs are unable to get a PMP certification (they would fail the test). The firm is not able to observe a PM’s ability, but is able to observe and verify whether or not the PM has a PMP certificate.
(a) Draw the extensive form of the game.
(b) Does a separating equilibrium exist in which high ability PMs get certified, low ability PMs do not, and the firm only hires PMPs?
Show all the conditions for this to be a PBNE. Separating equilibrium exists High PM gets PMP: $100k − $1k ≥ $80k Firm hires PMPs: $120k − $100k ≥ 0 Firm doesn’t hire non-PMPs: $80k − $100k ≤ 0
(c) Does a pooling equilibrium exist in which both high and low ability PMs get hired? Why or why not? What would the share of high ability PMs have to be for a pooling equilibrium to exist?
Pooling equilibrium does not exist. If it did, firm would want to hire from pool: 0.3 × (120 − 100) + 0.7(80 − 100) ≥ 0 which cannot hold To have a pooling equilibrium: pH × (120 − 100) + (1 − pH)(80 − 100) ≥ 0 20pH + (1 − pH)(−20) ≥ 0 pH ≥ 0.5 2
(d) Suppose there was no certification process. What would be the PBNE outcome? What is the economic value of having the certification process?
PBNE: No one would be hired T Scert = 0.3(120 − 100) + 0.3(99 − 80) = $11.7k T Snocert = 0 Economic value = $11,700