Notesale: Turn your study into money

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LECTURE NOTES ON THE
PRINCIPAL AGENT MODEL

1

SIMPLIFIED MODEL
The Set-Up Two players: a firm and a worker
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Firm proposes a wage contract
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Worker decides between accepting or rejecting the wage contract offered
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But if worker accepts wage
contract, then game moves to next stage
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Workers chooses effort level e
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Output is realized, wage is paid to worker,
and the game ends
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But
with probability 1 − ηe, no output is produced
and zero revenue obtained
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So note that worker’s effort generates ”random” output
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Expected profit to firm is:
where w is wage
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ce2 , where
w− 3

3

FIRST-BEST EFFORT LEVEL
¯
Maximize Eπ such that EU ≥ u
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e
3
First-Order condition:

2ce

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2c
4

FIRM CANNOT OBSERVE EFFORT, BUT
ONLY OUTPUT LEVEL
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But instead, firm’s wage contract is conditioned on observable and verifiable output
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, project is
a success) and w F is wage when output is low
(zero – project is a failure)
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e
3
FOC:

2ce

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2c

(1)

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RESULT 1:
ˆ
If w S − w F = v, then e = e∗
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Assume liquidity constrained
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Proceeding backwards, we now choose wage
contract (w S , w F ) to maximize firms’ expected
ˆ
payoff subject to e = e, as derived above in
equation 1
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First, we claim that in the solution, w F = 0
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Suppose instead at the optimum, w F > 0
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Hence, a contradiction
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wS
2c

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First Order Condition:

3η2 v 3η2 w S
−
= 0
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2
Conclusion: In the unique SPE, the wage contract offered is (w S , w F ) = ( v , 0) and effort is
2
ˆ
e = 3ηv
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9



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