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Economics 206
Spring 2007 (Prof. G. Loury)
Assignment 8: The PrincipalAgent Problem
(1) A principal needs to contract with an agent to get a risky project done. The project
can either succeed or fail. If it succeeds it generates output with gross value
V>
0
.
If it
fails, it’s output is worth
0
. The probability of success depends on the e
f
ort exerted by the
agent. Let
e
≥
0
denote the agent’s e
f
ort, and let
p
(
e
)
∈
(0
,
1)
be the probability of success
given level of e
f
ort
e
. Assume that
p
(
e
)
is strictly increasing, strictly concave, and satis
f
es:
p
(0) = 0
;
p
0
(
e
)
→∞
as
e
→
0
;
p
0
(
e
)
→
0
as
e
→∞
,and
p
(
e
)
→
1
as
e
→∞
.E
f
ort of the
agent is assumed not to be observable by the principal.
A contract is simply a pair of numbers (
w
0
,w
1
) specifying what the principal pays the
agent in the event of the project’s success (
w
1
) or failure (
w
0
). The principal is risk
π
neutral
and seeks to maximize the expected payo
f
from the project, net of payments to the agent.
The agent’s preferences are given by:
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 Spring '07
 G.LOURY
 Economics, Microeconomics

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