How about this compensation contract (a fixed salary of
$18,496) to agent? Would this work?
S1 Prob. 0.25
S2 0.25
S3 0.25
S4 0.25
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企业财务管理基础知识
What is 城市轨道交通 urban rail transport
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2Lecture Materials
Broadly defined, information is any device that helps to reduce uncertainty.
Alternatively, information should be helpful in:
If the Principal can observe effort, how would he pay the agent?
X ½ - 62 = 100
X = 18,496
What is 城市轨道交通 urban rail transport
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9Lecture Materials
Now, if the Principal cannot observe effort, how would he pay the agent?
Y2
S3
S4
0.25 0.25
0
0
0
18,496
18,496 18,496
Expected Utility to Agent with Private info
105.5 (100)
Expected Payoff to Principal with Private
info
7,754
(10,254)
What is 城市轨道交通 urban rail transport
Eliminating “information asymmetry” – so that ex ante (before-the-act) private information can be known ex post (after-the-act).
What is 城市轨道交通 urban rail transport
18,496 18,496
0
18,496
the18c,4o9n6ting1e8n,t49s6alary18c,o49n6tract18w,4i9ll6improve
by
forcing
the Agent to give (e3 = 6).
Let us now look at the “private information to agent” issue!
Signal:
Y1
Y2
S1
S2
S3
S4
S5
S6
e1=10 2
3
3
4
5
5
e2= 5 2
2
3
4
4
5
Question: Are the signals, Y1 and Y2, useful?
What is 城市轨道交通 urban rail transport
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7Lecture Materials
Not interesting
Financial reporting
What is 城市轨道交通 urban rail transport
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5Lecture Materials
How do we know, a priori, that information is “useful”?
Improving production decisions – telling us to do the right things.
Optimizing the scope for risk sharing – so that some people can not make profits by harming other people.
What is 城市轨道交通 urban rail transport
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3Lecture Materials
Prob. e1=0 e2= 5
e3= 6
S1 0.25
0 14,722 (20,000) 14,722 (20,000)
S2 0.25
0 14,722 (20,000) 20,544 (30,000)
0 0 (25,000) 20,544 (30,000)
0 20,544 (30,000) 18,496 (35,000)
Would the new plan work? Let us calculate the agent’s utility and the principal’s payoff.
Post-effort information
Post-payoff information
Timing
Pre-contract
Post-contract, pre-effort Post-effort, pre-payoff Post payoff (ex post)
Information Availability
e1=0 18,496 18,496 18,496 18,496
111
5,254
e2= 5 18,496 18,496 18,496 18,496 100
10,254
e3= 6 18,496 18,496 18,496 18,496
Thus, a fixed salary to someone whom you cannot observe
Consider the following payoff structure (known to all):
Prob. e1=0 e2= 5 e2= 6
S1 0.25
0 20,000 20,000
S2 0.25
0 20,000 30,000
S3 0.25
0 25,000 30,000
S4 0.25
Y1
{S1, S2}
Y2
{S3 ,S4}
Would the contingent salary of $18,496 to agent still
work?
Signal:
Prob. e1=0 e2= 5 e3= 6
Y1
S1
S20.25 0.250018,496 18,496
18,496 18,496
Consider this new contingent contract (corresponding payoffs):
S1
S2
S3
S4
Prob.
0.25
0.25
0.25
0.25
e1=0 e2= 5 e3= 6
0 14,722 (20,000) 14,722 (20,000)
0 14,722 (20,000) 20,544 (30,000)
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2Lecture Materials
Can Private Information to Agent Benefit the Principal?
Now, the new private information makes it easy for
the agent to cheat. So, what should the principal do?
Consider the following payoff structure (known to all):
Effort S1
S2
S3
S4
S5
S6
Expected Payoff
e1=10 2
3
3
4
5
5
3.67
e2= 5 2
2
3
4
4
5
3.33
What is 城市轨道交通 urban rail transport
detecting the current state of the world, or
forecasting the future state of the world
What is 城市轨道交通 urban rail transport
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3Lecture Materials
0 30,000 35,000
Expected Payoff to Principal before Payment to Agent
0
23,750
28,750
Agent’s Utility Function: U = X½ - e2 100
where: X = agent’s compensations e = the effort level used by the agent
S3 0.25
0 0 (25,000) 20,544 (30,000)
S4 0.25
0 20,544 (30,000) 18,496 (35,000)
Expected Utility to A
0
71.5
100
Expected Payoff to P
0
n/a
10,173.5
Summary of results:
What is 城市轨道交通 urban rail transport
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1Lecture Materials
Can Private Information to Agent Benefit