Design a Contract
Experiment
Design a contract Experiment
1. The owner (you, the principal) needs to hire an expert
(agent)
2. You have to design a contract
3. The expert can accept or reject the proposal
• If the expert rejects the proposal
•
He will earn 100 and the principal will earn nothing
• If the expert accepts the contract
•
He/she chooses his/her work effort
4. The expert’s effort determines the total return
5. Contract determines share of returns
2
Contract
• Two instruments of payment:
Only integers
– Fixed Payment a  (700,700)
– Share of return for expert b  {0%, 10%, 20%, ... , 100%}
•
•
•
•
•
Only in
multiples of 10
percent
If a  0 it represents a salary for the expert
If a  0 it represents a payment for the expert to the owner
If b  100% , for example, it means that the expert will receive all the return.
Cost of effort = C(e), C’(e) > 0
Total Return = P(e), P’(e) > 0
• The expert gets: b  P(e)  a  C (e)
• The owner gets: 100%  b P(e)  a
Note:
• No risk sharing only optimal incentives
• In this case total return is a perfect signal of effort.
3
Expert’s effort: e
1
2
3
4
5
6
7
8
9
10
Total Return from
expert’s effort
P(e) = 70x(e)
70
Total Cost of
effort for expert
C(e)
0
140
210
280
20
40
60
350
420
490
560
90
120
160
200
630
700
250
300
4
RUN EXPERIMENT
RUN EXPERIMENT
Go to b.socrative.com
Room: 60bdfd2f
Figure 1: Returns and costs
800
700
Maximum
surplus
when e = 10
(700 – 300
= 400)
Returns and Costs
600
500
400
300
Return
200
Cost
100
0
1
2
3
4
5
6
7
8
9
10
Effort
levels
7
How to implement the effort level = 10 ?
• If the principal could enforce the contract that stipulates effort
level, there would not be any need for an incentive contract.
• But the principal cannot enforce the contract. Instead, he has
to provide the incentives to the agent so that he rationally
chooses e = 10
• Principal thinks by backward Induction: How will the agent
react to a particular contract (b,a)?
• Agent: Maxe b×P(e) + a – C(e)
• Individual Rationality: b×P(e) + a – C(e) > 100
• Incentive Constraint (Eq. 8): b P’(e)=C’(e)
• Let’s first look how the agent will react to
different levels of b (Incentive constraint)
Agent’s
effort: e
1
2
3
4
5
6
7
8
9
10
Total Return Total Cost of Marginal Marginal Cost
from agent’s
effort for
Return
of effort
effort
agent
from effort
P(e) = 70e
70
140
210
280
350
420
490
560
630
700
C(e)
0
20
40
60
90
120
160
200
250
300
P’(e)
70
70
70
70
70
70
70
70
70
70
C'(e)
0
20
20
20
30
30
40
40
50
50
• The marginal cost of effort is always less than the marginal return from effort 
• All the principal needs to do is to give to the agent enough of a share of the
project (b) to get him to put in full effort
9
Deriving the Solution: Marginal Cost and
Marginal Return Faced by Agent
80
Marginal Cost or Marginal Return
70
60
50
Marginal Cost
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Effort
10
Deriving the Solution: Marginal Cost
and Marginal Return Faced by Agent
80
Marginal Cost or Marginal Return
70
60
return share 10%
return share 40%
return share 50%
return share 70 %
return share 80 %
return share 100%
Marginal Cost
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Effort
• Only five effort levels can be optimal (e = 1, 4, 6, 8 and 10) (de/db) > 0
• A return share of 80% is sufficient to induce full effort of an optimizing agent
11
Optimal and Efficient Contracts
• Assuming both agent and principal are profit maximizers and
have sequential rationality.
• Return share (b): at least 80%
• Participation Constraint:
– Outside option is $ 100
– So agent must get a total payoff of at least $ 101
• Optimal fixed payment
– If b = 100%, the principal will set a = $ - 299. Agent’s payoff:
a + 1 [700] – 300 > 100  -299 + 700 – 300 = 101
– If b = 90%, the principal will set a = $ - 229. Agent’s payoff:
a + 0.9 [700] – 300 > 100  -229 + 630 – 300 = 101
– If b = 80%, the principal will set a = $ - 159. Agent’s payoff:
a + 0.8 [700] – 300 > 100  -159 + 560 – 300 = 101
12
Expert’s Behavior
• Optimal response
– Accept if Total Payoff is > 100, reject otherwise
– If accept, choose optimal level of effort (e=1 if b=0%, 10%, 20%; e=4 if
b= 30%, 40%; e=6 if b=50%, e=8 if b=70%, 80%; e=10 if b= 80%, 90%
and 100%)
• Sub-optimal response
– Reject a contract when the contract is good
• (a=-299, b=100%)  Optimal behavior would be to accept and e=10  Max payoff = -299 + 700 –
300 = 101 > 100 (“unfair contract”)
• (a= 140, b=30%)  Optimal behavior would be to accept and e=4  Max payoff = 140 + 0.3(280)
– 60 = 164 > 100 (principal got unlucky)
– Accept a contract when the contract is bad
•
•
(a=-25, b=50%)  Optimal behavior would be to reject  Max payoff (e=6) = -25 + 0.5(420) – 120 = 65 <
100
(a= -99, b=70%)  Optimal behavior would be to reject  Max payoff (e=8) = -99 + 0.7(560) – 200 = 93
< 100
– Oversupply: accept a good contract but provide higher effort than
optimal
– Undersupply: accept a good contract but provide lower effort than
optimal
Results of the Classroom Experiment
• The results of our Classroom experiment exhibit
behaviors that are far from predicted by our
calculations.
• We have in total 57 participants. (N=57)
• When acting as principals many of you (51%)
proposed a positive payment.
• From the theory we know that this is not
efficient, since the expert has no incentives to
work hard since this payment is not based in the
performance of the agent.
Fixed Payment
Fixed Payment
49
47
45
43
41
39
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-500
-400
-300
-200
-100
0
100
200
Fixed Payment (cont’d)
• On average contracts had a positive payment
of -38.63 with a standard deviation of
141.521.
• Thus, the ones who wanted to give negative
fixed payments proposed a relatively larger
amount, in absolute terms, compared to those
who proposed a positive payment.
Return share
• On average the return share proposed by the
principals was 57%
• Thus, few of you decided to give the optimal
quantities of 80%, 90% or 100% of return
share. In total only 9 of you did so.
Return Share (cont’d)
1.2
1
0.8
0.6
0.4
0.2
0
Share Return
What explains these results?
• The fact that most of you choose a rate of 50%
could be associated to:
• Endowment effect: Most of you feel entitled
to the return rate and are reluctant to share it
or let it go. Kahneman, Thaler & Tversky
(1991)
• Fairness considerations: Many of you believe
that giving a high rate to the other party is
unfair. (Fehr & Schmidt, 1999)
Contracts
• In total we observed 8 efficient contracts, so only 14%
of the class could provide the contract that maximized
total output.
• On average the contracts give an average benefit of
136.48.
• Many of you decided to give a high wage to the worker
instead of only providing a number one unit above the
outside option (101). This could have an explanation.
• Gift exchange theory: Employers provide high wages
and in response workers work harder. (Akerlof,1984)
Acceptance Rate
• In total 71% of you accepted the contract.
• Given that, in average, the benefit of the
agent given the contracts was 136.48 this is
not surprising.
• 3 people accepted inefficient contracts, or
contracts whose total benefit for the agent
were less than 101. 
• 2 of you rejected efficient contracts. 
Effort
• Most of you decided to respond to the
incentives presented by the contract.
• The average effort of the contract was 6.61,
this makes sense since the average return
share was 57%.
• In this case you acted accordingly with the
theory.
Effort
Effort Exertion
12
10
8
6
4
2
0
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Series1
Conclusions
• When creating a contract, many of you did not
act in line with the “Homo-Economicus”
rationality.
• Nevertheless, your behavior is not “strange” since
many actual theories that look beyond the
framework of classical economics could predict.
• The “Endowment Effect” or “ Fairness
considerations” have been studied in Behavioral
Economics, which is the branch of economics that
is primarily concerned with the bounds of
rationality of economic agents.
Conclusions cont’d
• When evaluating whether to accept or Reject
the contract, it was easier for you to respond
to the incentives and to determine whether a
contract was actually providing you with
benefits or not.
• Perhaps you are more familiar with this type
of decision or is a simpler decision.