Study on Limited Partnership Based on an Analysis of Incentive
Mechanism Model of Venture Capitalist
Tian-jia Wang, Ya-na Chen
Economy & Management School, Wuhan University, Wuhan, China, 430072
(lujunshangjiang@163.com, chenyana613@gmail.com)
Abstract - In the system of venture investment, there exists
a kind of principal-agent relationship between the venture
investor and venture capitalist ， which will bring about a
series of problems such as moral hazard. The organizational
form of limited partnership is inclined to establish an incentive
mechanism which can maximize the utility of both the venture
investor and the venture capitalist with the coexistence of
incentive and constraint. The paper establishes an incentive
mechanism model in the organizational form of limited
partnership and systematically discusses the effectiveness of
the incentive pattern of limited partnership.
Keywords - Principal-agent Relationship, Venture Investor,
Venture Capitalist, Incentive Mechanism Model, Limited
Partnership
I.
INTRODUCTION
In the system of venture investment, there is a kind of
principal-agent relationship between the venture investor
and venture capitalist. The principal’s adverse selection of
the agent and the problem of moral hazard caused by
information asymmetry often exist.
A limited partnership is a form of partnership in which
investor and manager of venture capital form a limited
partnership enterprise, and the investor provides capital and
assumes the limited liability for the loss and debt of the
enterprise to the extent of its capital contribution, while the
manager takes charge of the management and operation of
the investment and assumes the unlimited liability for the
loss and debt of the enterprise[1]. In the limited partnership,
the venture investor invests equity capital which accounts
for 1% of the gross assets. But the equity capital is rarely in
the form of cash, out of the consideration of management
commitment and tax benefits. The venture capitalist can use
2.5% of the gross assets as their management fee. They can
generally get the 20% of total investment revenue in the
distribution of the investment income, but the premise is
that the lowest rate of return on investment has been reached
（ at least principal guarantying ） .Applying the limited
partnership into the venture investment, the organizational
form of limited partnership has an significant incentiveand-constraint effect on the venture capitalist. On one hand,
besides the fixed management fee as reward, the venture
capitalist can receive investment revenue according to a
relatively high proportion, which can generate a long-term
incentive. On the other hand, as the general partner, the
venture capitalist is obligated to assume unlimited liability
for the loss and debt of the venture investment, which, in
turn, urges him to work hard.
From the above, it can be seen that the organizational
form of limited partnership is inclined to establish a set of
covenant which can achieve the maximum utility for
venture investor on the condition that participation
constraints and incentive compatibility are satisfied
simultaneously. Scholars have undertaken a series of
discussions and researches on these problems. Sahlma
studies how the venture investor monitors and motivates the
venture capitalist to work hard by designing the covenant on
the basic of unilateral principal-agent relationship[2]. Jiang
Junfeng,et al. study the divisible covenant model of the
venture investment revenue by comparing the indirect
pricing theory with transaction efficiency and combining the
principal-agent relationship[3]. Bergmann and Hege find that
if a long-term contract is established between the venture
investor and venture capitalist, the venture investor actually
receives an incentive to not put off the successful
accomplishment of a project[4]. This paper establishes an
incentive mechanism model to make a systematic analysis
of the effectiveness of the incentive mechanism of a limited
partnership.
II.
THE MODEL AND ANALYSES
A. The basic analytical framework of the model
Hypothesis1: The degree of effort of the venture
capitalist is a . To simplify the analysis, assume that the set
consisting of all the degrees of effort has only two elements,
a  a , a，and a  a  0
Hypothesis2: The working cost of the venture capitalist
is C (a ) , which is solely related to the degree of
effort. C  0, C a   o
a
Hypothesis3: Within each venture investment cycle,
the total reward of the venture capitalist paid by the venture
investor is I which is related to the degree of effort of the
venture capitalist. The total revenue w is measured by the
degree of effort a in each venture investment cycle,
and w  0 . The total reward paid by the venture capitalist is
a
I w and the set consist of all the I has two elements,
namely, I  I , I 
Hypothesis4: Stochastic variable w  w, w,
and w  w  0 . w is influenced by the degree of effort of the
venture capitalist a ,which can be shown as
Pw a   p1 P w a  p0 ,in conditional probability.
optimization of the incentive model for the venture capitalist
can be transformed into the following problem:
Hypothesis5: The total utility function of the venture
capitalist is U c  U I   U a  and U I   I ， I  0 ,  2 I  0 .
According to assumption 3: I  I , I , there are only
two modes of payment that the venture investor can choose
from. The venture capitalist can choose either mode of
payment to simultaneously satisfy both the participation
constraint and incentive compatibility. To solve the problem
above, we have
 
a
The revenue of the venture capitalist
investment revenue is V (w) and. V  0 ,
w
a 2
w from the venture
 2V
.
0
w
According to the hypotheses above, the expected utility
function of the venture capitalist is
MaxE(U R )
s.t.  p I  (1  p ) I  C (a)  0 3

 p1 I  (1  p1 ) I  C (a)  p 0 I  (1  p 0 ) I  C (a)  4
1
1  p0
 *
I 
C (a)  5

p1  p 0


p0
*
I  
C (a)  6

p1  p 0

E(U C )  p1 I  (1  p1 ) I  C(a)1
The expected utility function of the venture investor is
E (U R )  p1 (V  I )  (1  p1 )(V  I )  2
1
The expected utility function of the venture investor
increases with the level of project benefits, therefore the
venture investor prefers the venture capitalist to take up high
degree of effort a .The expected utility function of the
venture capitalist increases with,the total reward paid by the
venture investor, thus the venture capitalist has to take up
high degree of effort a in order to obtain high expected
utility.
net
is U
B. The optimal incentive model for the venture capitalist
based on principal-agent relationship
In the process of entering into a reward contract,
information asymmetry often leads to the fact that the
degree of effort and the ability of the venture capitalist
cannot be observed[5][6]. To motivate the venture capitalist to
work hard, the venture investor need to design a new
incentive mechanism. The new incentive mechanism can
reach a equilibrium point where the revenue of both the
venture investor and the venture capitalist can be maximized
while the venture capitalist is also made to pay high degree
of effort.
The new incentive mechanism can be divided into
three stages. In the first stage, the venture investor offers a
kind of reward mechanism. In the second stage, the venture
capitalist decides whether to accept the incentive
mechanism provided by the venture investor. If the
incentive mechanism is accepted, then they will enter into
the third stage. In the third stage, the venture capitalist will
choose his action subject to the constraint of the accepted
incentive mechanism[7]. The incentive mechanism provided
by the venture investor need to satisfy two categories of
constraint conditions. The first category is participation
constraint, which means that the expected utility gained by
the venture capitalist when they pay high degree of effort is
no less than the utility when they accept this incentive
mechanism. The second category is incentive compatibility,
which means the utility gained by the venture capitalist
when they pay high degree of effort is no less than that
when they pay low degree of effort. Therefore, the
C.
c
When the revenue of venture investment is high, the
utility
of
the
venture
capitalist
*
*
1  p1
,
then
the
venture
capitalist
 I  C (a) 
C (a)  0
p1  p0
obtains award. When the revenue of venture investment is
low, the net utility of the venture capitalist
is U *  I *  C a    p1 C a   0 and then the venture
p1  p0
c
capitalist suffers loss.
Further discussion on the basic analytical framework
In the last section, there are only two elements in the
set consisting of three variables: the degree of effort, the
total reward and the revenue of the venture capitalist. Each
element in the set is studied in two extreme cases. The
expression of the total reward of the venture capital is
relatively simple. This section is a supplement to the basic
analytical framework in order to make the analysis more
generalized[8-10].
Hypothesis1: Within a venture investment cycle, the
degree of effort of the venture capitalist is a ,and a  0 .
The working cost of the venture capitalist is
2
C a  and. C a   ha , C  0
2
a
Hypothesis2: Within a venture investment cycle, the
total reward of the venture capitalist paid by the venture
investor is I , which includes the fixed reward f , the
variable reward n and the capital unvested by the venture
capitalist q . The fixed reward f depends on  , the rate of
management fee on investment funds agreed by both
venture investor and venture capitalist in advance. The
variable reward depends on the rate of management fee
 ,the total revenue n of venture investment w and the profit
sharing rate z agreed by both venture investor and venture
capitalist in advance.
Hypothesis3: Within a venture investment cycle, the
original capital of the venture investment is T , the capital
unvested by the venture capitalist S ,and the corresponding
shareholding proportion of the venture capitalist is M .
M 
S ,because the venture entrepreneur might get equity in
T
exchange of technology or other elements.
Hypothesis4: Within a venture investment cycle, the
total revenue of venture investment w is affected by the
degree of effort of the venture capitalist a and the random
factor  .Assume that w  a   .The probability of
sucessfully realizing the renvenue of venture investment
is p , shown as p w a  p in conditional probability, and
 
the probability of failing to realize the renvenue of venture
investment is（ 1  p ）.
Hypothesis5: Within a venture investment cycle, the
total utility function of the venture capitalist is
2I
U c  U I   U a  and U I   I ， I  0
 0 .The
a
a 2
revenue of the venture capitalist from the venture
2
investment revenue is V w and. V  0,  V  0 .
w
w2
According to the hypotheses above, within a venture
investment cycle, the fixed reward gained bu the venture
capitalist is
f  T 7
The variable reward gained by the venture capitalist is
n  w  pzw8
The capital unvested by the venture capitalist is
q  p1  z Mw  1  pS 9
So the total reward gained by the venture capitalist in
this investment cycle is
I  f  n  q  T  w  pzw  p1  z Mw  1  pS 10
That is
I  T   a     pza     p1  z M a     1  pS 11
The total utility function of the venture capitalist is
U c  I  C a 
That is
U c  T   a     pz a     p1  z M a     1  p S 
Take the derivative of (13) with respect to M ,we can
get a  1  M  0 . Thus, improving the profit sharing rate of
z
the venture capitalist as z proves to be able to improve his
degree of effort.
Take the first derivative of a with respect to M , we can
get a  1  z  0 . Thus, improving the shareholding
M
proportion of the venture capitalist as M proves to be able to
improve his degree of effort.
After the venture capitalist invest a certain amount of
capital, the low degree of effort will lead to the failure of
investment project. The failure ofinvestment project will
result in the loss of the revenue of the capital unvested by
the venture capitalist. Therefore, this payment model has
have incentive-and-constraint dual effect on the venture
capitalist , which supports the conclusion of the basic
analytical framework.
We use E U c  to represent the expected utility of the
venture capitalist:
E U c   EI  Ca14
We use EU r  to represent the expected utility of the
venture investor:
EU r   Ew  I 15
The venture investor designs a kind of covenant which
can maximize the utility of both the venture capitalist and
the venture investor. The premise of designing this contract
is to satisfy two covenant conditions. The first one is
participation constraints, which has been presented in
previous paper. The second one is incentive compatibility,
which means that the maximization of utility of the venture
investor has to be achieved by the maximization of utility of
the venture capitalist. We can put forward the following
questions from the above:
MaxEU r   MaxEw  I 16
s.t. EI  C a   U (17)
2
ha
 12
2
If we want to maximize the total utility function of the
venture capitalist, we can apply the definition of derivative
to (12) and set it equal to 0.

U c    pz  p1  z M  ha  0
We have
  p1  z M  z 
a
 13
h
This is the optimal degree of effort of the venture
capitalist. The greater the probability of success in
investment project, the greater the corresponding degree
of effort.

MaxI  C a (18)
Put Expression (13) into the target function(16), we
have Maxw  Ca   U 19
Take the derivative of (14) with respect to z and set it equal
to 0:
w a C a



 0 20 
a z a z
2
Put w  a   ， C a   ha ， a    p1  z M  z  into
2
h
Equation (19), we have
  p1  z M  z  121
When the rate of management fee  , the shareholding
proportion of the venture capitalist M and the probability of
success in investment project p are given[11-12]. We can get
the optimal profit sharing proportion p for the venture
capitalist
z*
z* 
1    pM
22
p1  M 
Likewise, When the rate of management fee  , the
profit sharing rate of the venture capitalist as z and the
probability of success in investment project are given,
take the derivative of (19) with respect to M and set it
equals to 0,we can get the optimal shareholding
*
proportion of the venture capitalist : M
M* 
III.
1    pz
 23
p1  z 
THE VENTURE CAPITALIST CONTRACT ARRANGEMENT
AND THE OPTIMAL INCENTIVE MODEL IN A LIMITED
PARTNERSHIP
A. Assume that the total revenue of the venture capitalist is
I , the rate of management fee is  ，generally from 1% to
2%.The profit sharing rate is  , generally from 10% to 30%.
The initial amount of venture investment is T , and the rate
of return on venture capital operation is r .
The total reveue of the venture capitalist is
I   T  T  r   Max  T  r,024
When the venture capitalist pays high degree of effort,
the income of the capitalist is
I   T  T  r     T  r 25
I
 T  T     T  26 
r
The equity capital of 1% to 2% which the venture
capitalist is required to invest in the initial phase can earn
20% of profits when the venture investment makes a profit.
The venture capitalist has a relatively major residual claim
for the venture investment.
If the venture capitalist pays low degree of effort, the
total revenue of the venture capitalist is
I  T  T  r 27
I
 T  28
r
When the venture capitalist pays low degree of effort,
he can earn no profit. but can only gain the basic fee for the
management of original venture capital. In reality ,if the
venture investment organization goes bankrupt, the venture
capitalist is obligated to assume unlimited liability for the
loss and debt of the venture investment organization.
B. From another perspective ， the venture investor’s
expected
payoff
for
the
venture
capitalist
is p1 I *  1  p1 I *  C a  ， exactly equal to the cost of the
venture capitalist when he pays high degree of effort.
Therefore, when U ( I )  I , the venture investor can carry
out the optimal incentive covenant through the covenant
arrangement of incentive compatibility. The optimal
incentive covenant not only avoids the extra cost of the
venture investor, but also guarantees the degree of effort
paid by the venture capitalist.
IV.
CONCLUSIONS
According to the theory on mechanism design, the
optimal incentive model, which is deduced under the
framework of principle-agent theory, features the
coexistence of incentive and constraint. The optimal
incentive model enables the venture capitalist to gain high
level of reward if he pays high degree of effort. And he is
held responsible for the loss of venture investment if he
pays low degree of effort.
In the limited partnership, contract arrangement for the
venture capitalist has the advantages of the above optimal
incentive model. The venture investor plays dual role as
both the manager and investor of venture funds. As the
manager of venture funds, the venture capitalist possesses a
relatively major residual claim and he can gain high level of
reward if he pays high degree of effort. If he pays low
degree of effort, the venture capitalist, as the investor of
venture funds, would not only lose the revenue of the
original capital he has invested, but also have to assume
unlimited reliability for the venture investment organization.
V.
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