Description
Corporate venture capital (CVC), distinct from corporate venturing, is the investment of corporate funds directly in external start-up companies. Corporate Venturing refers to when a company supports innovation and new projects internally.
Financial Study on the Function of Social Capital in
Venturing Finance
Qin Zhihua
1
, Xu Bin
2
, Zhang Minghui
3
1. Business School, Renmin University of China, Beijing, 100872;
2. Economics and Management School, Wuhan University, Wuhan, Hubei, 430072;
3. School of Agricultural Economics and Rural Development, Renmin University of China,
Beijing, 100872.
Abstract:
The venture financing from scratch depends on the social network. Social networks can not
only help investors to identify entrepreneurial ability, but also help entrepreneurs to supplement
material wealth with their own social capital, promote investors to increase entrepreneurial
investments for the more social capital, and decrease the investors' economic requirement —return
on investment. Therefore, social capital financing is an important means, or even a necessary one,
to promote the start-up from scratch. However, with the growth of material wealth, entrepreneurs
will decrease social capital financing, gradually shifting to capital market financing as the primary
means. This paper constructs a theoretical model of social capital financing, in which the
entrepreneurial ability, material wealth and social capital are the basic variables; and based on this
model, the reality of social capital financing is logically explained.
Key words:
Start-up from Scratch; Entrepreneurial Resource Acquisition; Venture Financing; Social Capital
1. INTRODUCTION
A predominant characteristic for set-up firms is that in most cases they need to finance
their capital or resources from scratch (Gartner, 1985). Capital acquisition decisions
thus are some of the greatest challenges and most difficult issues confronting small
firms, but are central to their viability(Auken, 2005). For this reason, how to acquire
enough capital/resources without appropriate self-owned wealth and collaterals can be a
basic problem for most of new entrepreneurs as well as for the research about the
ways set-up firms get access to resources (Zhang et.al 2008). Though the fact that
acquiring resources from scratch for set-up firms has been investigated on different
dimensions, the explanations based on unified theoretical foundations are scarce. By
putting the function of social capital into a theoretical model, this paper tries to
analyze the detailed mechanism concerning how it becomes true for new
entrepreneurs to get resources from scratch.
The following sections are organized as follow: Section 2 review the relevant
literature to discuss the main problem in the analysis of low cost financing in
entrepreneurial process; Section 3 lays out a self-contained model to find the
mechanism in which new entrepreneur use their social network to lower their
financing cost; Section 4 concludes.
2. LITERATURE REVIEW
The analysis concerning set-up firms getting expansion capital and resources from
scratch can be generally summarized as following three questions: Can they get them?
If they can, why and how they can do that?
As for the first question, modern economic theory gives us a negative answer.
Information economics forms a common approach for addressing such issue, which
proposes that in an environment of asymmetric information, the so-called Agency
Problem requires entrepreneur owning enough wealth to conduct any business with
loan. Tirole (2006) formulates above idea in a unified model frame, in which the
potential entrepreneurs lacking self-owned wealth are destined to face strict credit
rationing from investors. On the other hand, since entrepreneurial ability and the
safety of the project can't be verified ex ante, investors have to infer the expected
benefits they may gain if the project succeeds using some indirect signals, among
which the major one is just the net wealth of entrepreneur (Zhang 1994; Anderu et.al
1995). Thus, without enough self-owned assets, those entrepreneurs who have
positive NPV project may still fail to finance their investment.
But in reality, some entrepreneurs indeed are able to finance their necessary resources
without enough self-owned wealth (Blundel& Smith, 2001). Why so? To answer this
question, some explanations stress the importance of the Heterogeneous Resources in
entrepreneurial process (Foss et.al, 2006). In this view, since different individual holds
different view about the value attached on different resources, acquiring resources
with low or even without cost can be realized from those individuals who undervalue
the resources they hold. With their original business ideas, new entrepreneurs can find
extra value on the resources underpriced by others and thus can acquire them at low
cost based on such Asymmetry of belief(Hayek, 1945; Shane& Venkataraman, 2000) .
Two basic abilities are central to the process of finding and realizing new value of
resources for entrepreneurs: Entrepreneurial cognition (for finding) and Integration of
organizational resources (for realizing) (Alvarez& Busenitz, 2001). However,
entrepreneurial cognition can discover new value only from either those resources
which can't be measured by market fair price such as new ideas or the resources
which have direct productivity such as machine.
While the view of Heterogeneous Resources has its sense to explain many stylized facts
in entrepreneurial process, it fails to explain why some entrepreneurs can even get
monetary capital with cost under the market fair price. To address such issue,
Economic Sociology provide some original and useful insights, among which the main
idea is that entrepreneurs can finance their capital by their Social Network in which
the traits of social exchange can solve the problem of asymmetric information and
makes it possible for entrepreneurs lacking self-wealth to finance the investment
(Aldrich& Zimmer, 1986; Zhang et.al, 2008). Social Network is the social structure
constructed by mutual reliefs and relationships (Adler&& Kwon, 2002), in which the
interactions of its members undergo less adverse selections and moral hazards
(Fan&Zhou, 2009). Social exchange are not only economic but also can be politic and
social, which includes the exchange of wealth, power, reputation and even friendship,
etc. (Lin, 2005). According to Blundel& Smith (2001), social network indeed plays a
role for entrepreneurs financing capital from scratch. Ensley et.al(1999) confirms that
the members in entrepreneur's social network form the major part of business
companies for set-up firms. But why social network can play a positive role for
entrepreneurial financing? Some points of views believe that the beliefs between the
members in the same network can facilitate the exchange of information by which
reduce the cost for financing (Burt, 1992; Uzzi, 1997), which fails to figure out why
Strong Relationships in most cases are not helpful for acquiring capital(Granovetter,
1974; Au& Kwan, 2009). Thus, it is necessary to find a ground theoretical foundation
for explaining the role of social network for venturing financing.
3. MODEL
Most of relevant literatures stress two variables in entrepreneurial financing: the
ability of the entrepreneurs and their self-owned wealth. Classical economic views
believe that for those potential entrepreneurs who have enough ability to become a
successful real one, they still can't finance their investment if they lack necessary self-
owned wealth and thus would be strictly rationed in credit. Though the resource-
based view and economic sociology all provide many insightful ideas about these two
variables to tackle such issues, a whole and analytical theoretical foundation
has not been built. The model we try in this section can be regarded as a new
supplementary theoretical explanation about how social network facilitates the
entrepreneurs lacking wealth get access to the low cost loan in reality. The major
variables in our model are not only entrepreneurial ability and the wealth owned by
the entrepreneurs, but social capital owned by them as well.
3.1 Basic structure
The basic timing line for entrepreneurs financing investment in our model can be
stated as follow: First, the potential entrepreneur lacking enough capital gives the
signal that she wants to start a business if some particular conditions are satisfied. If
she decides to set up the firm, she needs to find appropriate channels to finance the
investment. There are two types of investor can provide capital for entrepreneur to do
such financing: by formal financial market and by her social network: friends,
relatives, colleague, etc. Meanwhile, these two kinds of capital provider decide what
the interest rate they charge according to the self-owned wealth of entrepreneur and
other relevant information. Finally, after measuring the cost she must face, the
entrepreneur makes her final decision to decide whether she indeed commences the
business.
Denote the ability of entrepreneur asu and her initial wealth w. The required amount of
investment is k but k>w. If the business succeeds, the firm renders benefits y=f(k);
Else, all initial investment would be lost. We can signify the expected benefits of the
business as Ey=uf(k), whereu can be also regarded as the possibility of the success of business.
So we assume 0su=ps1. Then let R>1 be the financing cost of the investment and r>1 be
the riskless interest rate. Suppose all individuals are risk-neutral. The break-even
condition for entrepreneur to commence the business can
be formulated as:
u [ f ( k ) ÷ R ( k ÷ w)] > r w (1)
Inequality (1) means the expected returns for the entrepreneur starting the business
should be greater than the opportunity cost of her self-owned assets. We assume that
both types of investors all live in a perfect competition environment, which makes
theexpected returns of their lending always equal to rw. In this case, the sufficient-
necessary condition for entrepreneur acquiring loan is that by providing the loan the
expected return rate for relevant investors is r-1.
Thus, two major direct conditions for entrepreneur to start a business are (1): the
ability of entrepreneur is high enough; and (2): the financing cost is low enough.
Generally, the relationship between these two variables is negative: high ability means
high successful probability of the project, which lowers the interest rate required by
the investors when they are competitive perfectly. But in reality, entrepreneurial
ability is invisible which must be inferred by other visible signals such as the self-
owned wealth of the entrepreneur. Zhang (1994) prove that the critical level of
entrepreneurial abilityu
*
below which the entrepreneur will not choose to start the
business is positive correlated with her initial self-owned wealth. In another word,
from the perspective of investors, the expected entrepreneurial ability for the
entrepreneur conditioned by her self-owned wealth (i.e., E(u|w)) is a monotonic
increasing function of w, which means cE(u|w)/cw>0
1
.
Denote R
1
-1 be the investment returns rate required by investors, the above
assumptions also means R
1
is determined by follow:
R
1
E(u w) = r (2)
The necessary condition for entrepreneur to start the business is thus:
u[ f (k) ÷ R
1
(k ÷ w)] > rw
s.t.
R
1
E(u w) = r
? u [ f ( k ) ÷ r ( k ÷ w) ] > r w
E(u w)
(3)
The following proposition is easily to be proved:
Proposition 1: the determination mechanism of interest rate using entrepreneur's
wealth as signal can make some potential entrepreneurs whose ability larger than that
expected by investors fail to finance her business.
Proof: Proposition 1 meansu>E(u|w) is not the sufficient condition for
u[ f (k) ÷ r(k ÷ w)] ÷ rw > 0 always true. Now assume that the inequalityu>E(u|w)
E(u w)
automatically leads to u[ f (k) ÷ r(k ÷ w)] ÷ rw > 0 ,or:
E(u w)
u f ( k ) ÷ rw
>
u
u r(k ÷ w) E(u w)
?
u f (k) ÷ rw s 1 ? u f (k) ÷u rk ÷u w ÷ rw s 0 always holds if
u r(k ÷ w)
u>E(u|w). Obviously, this is not always true. For a numerical example, we can just let
w = 1,u = 0.5, E(u w) = 0.4, r = 1.1, k = 2, f (k) = 3, substitute these number into the last
inequality we get ÷1.2 < 0 . Therefore we disprove that justu > E(u w) can't let
1
A simplified proof can be stated as follow:
since
u [ f (k) ÷ R(k ÷ w)] = rw
,
*
Under the assumption that f (k ) > Rk
,
it is easy to show that:
cu
=
r[ f (k) ÷ Rk] > 0 *
cw [ f (k) ÷ R(k ÷ w)]
2
;
Denote|(u) and? (u) as the density function and distribution function ofu respectively, we have:
}
1
u d|(u )
1
dE(u w
)
?(u
*
)}u* [1÷|(u )]du
c
u*
E(u w) =
u*
1÷|(u
*
)
, so
dw =( [1÷|(u
*
)]
2 )
cw >0
See Zhang (1996) for details.
inequality (2) always be true. Q. E. D.
The implication of proposition 1 is that by just using external financial market, some
potential entrepreneurs who have high ability may fail to finance their investment due
to the high cost of financing. Thus, normal economic theory predicts that a
predominant difficult for potential entrepreneur starting business is that investors may
charge high interest rate for their self-protection in an environment of asymmetric
information (Alvarez& Busenitz, 2001). The entrepreneurial ability stressed by
resource-based view also cannot help entrepreneur find appropriate financing channel
because it can be just verified ex post entrepreneur's behaviors (Casson, 2005).
3.2 The Implication of Social Capital for Venturing Finance
Many facts in realities show using entrepreneur's social capital can reduce her
financing cost significantly (Batjargal& Liu, 2004; Francis& Sandberg, 2000), which
is proposed mainly by New Economic Sociology (NES). We think such idea is useful
to provide appropriate explanation for the reason why entrepreneurial financing from
scratch can come true and further propose that entrepreneur can exploits the benefits
from her social capital based on which she can provide social support to those who
can lend her low interest rate loan.
There are several common definitions of social capital in the realm of NES.
Adler&Kwon (2002) points out that in general it refers to the social ties (for
example, friendship) which can be utilized for other particular purpose. A more
precise and useful definition comes from Lin (2005): Social capitals are the resources
embedded in social network where relevant individuals can gain and use them to
realize their goals in their objective-oriented behaviors. This definition stresses two
concepts: social network and objective-oriented behaviors. To optimize one's interests
in social network, individual can and should use any types of resources include those
exist between persons such as belief, reputation, prestige, friendship and especially
the expectation of interests in some forms in future by providing boons to others.
Different places in social network can provide occupants different advantage and
force to facilitate them to realize their goals (Lin, 2005).
In order to occupy an advantageous place in social network, individuals can invest on
the relationships between persons by providing material or non-material benefits to
relevant people, by which gain and increase their social capitals. For example, you
can help your friends without requiring material returns. By this way, the social
capital (remember it refers to the relationship resources contributive to your future
goal) you own may increase because it is very possible that in future your friends can
also help you without any requirements and conditions. The same logic applies to
venturing finance from scratch: by lending entrepreneur who lacks enough self-owned
wealth in formal financial institutions, the lender may also obtain a chance to get help
from the borrower in future, which may make such seeming non-profitable loan very
profitable.
For the model we will build in next step, we pose following behavioral assumptions:
Assumption 1: the purpose of social capital investment is to expect future material or
non-material benefits.
Assumption2: providing material or non-material support to others is the major way
for one to increase her own social capital.
Thus, we propose that the very reason why investors provide low interest loans to
those entrepreneurs who lack capital and self-owned wealth is that by this way the
investors can accumulate their own social capital. Accordingly, the further question is:
what do requirements must be met for those entrepreneurs lacking self-owned wealth
to get access to low interest loans? In other word, to whom can the investors increase
their social capital in the greatest scale by providing low interest rate loans? The
answer is simple: those entrepreneurs owned great amount of social capital are the
ideal targets for investors to gain their own social capital by providing loans, because
an individual with great social capital is identical to an individual who occupies aideal
place in social network, upon which the expected future return made by her may be
large and the promise she makes is more reliable. Furthermore, those individuals
having considerable social capital (for example, a official who can abuse her power )
not only can provide returns by themselves, but also have capability to make other
persons in social network to make such returns, which makes the social capital
investment towards them more profitable.
Finally, we should notice that using social capital as a financial tool has its own
underlying cost. It is obvious that when entrepreneur gets support from others, a
social responsibility may form to makes her conduct some future costly actions in
return. Such cost may be so large that makes entrepreneur hesitate to use her social
capital for financing. For example, the individuals providing monetary support may
regard themselves as meritorious ones and therefore claim considerable rewards from
entrepreneurs (Au, Kwan, 2009). If entrepreneur fails to satisfy these social
responsibilities towards their "benefactors", the pressure coming from social network
may debase her social status and thereby decrease their social capital.
As a summary for this sub section, we summarize two necessary conditions for
venturing financing by social capital: (1) entrepreneur owns plenty of social capital
and lacks necessary amount of monetary capital; and (2) the supporters providing low
interest rate loans have plenty of monetary capital and are eager to gain social
capital.Next we try to model these above ideas.
3.3 The Model of Using Social Capital for Venturing Finance
At this sub section, we will introduce the factor of social capital into the basic
entrepreneurial financing model to investigate the implication of social capital in
venturing financing from an analytical perspective.
3.3.1 The Preference Structure
First of all, we will make an assumption about the preference for behavioral
individuals in our model. Maslow (1954) points out that in humankinds' hierarchy of
needs, the needs of higher levels would be pursued eagerly if needs in base level are
generally satisfied. With this logic in our model context, it is reasonable to assume
that the need for monetary returns realized by starting a business corresponds to the
need of comparative lower level in hierarchy of needs, while the need for social
capital corresponds to the need of comparative higher level in hierarchy of needs
because the potential returns provided by one's social capital in most cases take some
non-material forms such as reputation and social support. This logic implies a
hypothesis that in general, following with their increase of self-owned wealth, people
tend to attach more importance on their social reputation& place and seek more social
support from their social capital, by which they can find comparative more utility
from their social capital than that from their wealth. Thus, we propose following
preference assumption:
Assumption 3: the utility of behavioral individual U is the function of her self-owned
wealth w and social capital w and U
ww
=0, U
ss
s0; the marginal rate of substitute
(MRS) of s and w is decreasing; U
ws
>0.
U
ww
=0 is consistent with the risk-neutral preference; MRS of s and w is small than
zero implies the utility function is quasi-concave, which guarantees a concave
preference normally held in economic analysis; U
ws
>0 means the increase of wealth
makes individual get smaller satisfaction from the same amount of social capital when
she has little wealth. In other word, wealthy person attaches more importance on her
social capital than that attached by poor one, which is coherent with Maslow (1954) if
the need for social capital indeed corresponds to high level need. An appropriate
example is that comparing to a bagger, a millionaire may be more hesitant to lose her
social status and reputation because the considerable amounts of wealth she owns
makes her social capital more valuable to her based on the assumption we set. Finally,
U
ss
s0 is a very weak assumption consistent with basic economic intuition which just
means the marginal utility of social capital is no increasing or the individual is not
risk-preference towards her social capital. .
Now utility function is dependent on two variables: w and s. To make our following
analysis be consistent with the model in sub section 3.1, we simplify it into a one
variable function. To do so, firstly it is obvious that we can always substitute a
particular amount of w into another particular amount of s to make total utility
unchanged. This is equal to say:
U (w, s + A
1
) +U (w + A
2
, s) = U (w + A
2
+ A
*
(w, s, A
1
), s) = U '(w + A
2
+ A
*
(w, s, A
1
)) (4)
WhereA
1
andA
2
are respect two incremental;A*(.) is a particular function which
makes (4) always hold; U'(.) is defined as another utility function which not only
makes (4) hold but also only depend on one variable: the self-owned wealth. In the
case where individual is risk-neutral for her wealth, U'(.) is just a positive linear
transform of its variable and thus can be reduced to its variable alone, i.e.:
w + A
2
+ A
*
(w, s, A
1
) (5)
Expand (5) at A
*
(w, s, 0) and notice that A
*
(w, s, 0) = 0 :
w + A
2
+ A
*
(w, s, A
1
) = w + A
2
+ dA (w, s, A
1
) *
dA
1
A
1
=0
A
1
+ o(A
1
2
)
(6)
Redefine dA (w, s, A
1
) *
dA
1
A
1
=0
÷ A '(w, s) and omit higher order term in (6):
w + A
2
+ A
*
(w, s, A
1
) ? w + A
2
+ A '(w, s)A
1
(7)
Where A '(w, s) is the derivative of A
*
(w, s, A
1
) about A
1
at A
1
= 0 , which can be
interpreted as a positive transform function of social capital/wealth. Using this
transform function, we can always transform s at a particular amount into w at another
particular amount while hold the total utility unchanged. Now we propose the
following lemma which will play an important role for our model analysis.
Lemma: Under the preference structure described by assumption 3, A '(w, s) satisfies
cA '(w, s) > 0 and
cA
'(w, s) s 0 .
cw cs
Proof: U
ss
s0 means the marginal incremental of s is non-increasing following with
increase of s, which implies that the utility identical amount of w about s will not
increases with the increase of s. Thus, we have cA '(w, s) s 0 directly; then based on
cs
the assumption U
ws
>0, we can infer that holding s unchanged, owning more w leads to
more marginal utility for s, which means more utility identical amount of w about s.
Thus, we have
cA
'(w, s) > 0 . Q. E. D.
cw
3.3.2 A Stylized Model for Social Capital Financing
In this context there are two kinds of channels for entrepreneur to finance investment:
from formal financial market and from her social capital. We assume that if the
business succeeds, entrepreneur should not only liquidates her formal debt for
financial institution, but also respond to the relevant people from whom she borrowed
money ex ante if she has used her social capital as a financing tool; But if the business
fail, everyone would gain nothing. Now using the simplified utility function, the
break-even condition (1) becomes:
s.t.
u ( f (k) + A ÷ R
1
C
1
÷ R
2
C
2
÷ h(| (s), s)C
2
) ÷ (1÷u )(o (w, s)C
2
+ B) > rw
C
1
+ C
2
= k ÷ w
(8)
Where C
1
and R
1
are the amount of loans provided by formal financial investors and
its interest rate; C
2
and R
2
are the amount of social capital finance and its required
interest rate respectively. A is the wealth-identical amount of the increase of the
entrepreneur's social capital resulted by the enhancement of her social status if the
business succeeds; Correspondingly, B is the decrease of her wealth-identical amount
of social capital resulted by when the business fails. Notice that A and B are both
caused by the success or failure of the business per se, which are not related to social
capital financing. o (w, s)C
2
is another part of wealth-identical loss of social capital2
when business fails, which reflects the entrepreneur's to their "benefactors" (which
can lead to the downgrade of her social status) for defaulting the loan she borrow
from them. According to the above lemma, we have
c
o
s
0 and co
>
0 ,whereo is
cs cw
just the transform function of social capital/wealth (which corresponds toA' in
(7)). h(| (s), s)C
2
denotes the wealth-identical cost for the entrepreneur taking actions
of return for her "benefactors" when business succeeds, in which h is the transform
function (again corresponds toA' in (7)) and|(s) is the wealth-identical wealth expected by
"benefactors" for their "selfless" monetary support to the entrepreneur's business.
According to the reasons expounded in section 3.2,| is determined by s
and
d
|
>
0
3
. Holding other things unchanged, since the "amount" of social capital ds
owned by the entrepreneur can decrease the cost of her actions for return (it isn't
difficult to imagine that the person occupied an ideal social status has more
conveniences to achieve her objective), we have
c
h < 0 . But since more| often
cs
means more costly actions for return, we also have ch > 0 . Thus, the sign of
c|
dh = ch c|
+
ch can't be determined unambiguously if the above sign assumptions
ds c| cs cs
of partial derivatives hold true, which means the overall effects of the social capital
owned by the entrepreneur imposing on the cost caused by her actions of return are
complex.
2
It is simplified by the method of (6). The formal expression of this term should beo(w,s)|(C
2
) where|(C
2
)
means the loss of social capital when the entrepreneur defaults the loan C
2
from her social network if the business
fails. Since C
2
is highly positive related to|, we simplifies| directly as C
2
; we conduct the similar manipulation
on the following h(.)C
2
and|(.)C
2
3
We assume the social capital endowment for two kinds of investors is exogenous about the entrepreneur's
decision. So we can just regard| as a uni-variable function of s.
Now we discuss the opportunity for supporters to accumulate social capital by
providing seeming unprofitable loans. If their necessary real return rate for such
lending is still r-1 and they are risk-neutral, R is solved by:
r ÷ E(u w)| (s)
E(u w)(R
2
+ | (s)) = r ? R
2
= E(u w)
(9)
Recalling (2), we immediately have R
2
< R
1
. Obviously, the reason why such
inequality holds is that the real gains from the supporter not only include monetary
returns, but social capital providing them chance to gain potential benefits in the
future as well.
Rational entrepreneur should allocate her amount of debts from external financing and
social capital financing optimally. The optimization problem for is:
max u ( f (k) + A ÷ h(| (s), s)C
2
÷ R
1
C
1
÷ R
2
C
2
) ÷ (1÷u )(o (w, s)C
2
+ B) ÷ rw
{C ,C }
1 2
s.t.
R
1
E(u w) = r
(R
2
+ | (s))E(u w) = r
C
1
+ C
2
= k ÷ w
C
2
s C
(10)
Where C denotes the upper cap for the amount by social capital financing. Then we
can deduce a sufficient condition for entrepreneur financing her business by her social
capital:
Proposition 2: If the entrepreneur: (1) has the same preference structure described in
assumption 4;(2)has enough entrepreneurial ability;(3)has enough social
capital;(4)has little enough wealth;(5) dh < d |
,
then she would choose to use her
ds ds
social capital as a financing means.
Proof: Letc be a positive number small enough such that the following equality holds:
u ( f (k) + A ÷ R
1
(k ÷ w) ÷ rw) ÷ (1÷u )B ÷ c = 0 (11)
(11) means if entrepreneur can only lends capital from formal financial market, she
will not choose to start her business. Then let entrepreneur decrease her external
financing from financial market byo and at the same time increase her social capital financing
byo, the change of her expected wealth return in the future if she starts the
business is:
Aw = ÷(1÷u )o (w, s)o ÷u h(| (s), s)o ÷ R
2
uo + R
1
uo
[ro ÷ E(u w)| (s)o ]u
= ÷(1÷u )o (w, s)o ÷u h(| (s), s)o ÷
E(u w)
E(u w)| (s)ou
= ÷(1÷u )o (w, s)o ÷u h(| (s), s)o +
E(u w)
= [÷(1÷u )o (w, s) ÷u h(| (s), s) +u| (s)]o
+ rou
E(u w)
?12?
Since | > 0?Thus the sufficient-necessary condition for Aw > 0 holds is:
| (s) > (1÷u
)
o (w, s) + h(| (s), s)
=
o (w, s) ÷o (w, s) + h(| (s), s)
u u
(13)
Which means the left-hand side of inequality (13) is large enough or the right-hand
side of (13) is small enough. Differentiate (13) with s and w we have:
d |
>
( 1 ÷1) co
+
dh(| (s), s) , and
ds u cs ds
d |
=
0 > ( 1 ÷1) co
+
dh(| (s), s) = ( 1 ÷1) co (14)
dw u cw dw u cw
According to the lemma and the relevant partial derivatives assumptions, we have
u<1,
c
o
s
0 , co
>
0 , so we can conclude definitely that under the assumption
cs cw
dh < d |
,
only if s andu large enough with w small enough can (13) be satisfied
ds ds
which makesAw>0. Sincec is small enough, we letc be a number such
that 0 < c < Aw , then by transferringo from formal financing to social capital financing, the
break-even condition for the entrepreneur starting the business can be satisfied. Q. E.
D.
dh d |
Proposition implies the inequality ds < ds is a necessary condition for the positive
effect of the increase of social capital facilitating the entrepreneur starting her
business, which means that the increase amount of the cost for actions of return led by
the increase of social capital is smaller than the decrease amount of the cost for
actions of return caused by the increase of social capital. However, such condition is
not always true in reality. If the high level of social capital the entrepreneur holds
makes the supporters expect too many future benefits by providing "altruistic" loans
which force the entrepreneur's actions of return too costly, the increase of social
capital the entrepreneur holds may not motivate her entrepreneurial behaviors. But if
(14) is satisfied, the entrepreneur may have a opportunity to finance her business with
low cost.
Now we discuss how the change of entrepreneur's endowments may lead to her
change of financing decision.
Proposition 3: The increase of self-owned wealth would decrease the entrepreneur's
social capital financing and borrow more from formal financial market.
Proof: Suppose the
inequality
C
2
s C
always
true and substitute the first two
restrictions in (10) into the objective function:
max u[ f (k) + A ÷ h(| (s), s)C
2
÷
{C
1
,C
2
}
s.t.C
1
+ C
2
= k ÷ w
(15)
r
E(u w)
C
1
÷ (
r
E(u w)
÷ | (s))C
2
] ÷ (1÷u )[o (w, s)C
2
+ B] ÷ rw
Since (15) is a linear programming with only one restriction, the optimal solution
must be a corner solution which means C
1
and C
2
are either 0 or (but not both) k-w
4
determined totally by the comparative real cost of the financing by financial market
and by social capital. With some simple manipulations, we denote:
r
The marginal cost of C
2
: F
1
÷ (1÷u )o (w, s) + [h(| (s), s) +
r
E(u w)
÷ | (s)]u
(16)
The marginal cost of C
1
: F
2
÷ E(u w)
u
( 17)
Thus we have: cF
1
= (1÷u ) co
+
rE(u w)
÷
2u
dE(u w) cF
2
,
= rE(u w)
÷
2u
dE(u w)
cw
cF
1
÷ cF
2
= (1÷u ) co
cw
dw
cw
dw
co
and
c
w cw
so:
c
F
1
÷ cF
2
> 0
cw cw
c
w
; According to the lemma,u<1 and the assumption
c
w > 0 ,
(18)
(18) means with the increase of w, the difference between the marginal cost of social
capital financing minus the marginal cost of financial market financing become larger,
which would lead the entrepreneur use more financial market as her financing channel.
Q. E. D.
The intuition behind proposition 3 is that when potential entrepreneur have few
wealth but have considerable amount of social capital to exploit, she is insensitive to
the decrease of social capital caused by the failure of the business when she use social
capital as a financial tool but is very longing to the increase of the wealth if the
business succeeds so that she is willing to risk the loss of social capital to get a
possibility to become wealthy. But when her wealth increase, since social capital can
bring her more utility (based on the assumption U
ws
>0), she may not want to risk her
social capital again to gain wealth.
4
Corner solution is led by our above first-order approximation about the individual utility function. Though in
reality corner solution is unusual, the qualitative conclusion about our model is significative.
Proposition 4: The increase of entrepreneurial ability may motivate the potential
entrepreneur to use her social capital for financing.
Proof: Differentiate F
1
and F
2
withu and let the former minus the later:
cF
1
÷ cF
2
= ÷o ÷ 0 = ÷o
cu cu
cF cF
(19)
Sinceo is a positive number,
c
u
1
÷ cu
2
<
0
, which means high ability entrepreneur
can use social capital with low real cost, which may motive her use it more for
financing. Q. E. D.
Proposition 4 implies that the financing function of social capital can only help high
ability entrepreneur with low self-owned wealth to finance her business. For those
potential entrepreneurs whose ability is low, social capital still can't make them to
become real entrepreneurs.
Finally, we analyze the change of financing approach along with the development of
new set-up firms. With another extra assumption, we can deduce following strong
proposition:
Proposition 5: If the monetary wealth brought by the success of new business is
enough larger than the increase of social capital brought by the success of new
business, the new set-up firms would gradually change their financing channels from
entrepreneur's social capital to formal financial market.
Proof: Suppose the success of business boost the endowments of the entrepreneur
cF cF
from (w, s) to (ì
1
w, ì
2
s) whereì
1
, ì
2
>0. Notice the fact
c
w
1
÷ cw
2
>
0
in (18) and:
cF
1
÷ cF
2
= (1÷u ) co
+
[ch + ch c|
÷
d |
]
u = (1÷u ) co
+
[ch + ( ch ÷1) d |
]
u
(20)
cs cs cs cs c| cs ds cs cs c| ds
Due to the assumptions of co
s
0, ch < 0, ch > 0, d |
>
0 , it is not difficult to know
cs cs c| ds
the sign of (20) is uncertain. But if the increase of s is comparatively small enough
than the increase of w, then regardless the sign of (20) the whole effect of increase of
w and the increase of s would make F
1
-F
2
larger than zero, which means that only if
ì
2
is comparatively smaller enough thanì
1
, the marginal cost of using social capital
for financing would become larger comparatively than the marginal cost of financing
capital from financial market. Thus, the success of the business leads the entrepreneur
to decrease her debts owning to her "benefactors" and demands more loans in formal
financial market. Q. E. D.
Proposition 5 implicitly assumes that entrepreneur mainly acquires monetary wealth
rather than social capital by starting a new business, which in general holds. In reality,
the main purpose for entrepreneur to initiate a firm is just to gain economic benefits
rather than others. If the main purpose for the entrepreneur want to grasp more social
capital, then setting up a new firm and operating it cannot be the most efficient way
because by some other behaviors (such as help her friends "altruistically") more social
capital she can accumulate. Thus, it is reasonable to hypothesize that the entrepreneur
wants to and indeed gain more wealth rather than social capital from her
entrepreneurial actions. The authenticity of proposition 5 in reality is confirmed by
Zhang, et.al (2008), in which they find empirically that while set-up firms tend to use
entrepreneur's social capital to finance its investment, the developed firms get access to
loans mainly from external financial market.
4. CONCLUSION
Now we conclude the main ideas of our paper:
The invisible and unverifiable character of entrepreneurial ability may lead the
investors in financial market conduct strict credit rationing towards those entrepreneur
who own few self-owned wealth (Zhang, 1994). On the other hand, the core value of
entrepreneur can't be identified ex ante, which can only be self-verified in
entrepreneurial process (Casson, 2005). Thus, how entrepreneur without enough self-
owned wealth finances her investment from scratch is the main problem faced by most
of potential entrepreneurs.
By discussing the intension of social capital and construct a stylized model to address
the issue about how entrepreneur's social capital can facilitate those high ability
entrepreneurs starting their business, we prove that they can just utilize their social
capital as a low cost financing channel. Such channel is crucial for the new set-up
firms in their initial phase and makes it possible for the potential entrepreneurs realize
their business.
Based on the model we built, we further discuss the particular conditions faced by
entrepreneurs and the potential supporters who can accumulate social capital by
lending loans to the entrepreneurs in low interest rate. We show that the more social
capital and the less self-owned wealth the entrepreneur own, the more incentive for
them to use her social capital to "finance her idea"; the more self-owned wealth and the
less the social capital the potential supporters have, the more motivation for them to
provide "altruistic" to the entrepreneurs. By this way, the individuals with different
economic capital and social capital can exchange their comparative more resources by
which optimize their utility (Lin, 2005). However, following with the development of
business, the firms would gradually substitute their financing channel from the social
capital of the entrepreneur to external financial market.
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doc_836120269.docx
Corporate venture capital (CVC), distinct from corporate venturing, is the investment of corporate funds directly in external start-up companies. Corporate Venturing refers to when a company supports innovation and new projects internally.
Financial Study on the Function of Social Capital in
Venturing Finance
Qin Zhihua
1
, Xu Bin
2
, Zhang Minghui
3
1. Business School, Renmin University of China, Beijing, 100872;
2. Economics and Management School, Wuhan University, Wuhan, Hubei, 430072;
3. School of Agricultural Economics and Rural Development, Renmin University of China,
Beijing, 100872.
Abstract:
The venture financing from scratch depends on the social network. Social networks can not
only help investors to identify entrepreneurial ability, but also help entrepreneurs to supplement
material wealth with their own social capital, promote investors to increase entrepreneurial
investments for the more social capital, and decrease the investors' economic requirement —return
on investment. Therefore, social capital financing is an important means, or even a necessary one,
to promote the start-up from scratch. However, with the growth of material wealth, entrepreneurs
will decrease social capital financing, gradually shifting to capital market financing as the primary
means. This paper constructs a theoretical model of social capital financing, in which the
entrepreneurial ability, material wealth and social capital are the basic variables; and based on this
model, the reality of social capital financing is logically explained.
Key words:
Start-up from Scratch; Entrepreneurial Resource Acquisition; Venture Financing; Social Capital
1. INTRODUCTION
A predominant characteristic for set-up firms is that in most cases they need to finance
their capital or resources from scratch (Gartner, 1985). Capital acquisition decisions
thus are some of the greatest challenges and most difficult issues confronting small
firms, but are central to their viability(Auken, 2005). For this reason, how to acquire
enough capital/resources without appropriate self-owned wealth and collaterals can be a
basic problem for most of new entrepreneurs as well as for the research about the
ways set-up firms get access to resources (Zhang et.al 2008). Though the fact that
acquiring resources from scratch for set-up firms has been investigated on different
dimensions, the explanations based on unified theoretical foundations are scarce. By
putting the function of social capital into a theoretical model, this paper tries to
analyze the detailed mechanism concerning how it becomes true for new
entrepreneurs to get resources from scratch.
The following sections are organized as follow: Section 2 review the relevant
literature to discuss the main problem in the analysis of low cost financing in
entrepreneurial process; Section 3 lays out a self-contained model to find the
mechanism in which new entrepreneur use their social network to lower their
financing cost; Section 4 concludes.
2. LITERATURE REVIEW
The analysis concerning set-up firms getting expansion capital and resources from
scratch can be generally summarized as following three questions: Can they get them?
If they can, why and how they can do that?
As for the first question, modern economic theory gives us a negative answer.
Information economics forms a common approach for addressing such issue, which
proposes that in an environment of asymmetric information, the so-called Agency
Problem requires entrepreneur owning enough wealth to conduct any business with
loan. Tirole (2006) formulates above idea in a unified model frame, in which the
potential entrepreneurs lacking self-owned wealth are destined to face strict credit
rationing from investors. On the other hand, since entrepreneurial ability and the
safety of the project can't be verified ex ante, investors have to infer the expected
benefits they may gain if the project succeeds using some indirect signals, among
which the major one is just the net wealth of entrepreneur (Zhang 1994; Anderu et.al
1995). Thus, without enough self-owned assets, those entrepreneurs who have
positive NPV project may still fail to finance their investment.
But in reality, some entrepreneurs indeed are able to finance their necessary resources
without enough self-owned wealth (Blundel& Smith, 2001). Why so? To answer this
question, some explanations stress the importance of the Heterogeneous Resources in
entrepreneurial process (Foss et.al, 2006). In this view, since different individual holds
different view about the value attached on different resources, acquiring resources
with low or even without cost can be realized from those individuals who undervalue
the resources they hold. With their original business ideas, new entrepreneurs can find
extra value on the resources underpriced by others and thus can acquire them at low
cost based on such Asymmetry of belief(Hayek, 1945; Shane& Venkataraman, 2000) .
Two basic abilities are central to the process of finding and realizing new value of
resources for entrepreneurs: Entrepreneurial cognition (for finding) and Integration of
organizational resources (for realizing) (Alvarez& Busenitz, 2001). However,
entrepreneurial cognition can discover new value only from either those resources
which can't be measured by market fair price such as new ideas or the resources
which have direct productivity such as machine.
While the view of Heterogeneous Resources has its sense to explain many stylized facts
in entrepreneurial process, it fails to explain why some entrepreneurs can even get
monetary capital with cost under the market fair price. To address such issue,
Economic Sociology provide some original and useful insights, among which the main
idea is that entrepreneurs can finance their capital by their Social Network in which
the traits of social exchange can solve the problem of asymmetric information and
makes it possible for entrepreneurs lacking self-wealth to finance the investment
(Aldrich& Zimmer, 1986; Zhang et.al, 2008). Social Network is the social structure
constructed by mutual reliefs and relationships (Adler&& Kwon, 2002), in which the
interactions of its members undergo less adverse selections and moral hazards
(Fan&Zhou, 2009). Social exchange are not only economic but also can be politic and
social, which includes the exchange of wealth, power, reputation and even friendship,
etc. (Lin, 2005). According to Blundel& Smith (2001), social network indeed plays a
role for entrepreneurs financing capital from scratch. Ensley et.al(1999) confirms that
the members in entrepreneur's social network form the major part of business
companies for set-up firms. But why social network can play a positive role for
entrepreneurial financing? Some points of views believe that the beliefs between the
members in the same network can facilitate the exchange of information by which
reduce the cost for financing (Burt, 1992; Uzzi, 1997), which fails to figure out why
Strong Relationships in most cases are not helpful for acquiring capital(Granovetter,
1974; Au& Kwan, 2009). Thus, it is necessary to find a ground theoretical foundation
for explaining the role of social network for venturing financing.
3. MODEL
Most of relevant literatures stress two variables in entrepreneurial financing: the
ability of the entrepreneurs and their self-owned wealth. Classical economic views
believe that for those potential entrepreneurs who have enough ability to become a
successful real one, they still can't finance their investment if they lack necessary self-
owned wealth and thus would be strictly rationed in credit. Though the resource-
based view and economic sociology all provide many insightful ideas about these two
variables to tackle such issues, a whole and analytical theoretical foundation
has not been built. The model we try in this section can be regarded as a new
supplementary theoretical explanation about how social network facilitates the
entrepreneurs lacking wealth get access to the low cost loan in reality. The major
variables in our model are not only entrepreneurial ability and the wealth owned by
the entrepreneurs, but social capital owned by them as well.
3.1 Basic structure
The basic timing line for entrepreneurs financing investment in our model can be
stated as follow: First, the potential entrepreneur lacking enough capital gives the
signal that she wants to start a business if some particular conditions are satisfied. If
she decides to set up the firm, she needs to find appropriate channels to finance the
investment. There are two types of investor can provide capital for entrepreneur to do
such financing: by formal financial market and by her social network: friends,
relatives, colleague, etc. Meanwhile, these two kinds of capital provider decide what
the interest rate they charge according to the self-owned wealth of entrepreneur and
other relevant information. Finally, after measuring the cost she must face, the
entrepreneur makes her final decision to decide whether she indeed commences the
business.
Denote the ability of entrepreneur asu and her initial wealth w. The required amount of
investment is k but k>w. If the business succeeds, the firm renders benefits y=f(k);
Else, all initial investment would be lost. We can signify the expected benefits of the
business as Ey=uf(k), whereu can be also regarded as the possibility of the success of business.
So we assume 0su=ps1. Then let R>1 be the financing cost of the investment and r>1 be
the riskless interest rate. Suppose all individuals are risk-neutral. The break-even
condition for entrepreneur to commence the business can
be formulated as:
u [ f ( k ) ÷ R ( k ÷ w)] > r w (1)
Inequality (1) means the expected returns for the entrepreneur starting the business
should be greater than the opportunity cost of her self-owned assets. We assume that
both types of investors all live in a perfect competition environment, which makes
theexpected returns of their lending always equal to rw. In this case, the sufficient-
necessary condition for entrepreneur acquiring loan is that by providing the loan the
expected return rate for relevant investors is r-1.
Thus, two major direct conditions for entrepreneur to start a business are (1): the
ability of entrepreneur is high enough; and (2): the financing cost is low enough.
Generally, the relationship between these two variables is negative: high ability means
high successful probability of the project, which lowers the interest rate required by
the investors when they are competitive perfectly. But in reality, entrepreneurial
ability is invisible which must be inferred by other visible signals such as the self-
owned wealth of the entrepreneur. Zhang (1994) prove that the critical level of
entrepreneurial abilityu
*
below which the entrepreneur will not choose to start the
business is positive correlated with her initial self-owned wealth. In another word,
from the perspective of investors, the expected entrepreneurial ability for the
entrepreneur conditioned by her self-owned wealth (i.e., E(u|w)) is a monotonic
increasing function of w, which means cE(u|w)/cw>0
1
.
Denote R
1
-1 be the investment returns rate required by investors, the above
assumptions also means R
1
is determined by follow:
R
1
E(u w) = r (2)
The necessary condition for entrepreneur to start the business is thus:
u[ f (k) ÷ R
1
(k ÷ w)] > rw
s.t.
R
1
E(u w) = r
? u [ f ( k ) ÷ r ( k ÷ w) ] > r w
E(u w)
(3)
The following proposition is easily to be proved:
Proposition 1: the determination mechanism of interest rate using entrepreneur's
wealth as signal can make some potential entrepreneurs whose ability larger than that
expected by investors fail to finance her business.
Proof: Proposition 1 meansu>E(u|w) is not the sufficient condition for
u[ f (k) ÷ r(k ÷ w)] ÷ rw > 0 always true. Now assume that the inequalityu>E(u|w)
E(u w)
automatically leads to u[ f (k) ÷ r(k ÷ w)] ÷ rw > 0 ,or:
E(u w)
u f ( k ) ÷ rw
>
u
u r(k ÷ w) E(u w)
?
u f (k) ÷ rw s 1 ? u f (k) ÷u rk ÷u w ÷ rw s 0 always holds if
u r(k ÷ w)
u>E(u|w). Obviously, this is not always true. For a numerical example, we can just let
w = 1,u = 0.5, E(u w) = 0.4, r = 1.1, k = 2, f (k) = 3, substitute these number into the last
inequality we get ÷1.2 < 0 . Therefore we disprove that justu > E(u w) can't let
1
A simplified proof can be stated as follow:
since
u [ f (k) ÷ R(k ÷ w)] = rw
,
*
Under the assumption that f (k ) > Rk
,
it is easy to show that:
cu
=
r[ f (k) ÷ Rk] > 0 *
cw [ f (k) ÷ R(k ÷ w)]
2
;
Denote|(u) and? (u) as the density function and distribution function ofu respectively, we have:
}
1
u d|(u )
1
dE(u w
)
?(u
*
)}u* [1÷|(u )]du
c
u*
E(u w) =
u*
1÷|(u
*
)
, so
dw =( [1÷|(u
*
)]
2 )
cw >0
See Zhang (1996) for details.
inequality (2) always be true. Q. E. D.
The implication of proposition 1 is that by just using external financial market, some
potential entrepreneurs who have high ability may fail to finance their investment due
to the high cost of financing. Thus, normal economic theory predicts that a
predominant difficult for potential entrepreneur starting business is that investors may
charge high interest rate for their self-protection in an environment of asymmetric
information (Alvarez& Busenitz, 2001). The entrepreneurial ability stressed by
resource-based view also cannot help entrepreneur find appropriate financing channel
because it can be just verified ex post entrepreneur's behaviors (Casson, 2005).
3.2 The Implication of Social Capital for Venturing Finance
Many facts in realities show using entrepreneur's social capital can reduce her
financing cost significantly (Batjargal& Liu, 2004; Francis& Sandberg, 2000), which
is proposed mainly by New Economic Sociology (NES). We think such idea is useful
to provide appropriate explanation for the reason why entrepreneurial financing from
scratch can come true and further propose that entrepreneur can exploits the benefits
from her social capital based on which she can provide social support to those who
can lend her low interest rate loan.
There are several common definitions of social capital in the realm of NES.
Adler&Kwon (2002) points out that in general it refers to the social ties (for
example, friendship) which can be utilized for other particular purpose. A more
precise and useful definition comes from Lin (2005): Social capitals are the resources
embedded in social network where relevant individuals can gain and use them to
realize their goals in their objective-oriented behaviors. This definition stresses two
concepts: social network and objective-oriented behaviors. To optimize one's interests
in social network, individual can and should use any types of resources include those
exist between persons such as belief, reputation, prestige, friendship and especially
the expectation of interests in some forms in future by providing boons to others.
Different places in social network can provide occupants different advantage and
force to facilitate them to realize their goals (Lin, 2005).
In order to occupy an advantageous place in social network, individuals can invest on
the relationships between persons by providing material or non-material benefits to
relevant people, by which gain and increase their social capitals. For example, you
can help your friends without requiring material returns. By this way, the social
capital (remember it refers to the relationship resources contributive to your future
goal) you own may increase because it is very possible that in future your friends can
also help you without any requirements and conditions. The same logic applies to
venturing finance from scratch: by lending entrepreneur who lacks enough self-owned
wealth in formal financial institutions, the lender may also obtain a chance to get help
from the borrower in future, which may make such seeming non-profitable loan very
profitable.
For the model we will build in next step, we pose following behavioral assumptions:
Assumption 1: the purpose of social capital investment is to expect future material or
non-material benefits.
Assumption2: providing material or non-material support to others is the major way
for one to increase her own social capital.
Thus, we propose that the very reason why investors provide low interest loans to
those entrepreneurs who lack capital and self-owned wealth is that by this way the
investors can accumulate their own social capital. Accordingly, the further question is:
what do requirements must be met for those entrepreneurs lacking self-owned wealth
to get access to low interest loans? In other word, to whom can the investors increase
their social capital in the greatest scale by providing low interest rate loans? The
answer is simple: those entrepreneurs owned great amount of social capital are the
ideal targets for investors to gain their own social capital by providing loans, because
an individual with great social capital is identical to an individual who occupies aideal
place in social network, upon which the expected future return made by her may be
large and the promise she makes is more reliable. Furthermore, those individuals
having considerable social capital (for example, a official who can abuse her power )
not only can provide returns by themselves, but also have capability to make other
persons in social network to make such returns, which makes the social capital
investment towards them more profitable.
Finally, we should notice that using social capital as a financial tool has its own
underlying cost. It is obvious that when entrepreneur gets support from others, a
social responsibility may form to makes her conduct some future costly actions in
return. Such cost may be so large that makes entrepreneur hesitate to use her social
capital for financing. For example, the individuals providing monetary support may
regard themselves as meritorious ones and therefore claim considerable rewards from
entrepreneurs (Au, Kwan, 2009). If entrepreneur fails to satisfy these social
responsibilities towards their "benefactors", the pressure coming from social network
may debase her social status and thereby decrease their social capital.
As a summary for this sub section, we summarize two necessary conditions for
venturing financing by social capital: (1) entrepreneur owns plenty of social capital
and lacks necessary amount of monetary capital; and (2) the supporters providing low
interest rate loans have plenty of monetary capital and are eager to gain social
capital.Next we try to model these above ideas.
3.3 The Model of Using Social Capital for Venturing Finance
At this sub section, we will introduce the factor of social capital into the basic
entrepreneurial financing model to investigate the implication of social capital in
venturing financing from an analytical perspective.
3.3.1 The Preference Structure
First of all, we will make an assumption about the preference for behavioral
individuals in our model. Maslow (1954) points out that in humankinds' hierarchy of
needs, the needs of higher levels would be pursued eagerly if needs in base level are
generally satisfied. With this logic in our model context, it is reasonable to assume
that the need for monetary returns realized by starting a business corresponds to the
need of comparative lower level in hierarchy of needs, while the need for social
capital corresponds to the need of comparative higher level in hierarchy of needs
because the potential returns provided by one's social capital in most cases take some
non-material forms such as reputation and social support. This logic implies a
hypothesis that in general, following with their increase of self-owned wealth, people
tend to attach more importance on their social reputation& place and seek more social
support from their social capital, by which they can find comparative more utility
from their social capital than that from their wealth. Thus, we propose following
preference assumption:
Assumption 3: the utility of behavioral individual U is the function of her self-owned
wealth w and social capital w and U
ww
=0, U
ss
s0; the marginal rate of substitute
(MRS) of s and w is decreasing; U
ws
>0.
U
ww
=0 is consistent with the risk-neutral preference; MRS of s and w is small than
zero implies the utility function is quasi-concave, which guarantees a concave
preference normally held in economic analysis; U
ws
>0 means the increase of wealth
makes individual get smaller satisfaction from the same amount of social capital when
she has little wealth. In other word, wealthy person attaches more importance on her
social capital than that attached by poor one, which is coherent with Maslow (1954) if
the need for social capital indeed corresponds to high level need. An appropriate
example is that comparing to a bagger, a millionaire may be more hesitant to lose her
social status and reputation because the considerable amounts of wealth she owns
makes her social capital more valuable to her based on the assumption we set. Finally,
U
ss
s0 is a very weak assumption consistent with basic economic intuition which just
means the marginal utility of social capital is no increasing or the individual is not
risk-preference towards her social capital. .
Now utility function is dependent on two variables: w and s. To make our following
analysis be consistent with the model in sub section 3.1, we simplify it into a one
variable function. To do so, firstly it is obvious that we can always substitute a
particular amount of w into another particular amount of s to make total utility
unchanged. This is equal to say:
U (w, s + A
1
) +U (w + A
2
, s) = U (w + A
2
+ A
*
(w, s, A
1
), s) = U '(w + A
2
+ A
*
(w, s, A
1
)) (4)
WhereA
1
andA
2
are respect two incremental;A*(.) is a particular function which
makes (4) always hold; U'(.) is defined as another utility function which not only
makes (4) hold but also only depend on one variable: the self-owned wealth. In the
case where individual is risk-neutral for her wealth, U'(.) is just a positive linear
transform of its variable and thus can be reduced to its variable alone, i.e.:
w + A
2
+ A
*
(w, s, A
1
) (5)
Expand (5) at A
*
(w, s, 0) and notice that A
*
(w, s, 0) = 0 :
w + A
2
+ A
*
(w, s, A
1
) = w + A
2
+ dA (w, s, A
1
) *
dA
1
A
1
=0
A
1
+ o(A
1
2
)
(6)
Redefine dA (w, s, A
1
) *
dA
1
A
1
=0
÷ A '(w, s) and omit higher order term in (6):
w + A
2
+ A
*
(w, s, A
1
) ? w + A
2
+ A '(w, s)A
1
(7)
Where A '(w, s) is the derivative of A
*
(w, s, A
1
) about A
1
at A
1
= 0 , which can be
interpreted as a positive transform function of social capital/wealth. Using this
transform function, we can always transform s at a particular amount into w at another
particular amount while hold the total utility unchanged. Now we propose the
following lemma which will play an important role for our model analysis.
Lemma: Under the preference structure described by assumption 3, A '(w, s) satisfies
cA '(w, s) > 0 and
cA
'(w, s) s 0 .
cw cs
Proof: U
ss
s0 means the marginal incremental of s is non-increasing following with
increase of s, which implies that the utility identical amount of w about s will not
increases with the increase of s. Thus, we have cA '(w, s) s 0 directly; then based on
cs
the assumption U
ws
>0, we can infer that holding s unchanged, owning more w leads to
more marginal utility for s, which means more utility identical amount of w about s.
Thus, we have
cA
'(w, s) > 0 . Q. E. D.
cw
3.3.2 A Stylized Model for Social Capital Financing
In this context there are two kinds of channels for entrepreneur to finance investment:
from formal financial market and from her social capital. We assume that if the
business succeeds, entrepreneur should not only liquidates her formal debt for
financial institution, but also respond to the relevant people from whom she borrowed
money ex ante if she has used her social capital as a financing tool; But if the business
fail, everyone would gain nothing. Now using the simplified utility function, the
break-even condition (1) becomes:
s.t.
u ( f (k) + A ÷ R
1
C
1
÷ R
2
C
2
÷ h(| (s), s)C
2
) ÷ (1÷u )(o (w, s)C
2
+ B) > rw
C
1
+ C
2
= k ÷ w
(8)
Where C
1
and R
1
are the amount of loans provided by formal financial investors and
its interest rate; C
2
and R
2
are the amount of social capital finance and its required
interest rate respectively. A is the wealth-identical amount of the increase of the
entrepreneur's social capital resulted by the enhancement of her social status if the
business succeeds; Correspondingly, B is the decrease of her wealth-identical amount
of social capital resulted by when the business fails. Notice that A and B are both
caused by the success or failure of the business per se, which are not related to social
capital financing. o (w, s)C
2
is another part of wealth-identical loss of social capital2
when business fails, which reflects the entrepreneur's to their "benefactors" (which
can lead to the downgrade of her social status) for defaulting the loan she borrow
from them. According to the above lemma, we have
c
o
s
0 and co
>
0 ,whereo is
cs cw
just the transform function of social capital/wealth (which corresponds toA' in
(7)). h(| (s), s)C
2
denotes the wealth-identical cost for the entrepreneur taking actions
of return for her "benefactors" when business succeeds, in which h is the transform
function (again corresponds toA' in (7)) and|(s) is the wealth-identical wealth expected by
"benefactors" for their "selfless" monetary support to the entrepreneur's business.
According to the reasons expounded in section 3.2,| is determined by s
and
d
|
>
0
3
. Holding other things unchanged, since the "amount" of social capital ds
owned by the entrepreneur can decrease the cost of her actions for return (it isn't
difficult to imagine that the person occupied an ideal social status has more
conveniences to achieve her objective), we have
c
h < 0 . But since more| often
cs
means more costly actions for return, we also have ch > 0 . Thus, the sign of
c|
dh = ch c|
+
ch can't be determined unambiguously if the above sign assumptions
ds c| cs cs
of partial derivatives hold true, which means the overall effects of the social capital
owned by the entrepreneur imposing on the cost caused by her actions of return are
complex.
2
It is simplified by the method of (6). The formal expression of this term should beo(w,s)|(C
2
) where|(C
2
)
means the loss of social capital when the entrepreneur defaults the loan C
2
from her social network if the business
fails. Since C
2
is highly positive related to|, we simplifies| directly as C
2
; we conduct the similar manipulation
on the following h(.)C
2
and|(.)C
2
3
We assume the social capital endowment for two kinds of investors is exogenous about the entrepreneur's
decision. So we can just regard| as a uni-variable function of s.
Now we discuss the opportunity for supporters to accumulate social capital by
providing seeming unprofitable loans. If their necessary real return rate for such
lending is still r-1 and they are risk-neutral, R is solved by:
r ÷ E(u w)| (s)
E(u w)(R
2
+ | (s)) = r ? R
2
= E(u w)
(9)
Recalling (2), we immediately have R
2
< R
1
. Obviously, the reason why such
inequality holds is that the real gains from the supporter not only include monetary
returns, but social capital providing them chance to gain potential benefits in the
future as well.
Rational entrepreneur should allocate her amount of debts from external financing and
social capital financing optimally. The optimization problem for is:
max u ( f (k) + A ÷ h(| (s), s)C
2
÷ R
1
C
1
÷ R
2
C
2
) ÷ (1÷u )(o (w, s)C
2
+ B) ÷ rw
{C ,C }
1 2
s.t.
R
1
E(u w) = r
(R
2
+ | (s))E(u w) = r
C
1
+ C
2
= k ÷ w
C
2
s C
(10)
Where C denotes the upper cap for the amount by social capital financing. Then we
can deduce a sufficient condition for entrepreneur financing her business by her social
capital:
Proposition 2: If the entrepreneur: (1) has the same preference structure described in
assumption 4;(2)has enough entrepreneurial ability;(3)has enough social
capital;(4)has little enough wealth;(5) dh < d |
,
then she would choose to use her
ds ds
social capital as a financing means.
Proof: Letc be a positive number small enough such that the following equality holds:
u ( f (k) + A ÷ R
1
(k ÷ w) ÷ rw) ÷ (1÷u )B ÷ c = 0 (11)
(11) means if entrepreneur can only lends capital from formal financial market, she
will not choose to start her business. Then let entrepreneur decrease her external
financing from financial market byo and at the same time increase her social capital financing
byo, the change of her expected wealth return in the future if she starts the
business is:
Aw = ÷(1÷u )o (w, s)o ÷u h(| (s), s)o ÷ R
2
uo + R
1
uo
[ro ÷ E(u w)| (s)o ]u
= ÷(1÷u )o (w, s)o ÷u h(| (s), s)o ÷
E(u w)
E(u w)| (s)ou
= ÷(1÷u )o (w, s)o ÷u h(| (s), s)o +
E(u w)
= [÷(1÷u )o (w, s) ÷u h(| (s), s) +u| (s)]o
+ rou
E(u w)
?12?
Since | > 0?Thus the sufficient-necessary condition for Aw > 0 holds is:
| (s) > (1÷u
)
o (w, s) + h(| (s), s)
=
o (w, s) ÷o (w, s) + h(| (s), s)
u u
(13)
Which means the left-hand side of inequality (13) is large enough or the right-hand
side of (13) is small enough. Differentiate (13) with s and w we have:
d |
>
( 1 ÷1) co
+
dh(| (s), s) , and
ds u cs ds
d |
=
0 > ( 1 ÷1) co
+
dh(| (s), s) = ( 1 ÷1) co (14)
dw u cw dw u cw
According to the lemma and the relevant partial derivatives assumptions, we have
u<1,
c
o
s
0 , co
>
0 , so we can conclude definitely that under the assumption
cs cw
dh < d |
,
only if s andu large enough with w small enough can (13) be satisfied
ds ds
which makesAw>0. Sincec is small enough, we letc be a number such
that 0 < c < Aw , then by transferringo from formal financing to social capital financing, the
break-even condition for the entrepreneur starting the business can be satisfied. Q. E.
D.
dh d |
Proposition implies the inequality ds < ds is a necessary condition for the positive
effect of the increase of social capital facilitating the entrepreneur starting her
business, which means that the increase amount of the cost for actions of return led by
the increase of social capital is smaller than the decrease amount of the cost for
actions of return caused by the increase of social capital. However, such condition is
not always true in reality. If the high level of social capital the entrepreneur holds
makes the supporters expect too many future benefits by providing "altruistic" loans
which force the entrepreneur's actions of return too costly, the increase of social
capital the entrepreneur holds may not motivate her entrepreneurial behaviors. But if
(14) is satisfied, the entrepreneur may have a opportunity to finance her business with
low cost.
Now we discuss how the change of entrepreneur's endowments may lead to her
change of financing decision.
Proposition 3: The increase of self-owned wealth would decrease the entrepreneur's
social capital financing and borrow more from formal financial market.
Proof: Suppose the
inequality
C
2
s C
always
true and substitute the first two
restrictions in (10) into the objective function:
max u[ f (k) + A ÷ h(| (s), s)C
2
÷
{C
1
,C
2
}
s.t.C
1
+ C
2
= k ÷ w
(15)
r
E(u w)
C
1
÷ (
r
E(u w)
÷ | (s))C
2
] ÷ (1÷u )[o (w, s)C
2
+ B] ÷ rw
Since (15) is a linear programming with only one restriction, the optimal solution
must be a corner solution which means C
1
and C
2
are either 0 or (but not both) k-w
4
determined totally by the comparative real cost of the financing by financial market
and by social capital. With some simple manipulations, we denote:
r
The marginal cost of C
2
: F
1
÷ (1÷u )o (w, s) + [h(| (s), s) +
r
E(u w)
÷ | (s)]u
(16)
The marginal cost of C
1
: F
2
÷ E(u w)
u
( 17)
Thus we have: cF
1
= (1÷u ) co
+
rE(u w)
÷
2u
dE(u w) cF
2
,
= rE(u w)
÷
2u
dE(u w)
cw
cF
1
÷ cF
2
= (1÷u ) co
cw
dw
cw
dw
co
and
c
w cw
so:
c
F
1
÷ cF
2
> 0
cw cw
c
w
; According to the lemma,u<1 and the assumption
c
w > 0 ,
(18)
(18) means with the increase of w, the difference between the marginal cost of social
capital financing minus the marginal cost of financial market financing become larger,
which would lead the entrepreneur use more financial market as her financing channel.
Q. E. D.
The intuition behind proposition 3 is that when potential entrepreneur have few
wealth but have considerable amount of social capital to exploit, she is insensitive to
the decrease of social capital caused by the failure of the business when she use social
capital as a financial tool but is very longing to the increase of the wealth if the
business succeeds so that she is willing to risk the loss of social capital to get a
possibility to become wealthy. But when her wealth increase, since social capital can
bring her more utility (based on the assumption U
ws
>0), she may not want to risk her
social capital again to gain wealth.
4
Corner solution is led by our above first-order approximation about the individual utility function. Though in
reality corner solution is unusual, the qualitative conclusion about our model is significative.
Proposition 4: The increase of entrepreneurial ability may motivate the potential
entrepreneur to use her social capital for financing.
Proof: Differentiate F
1
and F
2
withu and let the former minus the later:
cF
1
÷ cF
2
= ÷o ÷ 0 = ÷o
cu cu
cF cF
(19)
Sinceo is a positive number,
c
u
1
÷ cu
2
<
0
, which means high ability entrepreneur
can use social capital with low real cost, which may motive her use it more for
financing. Q. E. D.
Proposition 4 implies that the financing function of social capital can only help high
ability entrepreneur with low self-owned wealth to finance her business. For those
potential entrepreneurs whose ability is low, social capital still can't make them to
become real entrepreneurs.
Finally, we analyze the change of financing approach along with the development of
new set-up firms. With another extra assumption, we can deduce following strong
proposition:
Proposition 5: If the monetary wealth brought by the success of new business is
enough larger than the increase of social capital brought by the success of new
business, the new set-up firms would gradually change their financing channels from
entrepreneur's social capital to formal financial market.
Proof: Suppose the success of business boost the endowments of the entrepreneur
cF cF
from (w, s) to (ì
1
w, ì
2
s) whereì
1
, ì
2
>0. Notice the fact
c
w
1
÷ cw
2
>
0
in (18) and:
cF
1
÷ cF
2
= (1÷u ) co
+
[ch + ch c|
÷
d |
]
u = (1÷u ) co
+
[ch + ( ch ÷1) d |
]
u
(20)
cs cs cs cs c| cs ds cs cs c| ds
Due to the assumptions of co
s
0, ch < 0, ch > 0, d |
>
0 , it is not difficult to know
cs cs c| ds
the sign of (20) is uncertain. But if the increase of s is comparatively small enough
than the increase of w, then regardless the sign of (20) the whole effect of increase of
w and the increase of s would make F
1
-F
2
larger than zero, which means that only if
ì
2
is comparatively smaller enough thanì
1
, the marginal cost of using social capital
for financing would become larger comparatively than the marginal cost of financing
capital from financial market. Thus, the success of the business leads the entrepreneur
to decrease her debts owning to her "benefactors" and demands more loans in formal
financial market. Q. E. D.
Proposition 5 implicitly assumes that entrepreneur mainly acquires monetary wealth
rather than social capital by starting a new business, which in general holds. In reality,
the main purpose for entrepreneur to initiate a firm is just to gain economic benefits
rather than others. If the main purpose for the entrepreneur want to grasp more social
capital, then setting up a new firm and operating it cannot be the most efficient way
because by some other behaviors (such as help her friends "altruistically") more social
capital she can accumulate. Thus, it is reasonable to hypothesize that the entrepreneur
wants to and indeed gain more wealth rather than social capital from her
entrepreneurial actions. The authenticity of proposition 5 in reality is confirmed by
Zhang, et.al (2008), in which they find empirically that while set-up firms tend to use
entrepreneur's social capital to finance its investment, the developed firms get access to
loans mainly from external financial market.
4. CONCLUSION
Now we conclude the main ideas of our paper:
The invisible and unverifiable character of entrepreneurial ability may lead the
investors in financial market conduct strict credit rationing towards those entrepreneur
who own few self-owned wealth (Zhang, 1994). On the other hand, the core value of
entrepreneur can't be identified ex ante, which can only be self-verified in
entrepreneurial process (Casson, 2005). Thus, how entrepreneur without enough self-
owned wealth finances her investment from scratch is the main problem faced by most
of potential entrepreneurs.
By discussing the intension of social capital and construct a stylized model to address
the issue about how entrepreneur's social capital can facilitate those high ability
entrepreneurs starting their business, we prove that they can just utilize their social
capital as a low cost financing channel. Such channel is crucial for the new set-up
firms in their initial phase and makes it possible for the potential entrepreneurs realize
their business.
Based on the model we built, we further discuss the particular conditions faced by
entrepreneurs and the potential supporters who can accumulate social capital by
lending loans to the entrepreneurs in low interest rate. We show that the more social
capital and the less self-owned wealth the entrepreneur own, the more incentive for
them to use her social capital to "finance her idea"; the more self-owned wealth and the
less the social capital the potential supporters have, the more motivation for them to
provide "altruistic" to the entrepreneurs. By this way, the individuals with different
economic capital and social capital can exchange their comparative more resources by
which optimize their utility (Lin, 2005). However, following with the development of
business, the firms would gradually substitute their financing channel from the social
capital of the entrepreneur to external financial market.
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