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Financing Start-ups: Advising vs. Competing
Nicolas Boccard
July 2001
DIPARTIMENTO DI SCIENZE ECONOMICHE - UNIVERSITÀ DEGLI STUDI DI SALERNO Via Ponte Don Melillo - 84084 FISCIANO (SA)
Tel. 089-96 3167/3168 - Fax 089-96 3169 – e-mail: [email protected]
::2255..,,11** 33$$33((55 1122�� ����
Financing Start-ups: Advising vs. Competing
Nicolas Boccard*
Abstract High-tech start-ups get external finance and guidance mostly from venture capitalists and/or business angels. We identify a simultaneous double moral hazard for the management style of entrepreneurs and the decision to advise the firm for financiers. We embed this relationship into the financial competition where strategic choices are equity shares, liquidation rights and quality of advising. We show that the financier holds all liquidation rights, that more competition weakly decreases the financier's equity share. Surprisingly, the response in advising quality is non-monotone. In a regime of soft competition, the financier owns the start-up and more competition weakens advising quality. In a regime of acute competition, more competition improves advising quality and lowers the financier's equity share in the start-up. Hence, advising and equity, are substitutes at the industry level once competition effects are taken into account.\bigskip Keywords: Start-ups, Contract Design, Equity, Oligopoly Competition JEL Codes: D4, G3, L1, L2
* CSEF Università di Salerno, Italy. I thank Marco Pagano and seminar audiences at Universities of Padova, Bocconi (Milan), and Salerno for comment and suggestions. Financial support from EU (RTN Contract no. HPRN-CT-2000-00064 - Understanding Financial Architecture: Legal and Political Framework and Economic Efficiency) is gratefully acknowkedged.
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2
3
1
2
3
1 Introduction
capitalist
vision
http://www.oecd.org/dsti/sti/it/prod/it-out2000-e.htm
From interviews lead by J. Tirole and presented at the Internet session of the European Economic Association
Congress, Bolzano Sept. 2000.
While investments in intangibles like R&D create market values, key �nancial variables are often negative. Such
anomalous relations are typical of fast-changing, technology-based industries.
The OECD Information Technology Outlook 2000 stresses the differing rates of growth for the
information technologies (IT) sector among member states and traces one possible origin to differ-
ences in corporate banking methods and concentration of �nancial intermediaries (e.g., comparing
the US and the UK with Japan and Germany).
According to the classi�cation of Berger and Udell (1998), businesses less than 2 years old
are rather �nanced by relatives and business angels, while those aged between 3 to 4 years are
rather �nanced by venture capitalists and investment banks. It is indeed well known that high-tech
start-ups need large investments to initiate projects offering high potential but also high risk. Due
to their lack of reputation, of cash-�ow and of collateral, start-ups often cannot access security
markets (cf. Petersen and Rajan (1994), (1995)) and must rely instead on �nancial intermediaries.
We shall use the terminology keeping in mind that it applies to both angels and venture
capital funds.
The owner-manager of a start-up draws private bene�ts from the valuable reputation he can
obtain by running successfully its project according to its . This is indeed the case for
internet start-ups whose creators acknowledge the peer effect as a motivation for hard work and
entrepreneurship. This may lead the entrepreneur to neglect the management of its company and
reduce the odds of commercial success. In the traditional corporate �nance literature (e.g., Aghion
and Bolton (1992)), misbehavior is deterred by the use of collateral and takeover whenever bad news
arise. However, the world of high-tech start-ups seems to lack signals correlated to misbehavior
that could trigger the lender�s intervention (one exception is delays in software development but
this is a �soft� information). Rather, success arises suddenly when the �rm or its technology (e.g.,
molecule, software) is sold to a large corporation (e.g., Microsoft, Intel and Cisco) or is agreed by
the government.
2
4
4
business angels
quality
high-tech
We use this terminology to emphasize the difference alluded earlier with more traditionnal entrepreneurs.
Another speci�city of the start-ups world is that entrepreneurs often lack of management skills
since they graduate mostly in sciences and not in management. Thus, banks, venture capitalists and
wealthy investors have a new role to play. They can become the of entrepreneurs by
providing them support and governance to improve the pro�tability of their projects. This (costly)
decision is the moral hazard issue of �nanciers. As noted by many different sources like the OECD
2000 IT outlook, Kaplan and Strömberg (2000) and Prowse (1998), the commitment of �nanciers
into start-ups is quite variable in frequency and in quality across regions and also across countries.
An angel must decide how much time to devote to a start-up he is funding. Similarly, a venture
capital fund must decide how many advisors to recruit to later delegate them in its pool of client
start-ups. The investment into the business angel activity thus appears to be a strategic decision in
the competition among �nanciers. We analyze it as a variable to distinguish it from more
traditional pricing variables like �nancial rights or liquidation rights.
In this paper, we build a principal-agent model of a entrepreneur and its �nancier
depending on the contract they sign but also on the quality of the lender�s advising. The entre-
preneur can either adopt a visionary management or an obedient one. The �nancier can decide
to monitor the entrepreneur or not. We then embed this relationship into the �nancial sector to
understand how the rivalry among venture capitalists, whatever its origin, affects the equilibrium
design of the capitalist�s equity participation, its liquidation rights and the quality of advising he
provides to the entrepreneur.
In our model, the equilibrium of the principal-agent relationship involves positive frequencies
of visionary management and advising, as well as, obedient management and no-advising. A larger
equity participation of the capitalist and a better advising quality both contribute to reduce the
frequency of advising while the frequency of visionary conduct increases with the equity participa-
tion and decreases with the advising quality. Then, we show that in the equilibrium of the �nancial
sector, the liquidation rights are set at the maximum as they enable to reduce the cost of the en-
trepreneur�s moral hazard. Thus, capitalists compete on two dimensions, the equity participation
and the advising quality.
3
weakens
reinforces
Our �ndings in this respect are that more �nancial competition weakly decreases the equity
participation of capitalists (in equilibrium) and weakly increases the frequency of visionary man-
agement. The striking result we obtain is the non-monotonic response in advising quality as com-
petitiveness changes. In a regime of soft competition, capitalists own start-ups (maximal equity
share) as a result of the limited wealth of entrepreneurs. In this context, more competition
advising quality. On the other hand, in a regime of acute competition, more competition
advising quality and lowers the equity participation of capitalists. Hence, advising quality and
equity participation are substitutes at the industry level, once competition effects are taken into
account.
The intuition of this outcome is rooted in the way �nancial competition crafts the individual
contractual relationships. In equilibrium of this �nancial competition, the marginal rates of sub-
stitution between equity share and advising quality are equal for a capitalist and an entrepreneur,
if the latter retains some ownership in the start-up. Then, we show that the two variables are
negatively linked on the Pareto curve because equity serves to reduces moral hazard. Next, we
show that, if the success probability of the start-up is small, the equity share is the main channel
of competition transmission.
With these tools in hand we are able to con�rm in our model, the intuition according to which,
entrepreneurs obtain more utility in equilibrium when �nancial rivalry increases. This translates
de facto into a lower equity participation of the �nancier and surprisingly into a higher advising
quality, as the two variables move on the Pareto curve. Yet, this does not hold when market power
is high. Indeed, the equity participation is then so high that the capitalist owns the start-up. In
this soft regime, �nancial competition takes place only on the advising quality which is disliked by
entrepreneurs. Thus, more competition translates into lower a quality of advising.
Among recent papers, Repullo and Suarez (2000) analyze an entrepreneur-capitalist relationship
with two stages of �nancing and double moral hazard. The capitalist in their setting is modeled as
an in-house manager and not as an adviser delegated by a large �nancial institution. The emphasis
is thus on the optimal claim of this lender which resembles warrants or convertible preferred stocks.
Our view of the entrepreneur-capitalist relationship is simpler on several points but endogenizes the
4
5
6
5
6
s f
identical
K w
V > K V < K
K
L
2 A Model of Start-Up
2.1 Financing a risky project
It clearly matters at the development stage where, after an initial success, some information regarding the entrepre-
neur is revealed (possibly to himself too).
We regroup under this label investment funds, wealthy individuals (the so called angels), lenders (for more informa-
tion see http://www.v�nance.com).
involvement into the business angel activity and provide an analysis of the rivalry among capitalists.
While we concentrate on small �rms, Aghion et al. (1998) study the complementary problem
of public �nance under moral hazard for large �rms. The �rm issues equity to small investors and
signals its willingness to effort, instead of being monitored. The optimal contract bears similarities
with ours. When the need for external �nance is high (our soft competition regime), the business
is sold to the �nanciers and the signaling activity is inefficiently high. When the need for �nance
is low, the �rm keep some of the future pro�ts and tends to shirks more as the need for �nance
increases.
The paper is organized as follows. Section 2 introduces our model of risky project �nancing in
two stages. Section 3 derives the equilibrium of the second stage and section 4 solves for the �rst
stage perfect equilibrium. Section 5 concludes.
We concentrate on start-ups competing for the development of an innovation (and the reward
associated with it). Our model which is inspired by Hölmstrom and Tirole (1997) disregards the
issue of adverse selection. We consider a continuum of risk-neutral entrepreneurs. The
cost of development is larger than the cash-�ow of the start-up (capital brought by the
entrepreneur and its relatives). The monetary return in case of success (proceeds from an IPO or
from selling the technology to a large �rm) is while it is only in case of failure.
We assume that the cost of issuing public debt is too large for these entrepreneurs. Thus, their
only source of �nancing is venture capital. Without loss of generality, �nanciers have an equal
unbounded access to money at a rate normalized to zero. The project cost can be partially
funded by a venture capitalist who brings an amount of capital while the entrepreneur pays the
5
0
s s
f f
Payoffs
�
� �
� � �
� � �
= (1 ) + + =
= (1 ) + + =
�
Table 1
obedient visionary
2.2 A case for Double Moral Hazard
K L w
L K w.
�
�
u � V K L w � �V L
u � V K L w � � V L
B
p
B
p > p.
remaining out of his personal wealth . We immediately obtain a lower bound on the loan
size to be effective:
Kaplan and Strömberg (2000) report evidence that venture capitalists separately allocate cash-
�ow rights, voting rights, liquidation rights and other control rights. Hence, in our simple setting,
it make sense to distinguish the share of pro�ts going to the lender when the project succeeds
from the liquidation share which applies when the project fails. Financial payoffs are shown in
Table 1 below.
Entrepreneur Capitalist
Success
Failure
By running a start-up, an entrepreneur gathers a useful experience whose monetary equivalent is
denoted . Moreover, he can either be or . In the former case, he shares time
between project development and management. The failure probability is then . In the latter
case, the entrepreneur concentrates on project development to build a reputation among his peers.
He derives an additional private bene�t (cf. Hart and Moore (1994)) but also increases the
probability of failure to We shall later associate management styles and failure probabilities.
As we argued in the introduction, the capitalist is not only a lender but also a business angel
for the entrepreneur. Further, their relationship has a timing different from the usual one found
in corporate �nance. Indeed, the traditional responses to moral hazard do not seem to apply to
high-tech start-ups. First, there are no external signals correlated to visionary management that
could trigger an intervention (with the associated deterrence effect). Hence, start-ups should be
advised from inside, not monitored from outside. Secondly, the commitment to a high frequency
of random intervention (a typical remedy of the literature) is not credible in our context. Indeed,
inefficient visionary behavior would be eliminated in equilibrium which does not �t stylized facts.
Furthermore, capitalists would be tempted to deploy advisors in other activities once they believe
6
�
I
I
7
8
9
7
8
9
�
u
� u
a priori q
q p p
qB
F
� q
� q
q
� �
(� )
( )
( )
[0; 1]
= 0
(0) (0)
The early literature on costly audits assumed a commiment to carry out threats that are not optimal ex-post. A
recent stream of literature rejects this inconsistency and tackles the principal-agent interaction as a simultaneous one.
Some relevant papers are Gale and Hellwig (1989), Bolton and Scharfstein (1990) and Khalil and Parigi (1998).
Hellman and Puri (2000) observe from their data, that the venture capitalist reduces the time necessary to bring a
product to the market, thus increasing the probability of being able to preempt the market.
Prowse (1998) reports the sharing of information and co-investments behavior of angels, although they complain
about the low quality of information channels. cf. the new ACE-Net network set-up by the US Small Business Admin-
istration.
that entrepreneurs are obedient.
The natural timing thus appears to be the simultaneity of the management and advising deci-
sions. Still, the capitalist can invest into advising by committing to a quality . It could
be the recruitment of more or less advisors, to manage more or less carefully each project. The
better the quality, the better the advisor can help the entrepreneur, if the �nancier decides to advise
this particular client. Nonetheless, this effect should be more pronounced when facing a visionary
entrepreneur. To simplify the exposition, we assume that advising an obedient entrepreneur has no
effect while advising a visionary entrepreneur reduces the probability of failure by . Beyond
this efficiency effect, we assume that the presence of the advisor has two incentive effects:
it reduces the private bene�t by (e.g., fame is shared with the business angel)
if the project fails then, as the entrepreneur was visionary and advised, his misbehavior becomes
known to other venture capitalist.. Then, the entrepreneur will have to pay a risk premium to
lenders if he wants to start new projects in the future. The present value of this defaulting cost is
denoted .
Advising a client has a direct cost for the capitalist (advisor�s wage) and an opportunity
cost for the entrepreneur (loss of independence as in Dewatripont and Tirole (1994) and
Burkhart et al. (1997)). Both functions, de�ned over the interval, are differentiable, increasing
and convex. Letting stand for no speci�c investment, an intervention is then a simple audit
of the entrepreneur�s accounts (only the deterrence effect remains) so that both and
are positive.
7
=1
0
� �
�
H1
H2
I
I
I
I
� �� �
� �� �
= 1
�
�
+ (1 ) + ( )
+ ( )
( )
(� ) + �
i i i i
i i i i n
i
i i i i
i i i i
f s�
u
s
3 The Lender-Borrower Relationship
2.3 Timing of the Finance Competition
i n q � , � , L
q , � , � , L
p p
p p
q � , � , L .
q , � , � , L
.
pV p V > K w � q /q
B > w � q /q
q
�, �, L .
B > p p V pF
We consider the following timing of events describing the market for the �nancing of risky projects:
Capitalist to chooses an advising quality and offers a contract .
Entrepreneurs observe and decide whether to borrow (or not) and whom from.
Borrowers choose action (visionary) or (obedient) while capitalists simultaneously decide to
advise or not each of their clients.
Projects succeeds according to the chosen probability or and payments or liquidation take
place.
This two-stage game is solved by backward induction using the concept of Perfect Bayesian
Equilibrium (PBE). In the next section, we analyze the advising and obedience game between an
entrepreneur and its capitalist; it depends on the advising quality and the contract
Then, we compute the expected utility of entrepreneurs and capitalists conditional on choosing
and we derive in section 4 the symmetric equilibrium of competition between capi-
talists.
To guarantee that capitalists are active in equilibrium, the project must have a positive net
present value. In our setting, the expected pro�t has to be larger than the minimal loan size plus
the average cost of moral hazard for the capitalist Then, entrepreneurs are willing to conduct
projects if the value of experience is greater than the initial wealth plus the average cost of moral
hazard. The corresponding assumptions are
In this section, we analyze the relationship between a capitalist with advising quality and one of
its customer under the contract
To make the moral hazard issue relevant, we assume that private bene�ts are larger than the
default cost plus the efficiency effect of advising i.e., (otherwise the entrepreneur
would hire himself an advisor). Then, if the capitalist only acts as a lender (no intervention), the
8
10
10
0
0
�
� �
�
� �
� �
� �
� �
Proposition 1
s�
�,q
� ,q
s� ,q
f s
� ,q u
s s fu
� ,qs f
� ,q
s f
s f
s�,q
f s�
�
� � � � �
� � � � � �
� � �
� � � � � � �
� � � � � � � �
� � � � � � � � �
⇔ � � � � � � �
∈
� � � �
Otherwise he would own the business and contract the entrepreneur as a scientist.
In a PBE, the advising-management game following has a unique Nash
equilibrium in mixed strategies.
Proof
V < �
q
q, �, �, L
�
� p
p �q p p � p �p p � �q p p .
u �, � B w � V K L � p �p � V � V
� �q B �p F �� q
B w � V K L p � V � V �� q
� �q B p F �q p p � V � V
p
�q B pF �q p p F �q p p � V � V
� �q
pF
B p p � V � V F
� � < � , � � > � �
� � .
� �, � �V L � p �p � V �V �� q
(1)
( )
�
� (� ) (1 ) + � = + (1 )(� )
( ) = + + (1 ) + + (1 ) + � ((1 ) (1 ) )
+ (1 ) � ( )
= + + (1 ) + ((1 ) (1 ) ) ( )
+ (1 ) � (1 )(� ) ((1 ) (1 ) )
�
0 = (1 ) � + (� ) (1 )(� ) ((1 ) (1 ) )
=1
1(� ) ((1 ) (1 ) + )
= 1 = 0 [0; 1]
=
( ) = + (1 ) + � ( ) ( )
entrepreneur adopts a visionary management. We also assume that full control is too costly for the
lender i.e., (best advising quality and systematic advising).
In such a context, the equilibrium of the advising-management game will feature positive fre-
quencies of advising and visionary management. Moreover, both will be in�uenced by the contract
and the advising quality. Indeed, those elements are crucial for trading-off the expected bene�t of
advising and its cost for the capitalist, and for trading-off the bene�t of visionary management and
its expected cost for the entrepreneur. Note that, while is costly for the entrepreneur and the
capitalist, it brings bene�ts too as it in�uences the desire of the entrepreneur to be benevolent and
of the capitalist to advise.
The agent�s strategy is to be visionary with probability while the capitalist�s strategy
is to advise with probability . The failure probability in case of visionary management is
and we have The utility of the borrower is
(1)
The borrower is indifferent between its two actions if and only if the bracketed term of (1) is
nil. Developing yields
(2)
The optimal behavior of the entrepreneur is if if and if
Similarly, the capitalist�s pro�t is
9
�
H1
�
� u
ideal
� � � �
� �
( )
( ) ( )
�
�
�
�
� �
� �
� � � �
�
�
′
� �
� � � � � � �
� � �
� � � � �
� �
� � �
� � �
� � ⇔
� �
s f s�
s f
�
s f
s f
s f s
s f s
s f s
�
s f� qq
u � qq
� u � u
= + + (� ) ( ) ( ) (� ) ( )
=( )
(� ) ( )
� (� ) ((1 ) (1 ) )
0
1
= 1
1 = 0
(1 0) = + �( )
1 1 = 1 = 0
1 1 = =
( ) = + + (� ) ( )
= + ( )( )
(1 0)
(� ) ( ) 1
( = 1 = 0)
( )
( )
( ) ( )
( ) ( )
�V L p � p p � V �V � � q �q p p �V � V
� �� q
q p p �V � V
B pF > p p � V � V �
�. � > �
q � >
� � � q
� > � � �
� , �V L p � V �V
� < � > � , �
� < � < � � � �
� q, �, �, L �V L p � p p � V �V
�V L p � V �V� q
q> � ,
p p �V � V > � < .
q � , �
q �, �, L
� , � .
L
q
c q c q
q q c q c q
(3)
thus, he is indifferent between its two actions if and only if the bracketed term of (3) is nil. We
obtain
(4)
As moral hazard is relevant, we have whatever and
In turn, this implies . Hence, if the capitalist chooses a low frequency , it is optimal
for the entrepreneur to adopt a visionary management. If is small then is possible in
(2). In that case, any is smaller than so that is optimal for the entrepreneur. As is
small, also holds. Thus, any is smaller than so that is optimal. The pro�t of the
capitalist is then .
Over the domain where , if then the equilibrium is again . Moving
to the domain where and , the unique equilibrium is and yielding the
equilibrium pro�t for the capitalist
because this is exactly equivalent to
The capitalist who has chosen a low quality such that the equilibrium is would
be better of choosing a higher quality and the same contract in order to implement
the equilibrium Yet, this will work only if its clients get the same �nal utility level or
more under the new scheme, for otherwise they could pick another lender. Hypothesis (positive
NPV) tells us that this is possible using as a transfer variable. Hence, in a PBE, the equilibrium
of the advising-management game is never in pure strategies.
The effect of the advising quality on the payoffs of capitalists and entrepreneurs can be
summarized by the average cost functions and . The advising
quality of capitalists (resp. of entrepreneurs ) is de�ned as the minimum of (resp. )
10
→
11
11
H3
′
′ ′
�→ ∞∫ √√ 0
1
0
1
� �
� �
0
1
0 0 12
0 12
� �
�
� � � � �
�
s f
d
� u u bb
� aa
Proposition 2
0
0
(� ) (1 ) (1 ) +
� � � � �
� � � �
� �
� � �
� � �
�
ˆ = ( ) + ˆ 1 (1) =
( ) (1) ( ) = + ( ) = + =
=
� u
u �
s fu
s f
pF
B p p � V � V F
u
s f s
s f�
u �
m �/m � �/m � d m < �
� x dx < � � m a a m � m b b m m
m
[0; 1] (0) (0)
( ) = + + (1 )(1 ) + (1 ) + ( )
= + + (1 )(1 ) + (1 ) +
1( )
( )
( ) = + + (� ) ( )
= (1 ) + ( )
=
= 1
1
. � > �
q < q
� �
u �
u q, �, �, L w B p � V p � V L K � � q
w B p � V p � V L K
c q
� q, �, �, L �V L p � p p � V �V
p �V p� V L c q
L K w
�
q q
� <
The minimum of solves . It is positive because but because
(by convexity). If for example and then and
.
In a PBE, an optimal contract minimizes loan size ( ) and gives own-
ership to the capitalist in case of project failure ( ). Advising quality is always chosen between
and .
over The inequality being the most plausible, we assume that capitalists
prefer a higher degree of involvement into the management of the project than entrepreneurs do:
Using the equilibrium levels of visionary management and advising , we obtain the expected
utility levels of the entrepreneur and the expected pro�t of the capitalist as
(5)
(6)
The following proposition, whose proof is relegated to the appendix, will permit to focus on
advising quality and equity share by deriving the equilibrium value of other variables.
These results are quite intuitive to understand. If the capitalist does not hold complete liquida-
tion rights ( ), he can increase them and adequately decrease its equity share, so as to maintain
constant the entrepreneur�s utility. This substitution enables a reduction of moral hazard and thus
a larger per-capita pro�t. Since the capitalist�s clients keep the same utility level, its market share
is not affected. The switch to complete liquidation rights has therefore yielded a larger total pro�t.
Likewise, if the loan size exceeds the minimal level, the capitalist can substitute the difference by
11
� �
� ��
�
12
12
�quq
∝ � � �
�
� � �
�� �
� � ��
� �
� � � �
� � �
�
�
u q, � � q, � c q c q
� .
0 (� )((1 ) + )
0
�(� )
�
( �) (1 �) � +
( )
( )�
( �) � +
( �) + ( �) 1( )
( ) ( )
� = 0 = 1( )
s
eF
B e e � V F
u �
c q
c qeF
B e e V F
u u
�
spF
B p p � V Fu
f s�
u �
B pFB p p F
u
�
q
�
q
� ��
[0; ]
( ) = + (1 )(1 ) 1 ( )
( ) = + + (1 ) ( )
0 1 ( 0) 0
1
( )
1 ( )
( )
0 0
( )
�
u �
q q , q ,
q .
u q, � B p � V c q
� q, � pV K w p �V c q
q �
q q
. � q, < .
�
B
c q .
� q, �
u
u
�
�
q, � .
u < u >
�, q
The utilitarian Pareto optimum maximizes thus
is optimal while the quality solves
an additional pro�t share (a reduction of ) which motivates further the entrepreneur i.e., reduce
the cost of moral hazard. Finally, the intuition of the last result is that both and are increasing
with on thus the capitalist could commit to the quality improves its per-capita pro�t
and improve (weakly) its market share as its clients are now better off. The same process would
occur if the initial quality was larger than
We can now write the preferences of the various parties at the �rst stage where capitalists
compete for entrepreneurs. The utility of an entrepreneur and the per-capita pro�t of a �nancier
are
(7)
(8)
Note that and are goods for the capitalist but anti-goods for the entrepreneur. In the
competition among �nanciers, the advising quality can be chosen between and while the
equity share is between and However, it is readily observed that Thus, in a perfect
equilibrium, the only meaningful constraint for the equity share is
(9)
When this constraint is binding the entrepreneur simply becomes a manager working on behalf
of the capitalist; his utility is measured by the gains of experience minus the cost of moral
hazard
When the share constraint is not binding, a Pareto optimal pair equalizes the
marginal rates of substitution and . It is obvious that an equilibrium of the contract
competition where the share constraint (9) is not binding must be a Pareto optimum for otherwise,
the venture capitalist could attract more entrepreneurs and make more pro�ts with a better designed
pair Clearly, both parties prefer to retain a maximal equity share, but equity is better handed
to the entrepreneur as it reduces the extent of moral hazard ( and ). On Figure 1
below, we display iso-utility (dotted) and iso-pro�t (plain) curves in the space. Starting from
12
2
H4
( )
�
↘ ↗
�
uu
��
�� � �� �
� �u
�
q
�
q
13 14
15
13
14
15
� � � ∝ ��
�
�
Figure 1
absolute
� ( )( �)�
( �) (1 )� +
2
2
A B � q
B
�
q
�, q
� , q
p p < �
�
1 = (1 �) �( ( ))
0 0 0
0 =( )
0
= = 0 =( )
= 0
= 95% � = 2% 40%
H u e V < u > , u c <
u < . ∂ /∂�u u u u
u< .
� � ∂ /∂�� � � �
�.
e e e
�
q
�
q
�eFc q e e V
B e e � V F�� q
uq
q�uu
�� q � q�
q
�� q���
�� q � q�
q
Indeed, implies that , then we easily get
and Together these imply
Indeed imply
If for instance and then the success probablility increases by from the visionary to the
obedient management style.
an optimum , let us move to point by decreasing (keeping constant). The marginal rate
of substitution increases while remains unchanged. Hence, at point , the entrepreneur
values equity shares more than the capitalist. A Pareto improving trade sees the entrepreneur
buying more equity (a further decrease in ) from the capitalist in exchange of more control (an
increase in ). We deduce from this observation that the contract curve, the set of Pareto optima,
is downward sloping in the space.
We conclude that, in equilibrium of the �nancial competition, an increase in control goes along
with a lower equity share for the capitalist, if the share constraint (9) is not binding. What remains
unclear is the ultimate effect of an efficient substitution from equity to advising quality ( )
for the capitalist and the entrepreneur ? In other words, who gains and who loses ? The answer to
this question is fundamental to understand the consequences of the competition among �nanciers.
To derive clear-cut results, we assume that the increase of the success probability when
switching from visionary to obedient management is small i.e.,
where the threshold is determined in the proof of Proposition 3 (cf. appendix).
13
1 ′
� �
′
� �
v u.16
17
16
17
Lemma 1
�
�
�
�
� � �
� �
i i i i i i
i i i i i i
n
� �
� � �
f
if
� �i
�
� �
4 Competition among Lenders
( ) (0) = (0) =
( )
( )
( ) 0 1 ( ) ( )
( ) � ( ) ( ) ( )
( )
� q
v v
v
v D v v D D t
� nt
q , �
v u q , �
V w i
q , � � u q , � V i q , �
q , � , i q , � � q , � D u q , � v .
q , �
We shall denote the levels of utility to avoid confusing with the utility function
This formulation is directly inspired by
When the capitalist equity share decreases and the advising quality increases, so as
to maintain equality of the marginal rates of substitution, the utility of the entrepreneur increases.
Thanks to this assumption, we can derive the following lemma whose proof has been relegated
to the appendix.
This result means that, on Figure 1 above, the utility level is greater than . In other words,
the equity share is the main channel of utility or pro�t changes, thus the main strategic variable.
To analyze how the intensity of competition, whatever its origin, affects the equilibrium design of
contracts and the choice of advising quality, we use a �exible model of horizontal differentiation,
inspired by the circular city of Salop (1979). Entrepreneurs either bear a cost to visit �nancial
institutions or they are already in relation with a particular one and bear an administrative cost to
switch to a new one. These features give capitalists some market power which varies directly with
the size of this switching cost.
More speci�cally, the demand addressed to a capitalist offering an expected utility while all
other capitalists offer is where (symmetric market shares) and
(switching cost). The parameter is an index of competitiveness in this market for risky
loans.
Thanks to Proposition 2, a symmetric PBE is a pair since other variables are determined
by these. The equilibrium utility level of entrepreneurs is denoted . The default utility
for an entrepreneur being (no start-up), capitalist will be active only if its contract pair
is such that and . When capitalist offers while others
capitalists offer the pro�t of capitalist is The aim
of this capitalist being to maximize its pro�t, a symmetric equilibrium is therefore a pair
14
�
�
′
′
=
=
Figure 2
�
� � �
⇔
⇔
�
��������
q,�i
f
i
v vq q
i
v v� �
�
q
�
q
q
q
�
P � q, �
u q, � V , �
∂
∂q� D �D u
∂
∂�� D �D u
u
u
�
�
���
u
�
�,
q
�
ˆ( ) max � ( )
( ) 0 1
�= 0 (0) + (0) = 0
�= 0 (0) + (0) = 0
=
=
ˆ
= 1
solving the program
s.t.(10)
The system of �rst order conditions for an interior solution is
(11)
(12)
from which we deduce
(13)
(14)
On �gure 2 below, we display the decreasing contract curve characterized in Lemma 1. An
interior equilibrium is on the contract curve by (13) and its position is determined by (14). The
difficult part of the analysis (cf. Proposition 3 below) is to con�rm the intuition according to
which, less competition yields higher pro�ts for capitalists and lower �nal utility for entrepreneurs.
Combining this result with Lemma 1, we see on Figure 2 below that when the index falls, the
equilibrium moves down on the contract curve.
At some value the equity share constraint starts to bind. We then show that the only way
for capitalists to increase their pro�ts is to move up vertically towards their ideal advising quality
. The position of the equilibrium on the vertical line still obeys equation (14) but computed at
instead of being computed on the contract curve.
15
�
� q
q
I
I
I
I
I
�
�
� �
�u
ˆ
ˆ = 1
ˆ
0 ˆ
( ) =
ˆ
ˆ
ˆ
Proposition 3
Corollary 1
Corollary 2
�
� � � �.
� > � � �.
� �.
� � .
q � �.
� q, � w �� �
w
� w
w < w
w > w
There exists an index of competition separating two regimes:
(soft regime): the capitalist owns the start-up ( ), advising quality decreases with
(acute regime): the equity share decreases with , advising quality increases with
Comparative statics of the advising-obedience game:
The frequency of visionary management increases with the index of competition
The frequency of project advising increases from to over and then decreases
The advising quality expected ex-ante by entrepreneurs is weakly decreasing with
For a given , there exists a wealth level such that:
- For , capitalists own start-ups and advising decreases with wealth.
- For , the equity participation of capitalists decreases with wealth while advising increases
with wealth.
The following proposition, whose proof has been deferred to the appendix, completely charac-
terize the equilibrium of the market for the �nancing of high-tech start-ups.
The proposition has thus shown that a low degree of competition raises the equity participa-
tion of capitalists to the point where entrepreneurs become managers of their start-ups. Then,
the advising quality is the only strategic choice left to �ght for market shares among capitalists.
Contrariwise, when competition is �erce enough, capitalists are forced to lower their equity share to
attract entrepreneurs and compensate the reduction in their �nancial stake by choosing an advising
quality closer to their ideal.
An important question within our model remains: does more competition yield more visionary
management and more advising ?
Finally, we may reinterpret our �ndings with respect to the initial (observable) wealth of en-
trepreneurs. As is linear in , we can solve the equilibrium equation keeping
constant and taking as an exogenous parameter to obtain the following corollary.
This result is in line with Hölmstrom and Tirole (1997)�s �nding regarding the credit crunch
that hit Scandinavian �rms in 1990-91. Over the lower part of the wealth distribution, richer �rms
16
5 Conclusion
are less monitored than poorer ones. However, our model also suggests that several regimes may
coexist which call a careful econometric treatment of international data where various degree of
competition are likely to coexist.
Our paper offers a contribution, �rstly, on the external �nancing and management of high-tech
start-ups and secondly, on the competition among �nanciers for these high-growth opportunities.
We start from two observations: high-tech entrepreneurs are not experienced managers and start-
ups display few signals of good or bad management. We alter the traditional corporate �nance
framework to account for these speci�cities. Our vision of the lender-borrower relationship with
endogenous advising and visionary management seems rather well �tted with stylized facts as we
obtain positive frequencies of inefficient management and advising in equilibrium.
Our approach then permits to analyze how venture capitalists or angels compete to fund
these start-ups. We also depart from the standard literature by taking into account the multi-
dimensionality of capitalists strategies. We point at the relationship between the traditional price
variables (equity share, liquidation share,capital investment) and a new and increasingly important
qualitative dimension, the advising activity. We show that advising quality and equity share are
substitutes at the industry level (in the regime of acute competition).
As for empirical implications, the identi�cation of two possible regimes calls for a prudent
analysis of international data since the market concentration and other indicators of rivalry come
to play a determinant role (according to our model). Competition in private �nance seems to
be increasing everywhere in the world. Thus, beyond decreases in the equity shares retained by
venture capitalists, we should observe an increase of advising quality if the country under scrutiny
is already in a regime of acute �nancial competition (it should be the case for the US and Europe).
In developing countries however, it may well be the case that �nancial competition lies in the soft
regime where capitalists are the owner of start-ups. Advising quality should then decrease until
the degree of �nancial completeness of the country reaches a sufficient level.
17
�
2
Proof
︸ ︷︷ ︸
� �
� �
Appendix
f
s
f
uf
s f
s
s
��
�
�� � � � � �
� � �
� � �
� � � �
� � �
� � � � �
� � �
� �
�
� � � �
� � � �
Proof of Proposition 2
Proof of Lemma 1
(1 )
1
= 0
(� ) ( )
1 (� ) (1 ) (1 ) +
0 (� )((1 ) + )
0
(� )((1 ) + )
u �
u � u �
� u
u
�
pV
p V
s f s f
Vp
s fp p pFc q V
p B p p � V � V F
spF
B p p � V Fu
s f�
s
f s�
spF
B p p � V Fu u �
( ) ( )
[0; ] [ ; 1] ( )
( ) ( )
1 � 0 � = �
� = (1 )( � ) + ( � ) = 0 � + � =
� 0
� = � + �
= (1 )( � ) + ( � ) +( )( ( ))
� 0
= 1
( ) = + + (1 )(1 ) + 1 ( )
( ) = (1 ) + ( )
� 0
� = (1 )�
=
( ) = + + (1 ) ( ) ( ) = + (1
)(1 ) 1 ( ) [ ; ] [0; 1]
c c � q, �, �, L u q, �, �, L
q q q . q, �, �, L q < q q > q
q , �, �, L q , �, �, L
q
q .
� < � > � �
� � p � V p � V V � V �
� >
u∂ u
∂ ��
∂ u
∂��
p � V p � V � >
�
� �
u q, �, L w B p � V L K c q
� q, �, L p �V pV L c q
� >
L p �V � u.
L K w.
� q, � pV K w p �V c q u q, � B
p � V c q q q
The convexity of and implies that both and are increasing
with on and decreasing on Playing with or is strictly
dominated for a capitalist by or . Indeed, each alternative raise the clients
utility, thus guarantee that the market share will not fall. Then, as the per-capita pro�t also
increases, the deviation is strictly pro�table. We can therefore restrict qualities to lie between
and
Assume and consider and . With this new contract the pro�t
remains constant as but given that
we have
Hence the capitalist could alter the initial contract in order to keep its clients and make more
per-project pro�t. The process of increasing the liquidation share and decreasing the bene�t
share will continue until the constraint is met.
Payoffs are now
and it is readily observed that reduces the moral hazard cost so that a compensated
keeps constant while increasing Hence an optimal contract has minimal
loan size with
Recall that and observe that
is bounded over and spans an interval
18
�
2
3
2 2
2
unique
� �� �
� � � � � �� � � �
� � � �
� �
� �
√� �
q
�
�
su
s
q
�
q
�
s
s
s
uq�q
uq
s
q
�
�q
s
uq
s
�q
s s
� �� � � �
�
� � ��
�
� � �
�� � � �
�� � � �
��
�� � � �
� �� � � � � � � �
�
� �
�
�
� � � � � � �
� ��
� � � �
∞
� � � � �
⇒ �� �
�� �
��
� �
⇔ �
⇔ �
⇔ �
�
� � � �
⇔ � �� � �
�
� � �
�
�
1 2
11 2
2
(� ) ( )
(1 ) (� )((1 ) + )
(� )((1 ) + ) 2
(� )
(� )((1 ) + )
(� )
(1 ) (� )((1 ) + )
(1 )
2(� )
(1 ) (� )((1 ) + )
2(� )
(1 ) (� )((1 ) + ) (� )((1 ) + )
2
2
v v . u < , � � q, v v u q, � � <
� < q q v v
q, �u
�
pF
B p p � V F
c q
c q
q, �u
�
p p pFc q
p B p p � V F
v q, � q, v q, � q, v .
< q, � q, v
q q
q v
q � q � qq u
u
qu u u � /�
c c c c
c
c
c
c
c>
> >
q > >
c
c
c
c>
c
c
c
c>
c q c q , A Ac
c> A
c
c> A q q . c > c > c q q >
< p A A B p p V F V pFc q p p
p p < p A A B V F V pFc q D
p A A V F
D V pFc q p A A B V F V pFc q
� H v
� v � q v , v � < � <
[ ; ] 0 = ( ) = ( ) = 0
= 0 [ ; ] [ ; ]
� ( ) = 1(� ) ((1 ) + )
( )
( )
� ( ) = 1 +(� ) ( )
(1 ) (� ) ((1 ) + )
� ( ( )) = � ( ( ))
� =( )
0 � ( ( ))
+ 0 [ ; ]
( )
0 = � � + (� � ) + = � � + (� � )1
=� �
� � �=
� �
� � �
=
� = 1( )
= � 0
� =( )
0 � =( )
= � 0
0 � � � = 2�
�( )
( )( )
( ) = ( ) = 0
[ ; ] 0 ( ) 0
0 (1 ) ( + ) (� )( + ) + 2 ( )(� )
�(1 ) ( + ) ( + ) ( )
2(1 ) ( + ) ( + )
( ) 2(1 ) ( + ) ( + ) ( )
4
( ) ( ( ) ) 0 0
� quu
v uu �
q q
q s
uq
�q
� �
�
u
s
q �
��
p p V pFc q
p B p p � V F
q
u �
�q v
q�
�� q v v
�q v
q�
��
v q
�
v
��
q�
�q �
q� q
��
q�
�q
q� q �
��
uu
pF
B p p � V F
uqq
�q
uq
�q
quqq
uq
�q
q�
p p V pF
B p p � V F
c
c�q
p p pFc
p B p p � V F
q���
vqq
�q
q�
c
p V�q
quqq
uq
�q
p p pFc
p B p p � V Fuqq
uq
�q
p p pFc
p B p p � V F B pF p p � V F
uq
u �q
� u �uqq
uq
u
�q
� u � � �q
�q
uv
u �s s
�q
u
u �s s
�q
u
u �s
s�q
u u �s s
�q
u
q v
As the solution to the equation satis�es and
and is bounded over . Let us now introduce
(15)
(16)
An interior Pareto optimum yielding a utility level solves As
is bounded away from zero while varies from
to over the equation has at least a solution. We assume that it is , name it
and differentiate it.
(17)
using at the optimum.
We have ,
, thus
As there exists strictly positive constants and such that
and over Also, being convex, we have . The inequality
therefore holds if
(18)
(19)
where (we keep only the mean-
ingful root of the second degree equation (18)). In the next proof, we shall introduce the constant
that will characterize . Hence, on the contract curve, quality increases with while the
equity participation decreases as and .
19
18
18
P �
v
˜( )
2
3 2
Step 1:
��
��
�
′
′ �
′
Proof of Proposition 3
���� ����
� �
� � � �� �
� �{ }
� �
� � �
�
⇔ ⇔
⇔ � ��
⇔ �
⇔
� � �
� �
⇒ � �
�
q
�
q
q
i q
q
q v
�
�
�
�
q v
�
q
�q
�
��
�
su
s
u
s
�
�
�
� � � �
� � �
� � �
� � � � � � � �
� � � �
� � � �
�� � � �
�� � � �
�
�
�
= ( )= ( ( ) )
= ( )= ( ( ) )
1 �
1 1
�
(� ) ( )
(1 ) (� )((1 ) + )
(� ) ( )
(1 ) (� )((1 ) + )
(1 )
(1 )
We do not need a �xed point argument to derive the equilibrium because the solution of does not depend on
the level .
˜( ) max � ( ( ) ) = ( ) ( ( ) )
˜( ) = ( )
˜( ) 0 = = +
( )
= ( ) =
= ( )
1
( )= ( ) � ( )
= + = 0 = � +
� 0 � 0 0 � 0 0 0
( ) � ( ) = ( ) � ( )
�+ � = � + � + � = � + � 1
0 � + � +1
� + �
� � � �
� 2 �+
� 1
0� 1
� = �
( )1 +
( )
� min ( ( + ))
� ( ( + ))
(� ) ( ( + ))
P � q �, v , � D v v � q �, v , �
P � � v � v
P � v �� �
� v
� H v�
�. u
�
�. u
q � � q, v
H v� q , � q , �
� q � < q
� > > , q > , < � < . H >
� q , � q , � � q , � q , � .
�d
dv
d�
dv� q �
�
u� q �
H > q � q � <�
q <
u u<�
H >u
<�
>u
�
�
�
<�
�
p p < � , B V F
p p < B V F
p p V <�
�B V F
v,�i
�
��
uu
nu
∂∂q
�u
q
q� � v
q q � v ,v
�
�� � v
q q � v ,v
�
d�dv q v �
u qu
�u
ddv
�q v
�� v
�q v
�� v
� q
qq q
q vq� v
q �
�
qq v
q� v
qq v
q� q v v
qq v
q�
u qu �
��
q�
�
��
q�
��
q�
q�
�
u
��
�
��
� � �
p p V pFc q
p B p p � V F
� p p pFc q
p B p p � V F
p
� s
p
� s
s�
s
We solve the unconstrained problem �rst and then introduce the constraint in a way that eases the
resolution.
Solve the program
The FOC of with respect to is thus the optimal equity share given is (cf.
Lemma 1). The FOC of with respect to is and by replacing with
the optimal value we obtain a unique equation
(20)
Using the alternative derivation with and , we can write
(21)
Note that by the envelope theorem, while
as a consequence of and Hence to show we need
to analyze the behavior of the product
Differentiation yields
thus
(22)
As the LHS of (22) is bounded by , a sufficient condition for is
(23)
and a stronger sufficient condition is . Indeed, on the
one hand we have
20
�
19
19
� �
� �
( ) 0 ( )
1
0�
(� )
Step 2:
u q, � q, �
� �
��
� �
�
�� �
s s
�s
�s
s�
s
q,�
v v
f s� B pF
B p p Fu
� � � �
⇒ � � � �
� � � �
� � � �
� � � � � �
�
�
{ � � }
� � �
�
� � � �
Duality applies as the constraint set is convex in the space (cf. appendix).
(� ) ((1 ) + ) ( + )
(� ) ((1 ) + ) ( ( + ))
(� ) (� ) ((1 ) + )
1
( ) max ( ) ( ) 0 1
( )
0 1 0 1
( )
1
( )
( )
( ) 0 1 (�)
�
( ) ( ) ( )
� ˆ (1) ( )
( ( ) ( ( ) ))
= ˆ (1 (1 ˆ))
ˆ (ˆ)
(ˆ 1) =
+ (1 ) + ( )̂ 0 (ˆ 1) = ( )̂
ˆ
ˆ �
ˆ
B p p � V F > B V F
�
�B p p � V F >
�
�B V F
p p V <�
�B p p � V F
P v � q, � u q, � v � .
� q, �, �, L
� , � L K w
u q, �, �, L v
�
P v .
u q, �
� q, � � P v
v > v
P v q v � v
v v. v v � , � , q
� v , q � v , v
v v, , q , v v
q q v .
� q,
pV p V K w c q > u q, B c q > w
q
q � v < v.
v > v.
and on the other hand,
thus
which is a stronger condition than (23) (obtained by dropping the in the RHS).
Solve such that and
We study �rst the monopoly and the purely competitive markets. Since entrepreneurs have an
inelastic demand for one loan, a monopoly maximizes the per-capita payoff under the
feasibility constraints ( and ) and the participation constraint
. The arguments used in the proof of Proposition 2 apply for the monopoly as well,
thus only the equity share constraint remains. The monopoly therefore solves the program
The purely competitive outcome, on the other hand, maximizes under the set of con-
straints and ; by duality this amounts to solve for some indirect utility
level .
The solution of is very simple to �nd using and identi�ed in Lemma 1. Starting
from the largest level , one decreases As long as the contract
is optimal i.e., the equity share increases while the advising quality decreases.
For the optimal pair is simply and as decreases further the advising quality now
increases (direct effect only) since the equity share has reached its maximal value. Let us de�ne
Since we assumed that capitalist and entrepreneurs are active in equilibrium, we have
and . The �rst condition
means that the participation constraint of the capitalist is not binding at . Hence, an increase of
entrepreneur utility is possible by increasing and decreasing . This implies Symmetrically,
the second condition implies
21
�
q
q
s
� �
�
Step 3:
Proof of Corollary 2
1 0
1
=1
1 1 1
1
1
1 1
1(� )
( )
� �
� �
� �
�
′
� � �
�
�
� � �
�
� ��
�
��
� �
����
� �
� � � �
[ [ [ [� �
��
� �
� � � � � � �
� ⇔ � { }
� �
� �
⇔
∞
∝ �
∈ ∞�
⇔ �
� v q v�u
q,�i
� � � � � �
�
�
i i i i
q
q �
qq q
� u
� �
� � �
�p p V
c q�
��q
�� � �
�
�
� ��q
�
�
q v v
�q v
�
� �
v
�
�
v�q
�� �
�
q v
�
( ) ( )( (1 ) 1) ˆ
( ( ( ) ) ( )) ˆ
0 0 = 0
( ) ( )
( ) ˆ
ˆ( ) = max � ( ) ( ) 1
ˆ (ˆ) ( ) ( ) 1 ( )
ˆ( ) ˆ ( ) 1
[ ( (ˆ) ˆ) ; ]
( 1) (1 ) min (1 )
�̃ ( ) ( ( 1) (˜ 1)) ( 1) ˜
= ( )
� 0 0 � � ( ) 0
( ) (0) = (+ ) =
min ( ) (1 )
= 1 = min ( ) (1 ) ˆ
= ( ) = ( )
=
( )( )
0; ˆ = 0 0 0 0 ˆ; +
= ( ( ) ) = + =1
0 = 0
0 ( )( ) 1
P v W v� q , v , v < v
� q � v , v , � v v v
� > q < � q <
W . W .
P . v
P � q, � u q, � v, �
� � H v , v H � v > v � � v q q � , v
P � . � < �, � H � >
q � v , v q
u q, v q q , v , q , v , q .
q D u q , u q, � q , q
� G q�
�. u
< � > � > � G v <
G � G q G q
G � , q , v .
� q G � , q , v � < �
� � H � q q � ,H �
� ,
d�
d�c q
dq
d�
c q
�
d�
d�
� �d�
d�
d�
d�> c <
dq
d�< � ,
� � q v , vd�
d�� q �
dv
d�
u q
u
dv
d�<
dq
d�qdv
d�>
d�
d�> q c q >
c q
�
u q
u
The value of is thusif
if. The �rst term is decreas-
ing as and . The second is also decreasing because its derivative is
(envelope theorem). Hence is decreasing. It is also immediate to observe that both and
are continuous (including at ).
Solve s.t.
For we set , thus and solve
Yet when the fact that means that competition then takes place
over a single variable, the advising quality. It varies a priori in . The participation
constraint being the correct upper bound is thus
The pro�t function is now where denotes the equilibrium
advising quality. The unique FOC to be satis�ed at the symmetric equilibrium is similar but
different from (20):
(24)
Since and we have . The candidate Nash equilibrium
advising quality is ; it varies from to . The equilibrium is thus
To summarize, the symmetric equilibrium is and if ,
and otherwise.
As the frequency of visionary management in the symmetric PBE is we have
When , thus as and . Over we use
to obtain and , so that
22
�
LIX
105
� � � �
�
�
� �
� �
�
�
�
References
� � � �� �
� �� � � �
[ [ [ [
⇔ �
⇔ �
⇔ �
⇔ � � �
⇔ � ⇔ �
⇔
� � � � �
∞
Review of Economic Studies
Journal of Political
Economy
(1 )
+ =
=
1
(� � ) � � �
� � � � � �
� 0 � �
0 � 2�
:
1(� ) ((1 ) + )
0; ˆ 0 0 = 0 ˆ; + 0
0
0
q � u c < u q c
c > q � u c u c q u c � u �
c > q u c � ��
�
u
u
q u <
u > u u
u > u <�
�
< >
q > < .
q � �
q �pF
B p p � V F
� > < � <
>
<
q �
�
v���q q v
�
�v
���q q
�v q
� �� q
�v q
� ��
�
q
�
q
v q
��
q� q �
�q
q� q
�� q �
�q
��
�
q
�q
��
�q
vqq
�q
� � �
� ��
s
d�d�
dqd�
d�d�
d�d�
dqd�
d�d�
� �
using
a sufficient condition is thus
but as a stronger sufficient condition is which is true as we already proved
As for advising, we have a simple link between the product and the share
(25)
Thus, over , we see that as and . Over , implies
that the RHS of (25) is decreasing. Combining this with over the high regime, yields
.
Lastly, it is immediate to see from (25) that the advising quality expected by entrepreneurs
is weakly decreasing with competitiveness (constant over the soft regime and strictly decreasing
otherwise).
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22
LXXX
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24
