The Supply and Demand for Venture
Capital Funds: Information and Entry
Chris Yung∗
October 6, 2008

Abstract
The characteristics of both entrepreneurs and venture capitalists
are jointly determined by the set of real investment opportunities. An
improvement in these opportunities has two eﬀects: 1) it encourages
marginal, low-quality entrepreneurs to pool with high-quality entrepreneurs, and 2) it induces the entry of venture capitalists that are lesseﬃcient at screening new investments. The market for venture capitalfinancing is therefore plagued by a double-sided asymmetric information problem. The severity of both frictions severities is increasing but
concave in market heat, and this is shown to imply that supply and demand are more elastic in cold markets. The paradigm makes predictions
regarding the evolution of venture capital partnership quality.
∗

Assistant Professor of Finance, Leeds School of Business, University of Colorado. E-mailcontact: chris.yung@colorado.edu.

11Introduction

The venture capital market is characterized by dramatic fluctuations in theoverall level of activity. A major research agenda has been to empirically decompose these cycles into changes driven by demand-side factors and thosedriven by supply-side factors (Gompers and Lerner, 1998). This is a daunting
task given the endogeneity of the actions of capital suppliers and demanders.
For example, an across-the-board cut in tax rates aﬀects both the incentive toengage in entrepreneurial activity and the profit from financing it (Poterba,1989). Therefore without observing required returns − or making the heroic
assumption that realized returns equal required returns − it is diﬃcult to unambiguously attribute changing quantities to specific causal factors.
Instead, the approach has been to exploit natural experiments such as anunpredicted change to the interpretation of the Department of Labor’s Employee Retirement Income Security Act (ERISA). The 1979 ruling allowed thata moderate amount of pension fund investment could be allocated to private
equity if invested with the care of a “prudent man.” Accordingly, it serves as
an exogenous supply shock to capital in this market.
One emerging theme of this literature is that the supply of venture capitalfunds is “sticky” in the short-run. Private equity investing requires considerable skill and experience − attributes which are largely fixed in the short-run.
During hot markets, general partners in established funds become the scarce
resource in the market and earn significant economic rents (see also Ljungqvist
and Richardson, 2003). In the long-run, supply adjusts as new VCs choose
to enter the market, thereby competing away rents. However, this entry/exit
reaction can be sluggish and imprecise, so that the market can sometimes go
through episodes of over-investment followed by low returns (Lerner, 2002; Kaplan and Schoar, 2005) or under-investment with correspondingly high returns.
This evidence makes it clear that any formal analysis of the determinantsof supply and demand for VC funds ought to account for the entry incentives2

on both sides of the market. In other words, given an exogenous distribution ofquality across potential entrepreneurs, which agents choose to enter the market
and which do not? For an exogenous distribution of ability across potential
venture capitalists, which agents choose to operate and which do not? The
answers to these two questions determine 1) the severity of financing frictionsin the venture capital market, 2) the equilibrium distribution of private firm
value, and 3) the equilibrium quantity of funds in the market.
This paper takes a first step towards such a model using the paradigm ofinformation asymmetry. As is well known, financing of startups entails potentially extreme adverse selection costs given the absent track record of thefirms seeking capital, and given the risky nature of the industries in which
many of them operate. Exacerbating the problem, this scenario often involves
an innovator who has extensive technical knowledge (Denis, 2004) but lacks
the reputation capital necessary to convey this information credibly.
In such an environment of asymmetric information, perhaps the most natural definition of venture capitalist “ability” is eﬀectiveness in screening newinvestments.1 VCs go through an extensive process of due diligence before
investing (Kaplan and Stromberg, 2000) and the vast majority of funding proposals are rejected. Viewed more broadly, this skill has enormous social welfare
consequences because it determines how eﬃciently capital is directed toward
profitable projects.
The quantity of funds demanded depends upon economic conditions. In themodel, agents choose to either start entrepreneurial firms (with VC financing)1“Extensive due diligence in the private equity market is needed because little, if any,
information about issuers is publicly available and in most cases the partnership has had no
relationship with the issuer. Thus, the partnership must rely heavily on information that
it is able to produce de novo. Moreover, managers of the issuing firm typically know morethan outsiders about many aspects of their business [but] the problem of adverse selection is
mitigated by the extensive amount of due diligence conducted.”− Fenn, Liang and Prowse (1995, pg. 30)

3

or continue in their current employment. In equilibrium, better quality agentsare more likely to become entrepreneurs: their residual claim from doing so isrelatively more valuable. Yet there is overinvestment, as some entrepreneurs
with negative NPV projects pool with better entrepreneurs in an attempt toobtain the benefits of mispricing.
The capital supply side also has latent agents, i.e. information producers
who can choose to enter the market as venture capitalists if market conditions
warrant doing so. Obviously, this entry decision depends upon the agents’privately-known information production ability. The decision must also take
into consideration the distribution of entrepreneurial quality, because the heterogeneity therein dictates the severity of the information problems being
faced. In turn, entrepreneurial entry decisions are aﬀected by the equilibrium skill level of VCs. This is because the capital suppliers’ required returns
depend upon their costs of information production. In addition, entrepreneurs
face diﬀerential probabilities of being screened out (depending on their true
quality), and these probabilities depend upon the skill level of VCs. All ofthese interdependencies underscore the importance of modeling these supplyside and demand-side frictions simultaneously.
These agents generate a supply curve of information production. In statesof low capital demand (i.e., poor investment opportunities) only very eﬃcient
information producers are able to operate profitably. An improvement in real
investment opportunities causes the market to “step up” the supply curve toprogressively less eﬃcient information production agents. Therefore, the average intrinsic quality of supply-side agents is countercyclical.
Like the supply-side, the demand-side informational friction is of procyclical severity. Consider a positive shock to the value of investment opportunities. With more profitable investments, competitive venture capitalists would
be willing to hold smaller financial stakes in underlying firms, ceteris parabus.
However, such an improvement in the terms of finance would induce the entry4

of marginal, lower-quality entrepreneurs (see Yung, Colak and Wang (2008)
for an analogous argument and evidence in the context of initial public offerings). Thus the capital demand-side asymmetric information problem is ofprocyclical severity.
The model has the following properties. In all states of the world, VC information production is able to partially, but not fully, mitigate the demand-side
asymmetric information problem. In all states, within the set of active VCs,
the lowest quality agents make zero profits. By contrast, high-quality VCs
earn positive profits despite the fact that equilibrium profit-sharing rules arecompetitively determined. Their rents are increasing in the value of investment
opportunities. On both the supply-side and the demand-side, the average quality of agents is lower during good times, and the dispersion of quality acrossagents is higher during good times.
While the paper does not explicitly model the relationship between generalpartners (GPs) and limited partners (LPs), the findings give some reason to be
skeptical of partnerships founded during hot markets. This viewpoint seems
consistent with Gomper, Kovner, Lerner and Sharfstein (2005), who conclude
that experienced VCs react more accurately to changing market conditions.
By contrast, a particularly encouraging scenario might involve a partnership
operating during hot markets but founded during cold markets. The decision
to operate in a cold market (and subsequent survival) suggests high innate
ability, while the contemporaneous hot markets indicate attractive investment
opportunities. A more formal analysis of these claims would need to accountfor the ability (and incentive) of agents to signal their quality to LPs via theirchoice of contract. Noting that the venture capital investment process emphasizes “staged” finance (i.e. capital is released over time, rather all at once)such an analysis hinges on dynamic choices such as when to raise new funds,
and the role of intertemporal profit-sharing within a given fund. A full analysis of these contractual features is beyond the scope of the current focus.

5Endogenous entry in the model also permits examination of supply anddemand elasticity.2 When profitability is high, there are strong incentives toenter on both sides of the market. Consequently, marginal entry decisions
are relatively insensitive to sharing rules, i.e., the division of the firm between
VCs and entrepreneurs. This implies that both supply and demand are moreelastic in cold markets. Section 3.3 illustrates these points graphically.

1.1

Comparison to the Agency Theoretic Approach

Separation between financing and real decision-making − a pillar of classicalfinance theory − breaks down in private markets. Venture capitalists have a
myriad of non-financial roles, including the “professionalization” of the firm
(Hellman and Puri, 2002), the decisions to liquidate or replace management(Gompers, 1995; Bergemann and Hege, 1997) and the form and timing of theexit strategy.
With both the entrepreneur and the VC having real inputs to firm value,
the environment is one of double-sided moral hazard. This paradigm has important security design implications (Casamatta 2003; Repullo and Suarez,
1999; and Schmidt, 2003). Empirically, financial contracts cede to the VC avariety of state-dependent control rights (Kaplan and Stromberg, 2002), theterms of which are tailored to the circumstances of each individual firm. These
contractual feature vary on a deal-by-deal, round-by-round basis (Kaplan andStromberg, 2004).
By focusing on how these frictions vary with business conditions, two papers in the literature are particularly close to the spirit of the current model.
Inderst and Muller (2004) model the process of search and bargaining between
2

Previous literature assumes that long-run supply is “likely to be quite flat” (Gompersand Lerner, 1998, pg. 7) but has not identified determinants of this elasticity. I am notaware of any attempt to characterize demand elasticity, although Poterba (1989) emphasizes
the tax rate diﬀerential between wages and capital gains as a key determinant of the levelof demand.

6

VCs and entrepreneurs. The relative supply and demand for funds determines
the equilibrium stake held by VCs and the residual claim held by entrepreneurs, and in turn, the amount of eﬀort chosen by each party. Total firm value
can be nonmonotonic in the amount of capital market competition because atlow (high) values of competition for funds the VC (entrepreneur) contributes
too little eﬀort.
In Inderst and Muller’s analysis, shocks to investment conditions have adynamic eﬀect because the supply of venture capital is sticky in the short-run.
Therefore, given a positive shock, VCs temporarily earn positive profits. In thelong-run, these profits are driven away by the entry of new VCs. (The severityof frictions can either go up or down, depending on the pre-shock sharing rule.)
Kanniainen And Keuschnigg (2003) take an alternative approach to modeling the eﬀect of changing business conditions. They emphasize that VC
monitoring is a scarce resource (see also Sorensen, 2007) to be divided overmultiple, simultaneously-held portfolio firms. They demonstrate that whenindustry returns are high, VCs hold a greater number of portfolio firms andhence contribute less eﬀort to each firm. Hence, as in the current model, there
is a sense in which the average supply-side “quality” deteriorates during goodtimes, although the notion of quality is quite diﬀerent from the one employedhere.
A broader question is how these agency theoretic approaches might beempirically distinguished from asymmetric information models. In corporate
finance more generally, drawing such distinctions is not always straightforward.3 One diﬀerence is that in these agency models, VCs are homogeneousand all take the same actions. By contrast, an important property of thecurrent model is that the distribution of venture capitalist quality changes
3

In the context of managerial compensation, Hagerty and Siegel (1988) point out thatcanonical formulations of the principal-agent model and of screening models (i.e., models of
self-selection) are mathematically equivalent and therefore empirically indistinguishable.

7

over time. As an implication, the model makes testable implications regarding cross-sectional dispersion in returns; see Section 4. This heterogeneity hassome parallels in the literature, as Kaplan and Schoar (2005) conclude “wethink the most likely explanation for [our] results is a model of underlying
heterogeneity in the skills of GPs.”
On the other hand, these agency models have insights and applications
not shared by the current model. For example, they make predictions on the
search time and bargaining power (in Inderst and Muller’s case) and the evolution of the number of portfolio firms (in Kanniainen And Keuschnigg’s case).
As emphasized by Kaplan and Stromberg (2004), agency considerations play aparticularly important role in the governance of venture capital partnerships.
Undoubtedly, both imperfections merit further study.

2

The Demand for VC Finance

There exists a continuum of entrepreneurs in the economy with assets-in-placeworth V in current use. A new project is available which redeploys existing
assets at a cost K. Entrepreneurs have no available internal financing, so theproject requires external finance.
At T = 1, if the new project is undertaken, the firm is worth 1 with probability πi , or else 0. The subscript i indicates the entrepreneur’s privately known
type. Net present value is therefore πi − K − V . Assume that K + V ∈ (0, 1)
and that success probabilities πi are uniformly distributed on [0, 1]. Hence,some entrepreneurs have positive NPV projects while others have negative
NPV projects.
In this section, venture capitalists are homogenous information producers.
They can evaluate entrepreneurs, obtaining a signal s = G or s = B. Thissignal is associated with two costs. The VC incurs an information production
8

cost CV C , and the entrepreneur pays a direct transaction cost CE (interpreted
as the opportunity cost of meeting with VCs, preparing the pitch, etc.). The
distinction between these two costs is that while the entrepreneur bears CE
directly, he bears CV C only indirectly through its eﬀect on the venture capitalist’s required stake. Assume thatP rob {s = G | πi } = πi

(1)

Condition (1) implies that the signal is informative: higher quality firms
are more likely to yield the signal s = G.
Some fraction of the potential entrepreneurs opt to remain private rather
than seeking financing. Let πM IN denote the lowest quality entrepreneur thattries to obtain VC financing. This cutoﬀ value will be determined later. Theinterval [πM IN , 1] then determines the number of active entrepreneurs. It is
assumed that entrepreneurs are evenly distributed across VCs so that each VC
has n active entrepreneurs; see Fig 1 below.

Venture Capitalists

1

2

3

Entrepreneurs
Fig. 1

Evenly distributing entrepreneurs across VCs in this way ignores an “integer” problem, i.e., the number of entrepreneurs is unlikely to be divisibleby the number of VCs, so that each pool cannot literally be of exactly thesame size. However, in equilibrium, VCs have no incentive to lure away entrepreneurs from others’ pools: each evaluation is associated with zero expected
profit.

9

This section’s assumption is that VCs have suﬃcient capital to fund every
entrepreneur in their pool (even though not all entrepreneurs will be funded).
There is no economic cost to idle funds. Alternatively, in a large economy, it
can be assumed that VCs only have suﬃcient capital to fund the number ofentrepreneurs expected to have good signals in their pool. In that case, if a
venture capitalist exhausts her funds before completing all of the evaluationsin her pool, then any unevaluated entrepreneurs could approach another VC
with remaining funds.4 Even under that alternative scenario, by the law oflarge numbers, the proportion of unevaluated entrepreneurs goes to zero as
the economy gets large.
Assuming that entrepreneurial quality πi is drawn from a uniform distribution on [0,1] it can be shown that the unconditional average quality of active
entrepreneurs, and the quality condition on passing the VC screen, respectively, areE(π) =

πM IN + 122
E {π | s = G} =3X

3
1 − πMIN
2
1 − πM IN

(2)
~

(3)

Naturally, because the signal s is informative, E {π | s = G} > E(π).
Moreover, both the unconditional mean and the conditional mean are increasing in πM IN . An exogenous improvement in the entrepreneurial pool implies
a better expected quality conditional on passing the venture capitalist’s screen.
4

It is assumed here that rejections are public information, so that an entrepreneur receiving a signal s = B cannot re-enter another VC’s pool.

10

2.1

The VC’s Problem

Since payoﬀs are binary, it is without loss of generality to describe the securities
as equity. The VC takes the distribution of firm types as given and demands
an equity stake α in exchange for supplying capital K. In a competitive market,
these values satisfyw

W^

πM IN + 1
2α
∗
3
,2
1

P rob(s=G)

2.2



X

3
1 − πMIN
2
1 − πM IN,~− K ≥ CV C

Expected P rof it when s=G(4)

1

The Entrepreneur’s Problem

While it is defined as the value of assets-in-place, V also serves as a reservation
value for entrepreneurs. This is because if no additional funding is secured,then the NPV of the project is lost. Expected payoﬀ from accepting thecontract is
πi ∗ [πi (1 − α) − CE ] + (1 − πi ) ∗,1

P rof it given f unding[V − CE ]


,

1

(5)

P rof it otherwise

The bracketed terms indicate the expected payoﬀ if the project is fundedor unfunded, respectively, while the leading terms reflect the probability ofeach outcome. Note that because entrepreneurs know their type, from theirpoint of view the venture capitalist’s signal adds no value-relevant information.
Rather, the signal only determines whether the funding proposal is accepted.
Entrepreneurs seek funding when (5) exceeds V. Since this expression isincreasing in πi , it follows that there is a cutoﬀ quality πM IN , i.e., an entrepreneur just indiﬀerent between seeking funding and not doing so. In particular,
πM IN =V +

V 2 + 4(1 − α)CE2(1 − α).

(6)Putting these two participation constraints together yields the following
result.
11

Theorem 1 Equilibrium consists of the pair {πM IN , α} that jointly solve equations (4) and (6). This solution has the following comparative static properties:∂πM IN>0∂K∂πM IN
>0
∂V

(7)

∂α
>0
∂K

∂α
<0
∂V

(8)

Proof: Follows from the implicit function theorem; see the appendix.
Equation (7) indicates that as investment opportunities improve, lower
quality entrepreneurs are drawn into the market. That is, as V and K shrink
relative to terminal payoﬀs of a successful project), the cutoﬀ quality πM IN
drops. In this sense the demand-side asymmetric information problem is ofprocyclical severity.
This result is closely related to Yung, Colack and Wang’s (2008) analysis of
the market for initial public oﬀerings. In particular, their analysis focuses on
the dispersion of quality within the set of IPOs in a given economic state. Thisdispersion is predicted to be procyclical. Taking the view that true quality will
be revealed in the long-run, this result leads the prediction that cross-sectionalvariation in long-run returns should be higher within cohorts of firms that were
funded during hot markets. Furthermore, this hypothesized expansion is more
specific to the left side of the distribution rather than the right side. Consequently, financing waves will be associated with more portfolio firms goingbankrupt ex-post.5 Equation (7) indicates that these results generalize to an
environment with informed capital suppliers.
Equation (8) indicates how VC contracts respond to changing market conditions. Unsurprisingly, as the required capital contribution rises, VCs demand∂αa larger stake. The result ∂V> 0 has more subtle intuition. An increase in
5

The mean return is not predicted to change. Capital suppliers in the model are rational;
i.e. oﬀer prices fully account for changing demand-side conditions.

12the value of outside opportunities (relative to VC finance) leads to improvement in the quality of the entrepreneurial pool. Because of this reduction in
the severity of the asymmetric information problem, VCs are satisfied witha smaller stake. Putting these two results together, the model is ambiguous
regarding how α varies with the value of investment opportunities. If both V
and K shrink relative to terminal payoﬀs, then there are competing eﬀects on
α; this issue is explored again in a numerical example in Section 3.3.
The next result examines how the information production and transaction
costs aﬀect entrepreneurial entry and equilibrium financing terms.
Corollary 1 (Eﬀect of Costs) The equilibrium values {α, πM IN } satisfy∂πM IN>0∂CE∂πM IN
>0
∂CV C

(9)

∂α
<0
∂CE

∂α
>0
∂CV C

(10)

Proof: Similar to Theorem 1.
Equation (9) indicates that the two costs in the model have a symmetric effect on entrepreneurial entry: as either type of cost rises, marginal low quality
entrepreneurs exit the market. This is true because both costs are ultimately
borne by the entrepreneur.
As in Theorem 1, this symmetry is broken for α. As venture capitalist
costs CV C rise, the obvious direct eﬀect is that the VCs demand larger stakes
as compensation. On the other hand, as the entrepreneurial costs rise, lowquality entrepreneurs exit the market. Because of this reduction in the severityof the asymmetric information problem, VCs are satisfied with a smaller stake.

13

3

The Supply of VC Finance

In Section 2, venture capitalists are identical and perfectly competitive, which
drives their profits to zero. This modeling assumption precludes analysis ofincentives to enter the VC market. To address this issue, Section 3 introduces
heterogeneity in VC skill.

3.1

Two Venture Capitalist Types

Assume that some VCs have information production cost CL and all others
have cost CH > CL . Importantly, both types of venture capitalists obtainthe same signal; it is only the costs of production that diﬀer. Consequently,
there is no post-financing diﬀerence between VCs and so, for a given contract,
entrepreneurs have no strict preference regarding which VC supplies funding.
Further assume that there are some states in which aggregate capital demanded exceed the capital under control of the low-cost VCs, so that high-cost
VCs must also be active to ensure market-clearing.6
The assumption begs the question of how high-cost VCs could attract funds
in the first place. For example, why don’t low-cost VC simply raise larger
funds? In the long-run, it is clear that capital will tend to flow to more eﬃcient producers of information. The heterogeneity in this section requires onlythat this flow is not immediate and perfect.
There are several ways in which this imperfect flow can be motivated. Perhaps most obviously, it is diﬃcult to detect abnormal performance even whenmanagers have a fairly extensive track records. Kothari and Warner (2001)
show that even in a mutual fund environment (where both the fund returns
and the benchmarks are transparent and continuously observed) under rea6

There are also equilibria in which only the low-cost VC are active. In particular, theseare states of low demand for capital. These outcomes are economically equivalent to thoseof Section 2 (setting CV C = CH ) and so are not considered further.

14

sonable assumptions regarding the level of abnormal performance, it can takemany years of return observations to reliably identify skill.
The inference problem in venture capital market is more diﬃcult still.
Gompers and Lerner (1998) observe that “returns from venture capital investments can only be observed many years after the original investments
because private firms are valued at cost until they are sold or taken public
many years later... [and] information on fund returns is closely guarded, andeven the intermediaries who specialize in compiling this data do not have very
comprehensive coverage.”
Second, the logically extreme counterassumption would lead to a single
active fund manager − the one with the highest skill. But this outcome isproblematic if agents have decreasing returns to scale in portfolio management.7 As a result, there is some generality in the assumption that evenmanagers with less-than-perfect skill sets are allocated a positive amount ofinvestment capital.
The participation constraint of venture capitalist i isw

W^

πM IN + 1
2α
∗
3
,2
1

P rob(s=G)

X

3
1 − πMIN
2
1 − πMIN,~− K ≥ Ci .

Expected P rof it when s=G

(11)

1

Competition among high-cost VCs leads to equality in the participation constraint:w

W

P rob(s=G)

7^

πM IN + 1
2α
∗
3
,2
1



X

3
1 − πMIN
2
1 − πMIN,~− K = CH .

Expected P rof it when s=G

1

(12)

See Berk and Green (2003) for a model that exhibits this property in the context ofactive management of mutual funds. In the venture capital literature, Kaplan and Shoar(2005) find empirical support for decreasing returns to scale for active management.

15

Consequently the participation constraint of low-cost VCs does not bind:w

W^

πM IN + 1
2α
∗
3
,2
1

P rob(s=G)

X

3
1 − πMIN
2
1 − πM IN,~− K > CL

Expected P rof it when s=G

(13)

1

This equilibrium has the following properties. High-cost VCs break even.
Competition between them cannot reduce α∗ without violating equation (12).
Low-cost VCs earn expected profits CH − CL > 0. They have no incentive
to “separate” by reducing α∗ below the level oﬀered by competing high-cost
agents. Doing so would not increase business − their capital is exhausted inequilibrium − and would only serve to reduce profits.
Note that there is a sense in which entrepreneurs are apparently madeworse oﬀ when low-quality venture capitalists enter the market, because thisentry is associated with a discrete jump in the equilibrium α (which takes
the role of a “price” in this market). This statement is somewhat misleading,however. In any market with a downward-sloping demand curve and upwardsloping supply curve, a positive shock to demand causes consumers to moveup the supply curve to higher marginal costs of production. It cannot be said
that marginally more expensive additional supply hurts consumers, especiallycompared to the alternative of failing to meet demand at any price.

16

3.2

Continuum of VC Types

Section 2 demonstrates that venture capital funds demanded are a decreasing
function of the cutoﬀ quality πM IN . When πM IN is high, few entrepreneurs
are active and therefore aggregate capital demanded is low. More generally,
denote this demand function D = D(πM IN ) where D < 0.8
Next suppose that each potential VC is a associated with an information
production cost Ci drawn from some continuous distribution. Following the
logic of Section 3.1, there is a cutoﬀ CM AX indicating the highest-cost VC
active in equilibrium.
The VC with Ci = CM AX earns zero profit. All those with cost exceeding
CM AX drop out out of the market, while those with cost less than CM AX earnstrictly positive profits. The measure of active VCs therefore generates a supply of venture capital finance S = S(CM AX ) where S > 0.
Equilibrium consists of the triple {πM IN , CM AX , α} satisfying the following
system of three equations.
(DEMAND)(SUPPLY)πM IN [πM IN (1 − α) − CE ] + (1 − πM IN )(V − CE ) − V = 0
CM AX −

(MKT. CLEARING)pπMIN +1
2

Q}

2α
3

w

3
1−πMIN2
1−πMIN

W

]

−K =0

D(πM IN ) − S(CM AX ) = 0

8Although unconditionally πi ∼ U nif [0, 1], so that active entrepreneurs are drawn fromU nif [πMIN , 1], is not the case the demand is linear in πMIN . As more (marginal) entrepreneurs are added to the pool during a hot market, the quantity of funded demanded goes up
less than proportionally. The reason is that a smaller proportion of the added entrepreneurs
receive the signal s = G. Hence, funds demanded are increasing and concave in market
heat, or alternatively, decreasing and convex in πMIN . This issue is developed numericallyin Section 3.3.

17

The demand equation comes from equation (5). The left side of the equation is the profit of the worst entrepreneur active in equilibrium. By definition,
πM IN is the entrepreneurial quality associatied with zero profit. The supply
equation comes from equation (4). That is, CM AX is the signal cost associatedwith zero profit. Finally, markets must clear, i.e., the aggregate supply must
equal the aggregate demand.

Theorem 2 The equilibrium triple {πM IN , CM AX , α} has the following comparative static properties.
a) (Eﬀect of K)∂πM IN>0∂K∂CM AX
<0
∂K

∂α
>0
∂K

(14)

∂πM IN>0∂V∂CM AX
<0
∂V

∂α
<0
∂V

(15)

∂πM IN>0∂CE∂CM AX
<0
∂CE

∂α
<0
∂CE

(16)

b) (Eﬀect of V)b) (Eﬀect of CE )Proof: Follows from the implicit function theorem; see the appendix.
Equation (14) formalizes the intuition laid out in the introduction, whichemphasizes how the double-sided asymmetric information problem depends
upon real investment opportunities. A positive shock to the economy (as indicated by a drop in K) has several implications. Most obviously, venture
capitalists’ required stakes fall because they are being asked to provide lesscapital while terminal payoﬀs are unchanged.
More importantly, as emphasized in Section 2, a key property of this asymmetric information paradigm is that πM IN drops in response to a positive shock18

to investment opportunities. Financing frictions worsen because as the set ofreal opportunities improves, low-quality entrepreneurs enter the market. Analogously on the supply side, CM AX deteriorates in response to this economic
shock.
The model also makes a related observation regarding the rents to highquality information producers. In Section 3.1, it was determined that the
profit to high-quality VCs is zero when they are the only agents active (i.e.,
states of low demand) but is CH − CL > 0 in states of high demand. Thatis, high-quality agents’ profits depend upon the diﬀerence between their own
quality and that of the worst active agent. Analogously here, since the qualityof the worst agent is continuously decreasing in market heat, the profits ofa fixed (active) VC are continuously increasing in market heat. As a result,
total profits to the VC industry are also increasing in market heat.
Equations (15) and (16) have straightforward interpretations. As the relative costs to entrepreneurs of seeking VC finance increase, marginal entrepreneurs are forced out of the market − that is, πM IN grows. Though VCs
do not bear these costs, there is an indirect eﬀect on their required returns.
Specifically, because the quality of pool improves, this enables VCs to demandsmaller stakes.
The final indirect eﬀect is that because demand falls, the equilibrium number of VCs operating must fall. Such a drop would be impossible if α rose,
because in that case VCs would make higher profits even for a fixed level ofasymmetric information. These higher profits would encourage entry, not exit.

3.3

An Example

Fig. 2 displays supply and demand curves for a particular numerical example. The supply and demand curves are governed by the equations on pg. 17.
In this example the parameters are set to {V = .2, K = .2, CE = .1}. It is19further assumed that supply is proportional to CM AX , which is equivalent tothe assumption that information production costs are drawn from a uniform
distribution.
The horizontal axis indicates α, the share of the firm oﬀered to the venture
capitalist. The entrepreneur’s residual claim is 1-α. The vertical axis indicatesthe quantity of funds. More specifically, it reflects the percentage of projects
in the economy that receive funding in equilibrium. (Recall that some negative NPV projects are screened out by the VC whereas others self-select; thevertical axis here reflects the net eﬀect of both types of removal.)
The demand curves in Fig. 2 have a downward slope. This is because
a greater share α of the firm ceded to VCs implies that fewer entrepreneurs
find it profitable to seek funding. Likewise, the supply curves have an upward
slope because when a greater share of the firm is ceded to VCs, venture capital profits are higher (all else equal) and therefore more VCs enter the market.

D’

S’
D

S

Fig. 2: Soli

Fig. 2: Supply and Demand for VC Funds: The vertical axis indicates the proportion offunded projects in the economy. The horizontal axis indicates the share of the firm ceded toventure capitalists. The intersection of the solid lines depicts equilibrium under theassumptions {V=.2, K=.2, CE=.1} while the dotted lines correspond to {V=.1, K=.1, CE=.1}.

20

Next, consider a positive shock to the value of investment opportunities.
The dotted lines show the supply and demand curves when V and K fall tofrom .2 to .1. This drop in V and K is economically equivalent to an increasein the terminal payoﬀs relative to other parameters. However, Theorem 2
indicates (and as will be emphasized here) the eﬀects of V and K are economically distinct. It is therefore pedagogically preferable to treat them separately.
The decrease in V shifts the demand curve up. As entrepreneurs’ outside
options become less valuable, they are more willing to enter the VC market.
The drop in K has no direct eﬀect on demand. Rather, entrepreneurs bear K
only indirectly through the VCs’ required stake.
The decrease in K shifts the supply curve up. This is a direct eﬀect:
for a given α, reducing the required capital contribution would increase VC
profitability. Consequently, more VCs would enter, increasing the willingness
to supply capital.9 By contrast, the decrease in V shifts the demand curve
downward. This is an indirect eﬀect. The adverse selection eﬀect emphasizedin Section 2 implies that the quality of the entrepreneurial pool deteriorates.
This deterioration indirectly reduces the profitability to capital suppliers, andthe resulting exit of marginal VCs causes supply to fall. Over the relevant
range in the graph, the direct eﬀect dominates and leads to higher supply.
In this numerical example, the eﬀect of the demand shock dominates thatof the supply shock, leading to a higher equilibrium venture capital stake α.
This comparative static result is not general, however, as Theorem 2 makes
clear. That is, one can also construct shocks to {V, K} such that the supply
eﬀect dominates the demand eﬀect and hence equilibrium α is lower in hotmarkets.
9

This point also emphasizes why Fig 1 uses the proportion of projects funded on thevertical axis rather than (numeraire-denominated) funds supplied. Otherwise, shocks to K
trivially change the amount of capital supplied and demanded.

21

It is also apparent in Fig 2 that both demand curves are less elastic (flatter)in hot markets. This property is driven by V . To see why this eﬀect occurs,consider the extreme case when V is very low compared to other parametersin the model. In that case, virtually every entrepreneur is active because noother choice is economically viable. Their collective entry decisions are therefore relatively invariant to α. Hence the demand curve is relatively flat in α.
A similar argument motivates why supply elasticity is a function of investment opportunities. In any economic state, increasing α increases VC profits
both directly (they keep a larger share of the firm) and indirectly (because
higher α improves the quality of the entrepreneurial pool). This indirect effect is most important in cold markets, however, when the incentives of all
entrepreneurs to enter the market is weak. In that case, small changes in the
sharing rule cause large changes in the average quality within the pool, andhence in VC profits.

D

S

Fig. 3: Supply and Demand for VC Funds: The vertical axis indicates the proportionof funded projects in the economy. The axis towards the front of the diagram indicatesthe share of the firm ceded to venture capitalists, and the final axis (going front to back)represents the reservation utility of entrepreneurs. The parametric assumptions are K=.2
and CE=.1.

22

Fig. 3 generalizes figure Fig. 2. The axis toward the front of the pictureis α, the share oﬀered to VCs. The vertical axis is again the proportion ofprojects funded. The final axis, moving front to back in the picture, indicates
entrepreneur’s reservation utility V . Taking a slice of the figure along the Vaxis one can see the supply and demand curves of the previous figure. Again
it is clear that both supply and demand curves are more elastic when V ishigh. In this case, few entrepreneurs are active and so small changes rapidly
alter the composition of the pool. Moving “backwards” in the picture toward
lower V (interpreted as a positive shock to investment opportunities) causes anincrease to both the equilibrium amount of capital supplied and to the stakeof VCs.

4

Conclusions

The venture capital market is central to the financing of innovation but issubject to dramatic variation in the level of activity. Understanding the determinants of the underlying supply and demand curves is therefore a financial
economic question of first-order importance.
This paper endogenizes this supply and demand in an environment of twosided information asymmetry. Entrepreneurs have heterogeneous, private information about the quality of their projects. Venture capitalists have hetergeneous ability levels. In eﬀect, these agents generate a supply curve of
information production. Though all agents appear identical, there is equilibrium heterogeneity in abilities of active agents on both supply and demandsides of the market. Thus, there are two distributions of agent quality, bothof which vary continuously in the heat of the market.
Both types of variation have some support in the literature. Regarding thephenomenon of wider pooling during hot markets, Lerner (2002) comments“[F]unds appear to be deployed much less eﬀectively during the23boom period. In particular, all too often these periods find venture capitalists funding firms that are too similar to one another.”Yet even when firms appear similar ex-ante, there is evidence − at leastin the IPO market (Yung, et. al, 2008) − that firms funded during booms
exhibit heightened variability in long-run returns. These findings together
suggest that, while the firms may be diﬃcult to distinguish ex-ante, there isactually significant heterogeneity revealed in the long-run.
The scientific study of returns in the VC market is a relatively young field,
and is somewhat hindered by data availability issues. As Gompers, Lerner,
Kovner and Sharfstein (2005) (hereafter, GLKS) point out that Venture Economics “does not collect valuation information for all the companies that weremerged or acquired and it is possible that these outcomes are not as lucrative
as those where the company exited with a public oﬀering.” Thus, for describing outcomes at the portfolio firm level, researchers have typically employedcoarse measures such as whether a firm was liquidated, merged or went public.
Recent empirical papers circumvent the data problems alluded to by GLKS
by using either proprietary databases (Ljungqvist and Richardson, 2003) orusing fund-level cash flows (Jones and Rhodes-Kropf, 2004) rather than portfolio firm level cash flows. While this latter approach is useful for characterizing
the returns of the asset class, it does not permit analysis of the demand-side
heterogeneity posited by the current model.
Similarly, the model’s prediction of time-varying heterogeneity in the quality of supply side agents has not been subject to formal testing. Nervertheless,it has some parallels in Kaplan and Schoar’s (2005) findings. They conclude
that a large fraction of fund inflows during hot markets go to new entrants,
and that these entrants appear to have poor ex-post performance. Among
possible explanations for these findings, Kaplan and Schoar list a variety ofdisadvantages faced by new entrants, including lack of access to deal flow andbetter bargaining power vis-a-vis entrepreneur. Perhaps their strongest word24

ing, however, is reminiscient of the current analysis: “we think the most likely
explanation for [our] results is a model of underlying heterogeneity in the skillsof GPs.”Hochberg, Ljungqvist and Vissing-Jorgensen (2008) also model an environment of GP heterogeneity. As funds season, LPs acquire a form of inside
information vis-a-vis outside investors. In particular, LPs may be able todistinguish luck from skill. The resulting informational hold-up leads to underadjustment of fees and performance persistence. There is also a possible
eﬃciency gain, however, because LPs are sometimes willing to fund untested
GPs owing to the inherent option value in doing so. Thus, the informational
hold-up does not serve as a friction. Rather, it prevents a market failure.
The above story potentially interacts with the current analysis. Given a
positive shock to investment opportunities, both incumbent GPs and their LPs
earn economic rents on follow-up funds. In fact, the expected positive profits
in hot markets accruing to LPs − who eﬀectively share residual claimancy with
GPs in Hochberg at. al’s story − could subsidize their losses in cold markets.
This eﬀect would tend to smooth out the supply of capital over the market
cycle. The full range of implications (including time-varying incentives of GPs
to signal quality) is left to future research.

25

5References

Berk, J., and R. Green, 2003. Mutual Fund Flows and Performance in Rational Markets, NBER Working Paper.
Denis, D., 2004. Entrepreneurial Finance: an Overview of the Issues and Evidence, Journal of Corporate Finance 10, 301-326.
Fenn, G.. Liang, N. and S. Prowse, 1995. The Economics of Private Equity,
Board of Governors of the Federal Reserve System.
Gompers, P., 1995. Optimal Investment, Monitoring, and the Staging of Venture Capital, Journal of Finance, 50, 1461-1489.
Gompers, P. and J. Lerner, J., 1998. What Drives Venture Capital Fundraising, Brookings Proceedings on Macroeconomic Activity, 149-204.
Gompers, P. and J. Lerner, J., 2000. Money Chasing Deals? The Impact ofFund Inflows on Private Equity Valuations, Journal of Financial Economics
55, 281-325.
Gompers, P., Kovner, A., Lerner, J. and D. Sharfstein, 2005. Venture Capital
Investment Cycles, Working paper.
Hagerty, K. and D. Siegel, 1988. On the Observational Equivalence of Managerial Contracts Under Conditions of Moral Hazard and Self-Selection The
Quarterly Journal of Economics, 103, 425-428.
Hellman, T. and M. Puri, 2002. Venture Capital and the Professionalizationof Start-up Firms: Empirical Evidence, Journal of Finance, 57, 169-197.
Inderst, R. and H. Muller, 2004. The Eﬀect of Capital Market Characteristics
on the Value of Start-up Firms, Journal of Financial Economics 72, 319-356.
26

Kanniainen, V. and C. Keuschnigg, 2003. The optimal portfolio of start-up
firms in venture capital finance, Journal of Corporate Finance, 9, 521534.
Kaplan, S. and A. Schoar, 2005. Private Equity Returns: Persistence andCapital Flows, Journal of Finance 60, 1791-1823.
Kaplan, S. and P. Stromberg, 2000, How Do Venture Capitalists Choose Investments?, Working paper.
Kaplan, S. and P. Stromberg, 2002. Financial Contracting Theory Meets theReal World: An Empirical Analysis of Venture Capital Contracts, Review of
Economic Studies 00, 1-35.
Kaplan, S. and P. Stromberg, 2004. Characteristics, Contracts and Actions:
Evidence from Venture Capital Analyses, Journal of Finance 109, 2173-2205.
Kirsch, Goldfarb and Gera, 2006, Form or Substance? The Role of Business
Plans and Social Networks in Venture Capital Decision Making, UnpublishedWorking Paper
Kothari, P. and J. Warner, 2001. Evaluating Mutual Fund Performance, The
Journal of Finance, 56, 1985-2010.
Lerner, J. and A. Schoar, 200x. The Illiquidity Puzzle: Theory and Evidence
from Private Equity, Journal of Financial Economics xx, xxx-xxx.

27

Lerner, J., 2002. Boom and Bust in the Venture Capital Industry and the
Impact on Innovation, Federal Reserve Bank of Atlanta Economic Review 4,25-39.
Ljungqvist, A. and M. Richardson, 2003. The Investment Behavior of Private
Equity Fund Managers, New York University Working Paper.
MacMillan, I. and P. Narasimha, Characteristics distinguishing funded fromunfunded business plans evaluated by venture capitalists, Strategic Management Journal, 8, 579-585.
Repullo, R. and J. Suarez, 1999. Venture Capital Finance: A Security Design
Approach, Unpublished working paper.
Schmidt, K., 2003. Convertible Securities and Venture Capital Finance, 58,
1139-1166.
Sorensen, K., 2006. How Smart is Smart Money?: An Empirical Two-Sided
Matching Model of Venture Capital, University of Chicago Working Paper.
Yung, C. and G. Colak and W. Wang, 2008. Cycles in the IPO Market, Journal of Financial Economics, 89, 192-208.

28

6

ProofsM IN
Proof of Theorem 1. I derive the comparative static result ∂π∂K
> 0 here.
The others are similar. The two first order conditions are:2
F := α3X3
1 − πMIN
2
1 − πMIN~−K

2
G := πM
IN (1 − α) − πM IN V − C

(17)
(18)

Totally diﬀerentiating this system with respect to K, one obtains∂F∂F ∂πM IN
∂F ∂α
+
+
=0
∂K ∂πM IN ∂K
∂α ∂K

(19)

∂G
∂G ∂πM IN
∂G ∂α
+
+
=0
∂K ∂πM IN ∂K
∂α ∂K

(20)

The above is a system of two equations to be solved for two unknowns,∂αM INand ∂K. The solution for ∂π∂K
is

∂πM IN
∂K

∂G
∂G ∂F
− ∂F
∂πM IN∂α ∂K∂α ∂K= ∂F ∂G∂F∂K− ∂G∂α ∂πMIN∂α ∂πMIN(21)

Reporting only the signs of each of these partial derivatives, and noting that
∂G
= 0,
∂K
X

∂πM IN
sign∂K
Q.E.D.

~

=

−⊕0
⊕
=
=⊕
⊕⊕− ⊕
⊕

29

(22)

M IN
Proof of Theorem 2. I derive the comparative static result ∂π∂K
> 0 here.
The others are similar. Denote H:=0, J:=0, M:=0 as the demand, supply andmarket clearing identities listed on page 16. Totally diﬀerentiating this systemwith respect to K, one obtains∂H ∂πM IN∂H ∂CM AX ∂H ∂α
∂H
+
+
+
=0
∂K ∂πM IN ∂K∂CM AX ∂K
∂α ∂K

(23)

∂J ∂πM IN∂J ∂CM AX ∂J ∂α
∂J
+
+
+
=0
∂K ∂πM IN ∂K∂CM AX ∂K
∂α ∂K

(24)

∂M
∂M ∂πM IN∂M ∂CM AX ∂M ∂α
+
+
+
=0
(25)
∂K
∂πM IN ∂K∂CM AX ∂K∂α ∂KNote that the above is a system of three equations to be solved for three
∂α
M IN
MAX
unknowns ∂π∂K
, ∂C∂Kand ∂K. Solving the system, and using the fact that∂H
four of twelve leading terms are zero (e.g. ∂K= 0 by inspection on H), one
obtains the solution∂πM IN
=
∂K

∂H ∂M
∂J
∂α ∂CM AX ∂K

=
∂M
∂H ∂J
∂J
∂H
∂M ∂H
−
+ ∂C∂J∂CMAX ∂πMIN ∂α∂πM IN ∂α
MAX ∂πM IN ∂α(26)

Reporting only the signs of each of these partial derivatives,X∂πM IN
sign
∂K

~

=



⊕

−

⊕

=

+⊕

(27)

By inspection, both the numerator and denominator are positive. Therefore
the fraction is positive.
Q.E.D.

30