Crowdfunding: An Industrial Organization Perspective

Abstract

The first objective of the paper is to identifiy a number of issues related to crowdfunding that are worth studying from an industrial organization (IO) perspective. To this end, we first propose a definition of crowdfunding; next, on the basis on a previous empirical study, we isolate what we believe are the main features of crowdfunding; finally, we point to a number of strands of the literature that could be used to study the various features of crowdfunding. The second objective of the paper is to propose some preliminary efforts towards the modelization of crowdfunding. In a first model, we associate crowdfunding with pre-ordering and price discrimination, and we study the conditions under which crowdfunding is preferred to traditional forms of external funding. In a second model, we see crowdfunding as a way to make a product better known by the consumers and we give some theoretical underpinning for the empirical finding that non-profit organizations tend to be more successful in using crowdfunding.

Full text

Crowdfunding: An Industrial Organization
Perspective∗
Paul Belleflamme†Thomas Lambert‡Armin Schwienbacher§
June 10, 2010
Abstract
The first objective of the paper is to identifiy a number of issues
related to crowdfunding that are worth studying from an industrial
organization (IO) perspective. To this end, we first propose a definition
of crowdfunding; next, on the basis on a previous empirical study, we
isolate what we believe are the main features of crowdfunding; finally,
we point to a number of strands of the literature that could be used to
study the various features of crowdfunding. The second objective of the
paper is to propose some preliminary efforts towards the modelization
of crowdfunding. In a first model, we associate crowdfunding with
pre-ordering and price discrimination, and we study the conditions
under which crowdfunding is preferred to traditional forms of external
funding. In a second model, we see crowdfunding as a way to make a
product better known by the consumers and we give some theoretical
underpinning for the empirical finding that non-profit organizations
tend to be more successful in using crowdfunding.
JEL classification codes: G32, L11, L13, L15, L21, L31
Keywords: crowdfunding, price discrimination, non-profit
∗This paper has been prepared for the workshop ‘Digital Business Models: Understand-
ing Strategies’, held in Paris on June 25-26, 2010. The paper is VERY PRELIMINARY
AND INCOMPLETE. Please do not quote without prior consent of the authors.
†CORE and Louvain School of Management, Universit´e catholique de Louvain (34 Voie
du Roman Pays, B-1348 Louvain-la-Neuve, Belgium), Paul.Belleflamme@uclouvain.be.
Other affiliation: CESifo.
‡Louvain School of Management, Universit´e catholique de Louvain (1 Place des Doyens,
1348 Louvain-la-Neuve, Belgium), Thomas.Lambert@uclouvain.be.
§Louvain School of Management, Universit´e catholique de Louvain (1 Place des Doyens,
1348 Louvain-la-Neuve, Belgium), Armin.Schwienbacher@uclouvain.be. Other affiliation:
University of Amsterdam Business School.

1 Introduction
In the music industry, a new type of Internet-based record labels have re-
cently been created. Labels, such as SellaBand,MyMajorCompany or Artist-
share, share the following business model: artists can post a number of songs
on a website; visitors to the site can then listen to the music free and may
choose artists they want to invest on (with a minimum pledge); when artists
reach a threshold pledge (e.g., $50.000 on SellaBand ), the company uses
the money to produce and distribute their album; investors are either com-
pensated by receiving a share of the revenues from the album (SellaBand
and MyMajorCompany), or are rewarded by having privileged access to the
creative process or by being credited on the album (ArtistShare). Although
SellaBand (created in 2006) filed for bankruptcy in February 2010, other
labels organized around this business model seem to thrive; for instance,
the French songwriter Gr´egoire reached the Top 5 in France with his single
‘Toi + Moi’ after having been discovered and funded by the public through
MyMajorCompany.
While this model has been primarily used in the entertainment indus-
try so far (especially music and movie), a few initiatives have been under-
taken recently in other industries such as journalism (Spot.Us), beer (Beer-
Bankroll), software (Blender Foundation,Trampoline Systems) and fashion
(Cameesa).1The basic idea is always the same: instead of raising the money
from a very small group of sophisticated investors, entrepreneurs try to ob-
tain it from a large audience, where each individual will provide a very small
amount. As a “crowd” of investors is tapped, the term “crowdfunding” has
been coined to describe this new source of finance
The concept of crowdfunding finds its root in the broader concept of
crowdsourcing, which uses the “crowd” to obtain ideas, feedback and solu-
tions in order to develop corporate activities. In the case of crowdfunding,
the objective is to collect money for investment; this is generally done by us-
ing social networks, in particular through the Internet (Twitter, Facebook,
LinkedIn and different other specialized blogs). The crowd-funders (those
who provide the money) can at times also participate in strategic decisions
or even have voting right.
Obviously, the main objective of crowdfunding is to provide entrepreneurs
1For a list of similar intiatives, visit http://crowdfunding.pbworks.com/ (last consulted
on June 9, 2010).
1

with an alternative way to raise funds. It is indeed well recognized that new
ventures face difficulties in attracting external finance at their very initial
stage, be it through bank loans or equity capital (see, e.g., Cosh et al.,
2005). While business angels and venture capital funds fill gaps for larger
amounts, the smallest amounts are provided by entrepreneurs themselves
and the 3Fs (friends, family and fools). Still, many ventures remain un-
funded, partially because of a lack of sufficient value that can be pledged
to investors, partially because of unsuccessful attempts to find and convince
investors. Crowdfunding may then appear as a useful alternative route.
However, our contention in this paper is that there is more to crowdfund-
ing than just funding. Because appeal is made to consumers and because
Web 2.0 tools are used, crowdfunding may also help firms in testing, pro-
moting and marketing their products, in gaining a better knowledge of their
consumers’ tastes, or in creating new products or services altogether. There-
fore, all the recent entrepreneurial experiences in raising capital through
crowdfunding raise new and interesting questions not only in the area of
corporate finance but also in the area of industrial organization.
Our goal in this paper is twofold. First, we want to identify a number of
issues related to crowdfunding that are worth studying from an industrial
organization perspective. To this end, we proceed in three steps (Section 2):
we start by defining more precisely what we hear by crowdfunding; next,
on the basis on a previous empirical study, we isolate what we believe are
the main features of crowdfunding; finally, we point to a number of strands
of the literature (in industrial organization or, more generally, in microe-
conomics) that we could use to study the various features of crowdfunding.
We move then to our second objective, which is to propose some preliminary
efforts towards the modelization of crowdfunding. We develop two models
that address different features of crowdfunding. In Section 3, we associate
crowdfunding with pre-ordering and price discrimination, and we study the
conditions under which crowdfunding is preferred to traditional forms of
external funding. In Section 4, we see crowdfunding as a way to make a
product better known by the consumers and we give some theoretical un-
derpinning for the empirical finding that non-profit organizations tend to be
more successful in using crowdfunding. Our main results are summarized in
Propositions 1 and 2. We offer some concluding remarks and directions for
future research in Section 5.
2

2 A road map for studying crowdfunding
Our objective in this section is to answer the following three questions:
(i) What is exactly crowdfunding? (ii) What are the particular aspects of
crowdfunding that make it interesting to study from an industrial organiza-
tion perspective? (iii) Which strands of the literature could we use to study
the issues raised by the practice of crowdfunding?
2.1 A definition of crowdfunding
The concept of crowdfunding2can be seen as part of the broader concept
of crowdsourcing, which uses the “crowd” to obtain ideas, feedback and
solutions in order to develop corporate activities. The term “crowdsourcing”
has been first used by Jeff Howe and Mark Robinson in the June 2006 issue
of Wired Magazine, an American magazine for high technology.3Kleemann
et al. (2008) propose the following definition:
Definition 1 “Crowdsourcing takes place when a profit oriented firm out-
sources specific tasks essential for the making or sale of its product to the
general public (the crowd) in the form of an open call over the internet, with
the intention of animating individuals to make a [voluntary] contribution
to the firm’s production process for free or for significantly less than that
contribution is worth to the firm.”
Although this definition of crowdsourcing is a useful starting point, sev-
eral caveats and clarifications need to be made in order to transpose it to
crowdfunding. Hereafter, we offer a discussion on the application of this
definition to crowdfunding; we ultimately provide key elements in under-
standing why crowdfunding is embedded in the definition of crowdsourcing.
Raising funds by tapping a general public (or the crowd) is the most
important element of crowdfunding. This means that consumers can vol-
unteer to provide input to the development of the product, in this case in
form of financial help.4From this perspective, crowdfunding is a subset of
2We follow here closely Section 2 of Lambert and Schwienbacher (2010).
3For a non technical introduction of crowdsourcing, see Howe (2008).
4We note that an important motivation for relying on crowdsourcing is that it may
contribute in reducing production costs (Kleemann et al., 2008). For instance, the phar-
maceutical company Innocentive has organized its crowdsourcing practice in form of a
tournament, where the provider of the best solution was rewarded with a prize (Albors et
al., 2008).
3

crowdsourcing, since the latter encompasses also financial help.
Several platforms have emerged recently, such as Fundable,Kickstarter,
Kiva,Sandawe, and SellaBand. These intermediate between entrepreneurs
and potential crowd-funders. Therefore, a distinction can be made between
direct and indirect fundraising because at times entrepreneurs make use
of such crowdfunding platforms instead of seeking direct contact with the
crowd. These platforms at times share some similarities with online lending
markets (Everett, 2008; Freedman and Jin, 2010); while the latter more
prominently target social entrepreneurship, crowdfunding platforms have a
broader scope of entrepreneurial initiatives.
As pointed out by Brabham (2008) and Kleemann et al. (2008), among
others, the development of Web 2.0 is a critical ingredient that has facil-
itated the access to the “crowd”. Roughly speaking, Web 2.0 is a Web-
as-participation-platform that facilitates interaction between users.5This
structure is crucial for entrepreneurs to be able to easily reach networks of
investors or consumers. Through a case study, Larralde and Schwienbacher
(2010) highlight the importance of efficient communication and networking.
They argue that this is an inherent component of any crowdfunding process.
The argument is also in line with the study of Lee et al. (2008), who iden-
tify three properties of Web 2.0 that enhances the ability of entrepreneurs:
openness, collaboration, and participation. In contrast to the Internet that
existed before the bursting of the dot-com bubble, the more recent Web 2.0
technology allows user to provide content (beyond simply reading existing
one), interact with each other and thereby create value for the company
(Lee et al., 2008).
While the use of the Internet to make an “open call” may be very efficient
for crowdsourcing in general, it can become more problematic for crowd-
funding, especially if it involves the offering of equity to the crowd. Indeed,
making a general solicitation for equity offering is limited to publicly listed
equity. Companies cannot do a general solicitation, unless they received
prior authorization from their national securities regulator. In many coun-
tries, there is also a limit as to how many private investors a company can
have. For instance, MediaNoMad could not have more than 100 sharehold-
ers, as imposed by French law (Larralde and Schwienbacher, 2010). While
the crowdfunding process of this company was made in the public domain,
5Refer to O’Reilly (2007) for an in-depth understanding of Web 2.0.
4

shareholder contracts for the purchase of shares were however only signed
with 100 individuals, as a way to overcome these legal problems. This cre-
ates important legal limitations to crowdfunding initiatives, given that the
input of the crowd is capital and not an idea or time. In the case of Tram-
poline Systems, the company was required to prepare a detailed mechanism
in order to avoid any problems with the UK financial markets regulator.
Therefore, most initiatives do not offer shares but provide other types of
rewards such as a product or membership.
Crowd-funders make voluntary financial contributions with or without
the expectation of receiving compensation. This can take various forms, in-
cluding cash, bonds, stocks, profit sharing and pre-ordering of products. At
times, this can be accompanied by voting rights or other active involvement
in the crowdfunding initiative. In practice, entrepreneurs relying on crowd-
funding may combine it with other forms of crowdsourcing. This is the case
for instance of MediaNoMad that also obtained from the crowd time and
expertise (Larralde and Schwienbacher, 2010).
Crowdsourcing differs in many ways from open-source practices (Brab-
ham, 2008); some of these differences can be transposed to crowdfunding.
An important distinction is that in the of open-source case, the idea belongs
to the community who can then exploit it on an individual basis (there is no
restriction on who can use it); in the case of crowdsourcing, the generated
idea ultimately belongs to the company who will be the only one to exploit
it. This distinction with open-source practices becomes even more obvious
when related to crowdfunding, since capital cannot be shared. Unlike an
idea or a software code, capital is not a public good in the economic sense
that assumes non-rivalness and non-excludability. Under these conditions,
a public good is a good that can be used by many consumers at the same
time, without duplicating costs.
Based on this discussion and in the spirit of Kleemann et al. (2008), we
offer the following, refined definition:
Definition 2 Crowdfunding involves an open call, essentially through the
Internet, for the provision of financial resources either in form of donation
or in exchange for some form of reward and/or voting rights.
5

2.2 Key features of crowdfunding
We summarize here the main findings of the recent empirical study of Lam-
bert and Schwienbacher (2010). This study is helpful in providing a better
understanding of how crowdfunding initiatives are structured and what mo-
tivates them.
Data. The authors hand-collected data from various sources on all possible
crowdfunding initiatives that they could identify on the Internet. Data
collection took place end of 2009 and early 2010. Since there is no database
available or even listing, the authors relied on the Internet to construct their
sample.6The focus was on crowdfunded ventures and projects, which largely
excludes all initiatives made by artists. In total, they identified 88 cases and
were able to collect sufficient (but still partially incomplete) information on
51 of them. A questionnaire was then used to obtain further information.
Out of the 69 entrepreneurs that could be contacted, 21 returned complete
(or partial) answers (a response rate of about 30%).
Summary statistics. Here are the main facts that can be extracted from
the collected information.
•Demographics: 35.3% of the initiatives are from the United States and
49% from Europe.
•Type of organizational form: out of the 50 crowdfunding initiatives for
which the information was available, 23 are connected with a specific
project only, 18 stem from for-profit companies, 8 stem from non-profit
associations, and 1 is the work of an individual.
•Crowdfunding is a recent phenomenon: over 80% of the respondents
have used crowdfunding for projects or for their own company only
very recently (i.e., since 2007).
•Motivation: raising money was a strong motivation for all respondents,
getting public attention was relevant (or highly relevant) for over 85%,
and obtaining feedback on the product/service offered was relevant (or
highly relevant) for about 60% of the respondents.
6One advantage is that firms and individuals using crowdfunding as a way to collect
funds typically use the Internet to do so, as well as social networks (such as blogs, Facebook
and Twitter). This clearly facilitated the construction of the sample.
6

•Source of funding: many of the respondents combine crowdfunding
with other sources of finance, notably with own money, friends & fam-
ily money, business angel and government subsidy.
•Type of investment: three forms of investment are observed in the sam-
ple, namely donation, active investment, and passive investment; pure
donation constitutes 22% of crowdfunding; the rest represents invest-
ments (i.e., the crowd-funder expects to receive a return or reward),
ventilated between active investment (32%) and passive investment
(60%).
•Return/reward to investors: 76.5% of the respondents offer a reward
to their crowd-funders, mostly in form of a right to receive the product
(2/3 of the cases) or shares that may yield dividends in the future (1/3
of the cases); direct cash payment is expected in 22.2% of the cases
where a reward/return is promised; in two thirds of the cases, also
other forms of reward are proposed (e.g., getting credit on an album
or a film, giving money to a charity of the person’s choice, etc.).
•Means of communication: almost all respondents used very extensively
the Internet as a mode of communication with the “crowd”, evidenc-
ing the reliance on Web 2.0 for modern crowdfunding; the most widely
used methods of Internet is an own website, community blogs, Face-
book, personal emails and Twitter; other methods are used by less
than 50% of the respondents; however, only 20% of the respondents
(according to the survey) used a crowdfunding platform such as Couch
Tycoon.
Interesting correlations between variables
•Crowdfunding initiatives taking place as a company tend to involve
more often active investments and fewer passive investments.
•Companies are more likely to enable individuals to provide input or
vote on the project; conversely, non-profit organizations offer active
involvements of investors less often.
•A negative correlation exists between whether a reward is offered and
whether it is a passive investment, which suggests that rewards and
7

control are used as substitutable incentives (investors may require
more rewards if they cannot be involved in the happening of the ini-
tiative).
•Through a multivariate analysis, the authors examine what drives the
chances of success of crowdfunding initiatives. A striking result is that
non-profit associations are significantly more likely to achieve their
target level of capital in comparison with other organizational forms
(corporation, individual or in connection with a single project). This
result appears robust to different econometric specifications.
2.2.1 Key features from an industrial organization perspective
We propose here our own reading of the previous data, with the aim to
identify a number of issues that seem interesting to study from an industrial
organization (IO) perspective.
1. Crowdfunding is not just about funding; it is also about information.
Although raising money is reported to be a strong motivation for orga-
nizations to use crowdfunding, it is also observed that crowdfunding is
rarely used as the only source of funds. Moreover, other motivations for
resorting to crowdfunding are seen as equally important; in particular,
getting public attention and obtaining feedback on the product/service
offered. Crowdfunding seems thus to have implications that go beyond
the financial sphere of an organization: it also affects the flow of in-
formation between the organization and its customers. Crowdfunding
can be used as a promotion device, as a means to support mass cus-
tomization or user-based innovation, or as a way for the producer to
gain a better knowledge of the preferences of its consumer. All these
topics have already been studied in IO but never (to the best of our
knowledge) in combination with the funding issue.
2. Crowdfunding is a peculiar form of funding, with customers as in-
vestors. The data reveal that a large share of crowdfunding initiatives
are based on passive investments, i.e., investments with a promise of
compensation but no direct involvement in the decision-making pro-
cess, or provision of time or expertise for the initiative. Moreover, in
most of the cases, the compensation is to receive a product or service
8

from the financed activity. Hence, crowdfunding blurs the usual divide
between the roles of investors and of customers: some investors are
customers and some customers are investors. To account for this pos-
sible double role, traditional models of industrial organization should
be extended in two directions: first, by enlarging the set of actions for
consumers (who can decide to become investors of the firm); second, by
redefining the objective function of the firm as some investors, namely
these customers/investors, may have different motivations than profit-
maximization.
3. Non-profit organizations tend to be more successful in using crowd-
funding. This finding suggests that the choice of a funding method
(crowdfunding vs. other sources of funding) has to be considered in
combination with the choice of an organizational form (for-profit vs.
non-profit). The latter choice is not commonly studied in IO where
profit-maximization is most often implicitly assumed to be the objec-
tive of an organization. One may argue that non-profit organizations
stand outside the scope of IO, and are more relevant to public eco-
nomics. This may be true for charities, but this is not with charities
that we are dealing here: all crowdfunding initiatives in the sample are
commercial ventures; it is also observed that only a limited fraction of
initiatives is based on donations.
In Sections 3 and 4, we present preliminary modeling efforts in the di-
rections that we have just outlined. In particular, the model of Section 3
is an attempt to address our first point, namely that crowdfunding mixes
funding and information motivations; in this model, the firm uses crowd-
funding to induce consumers to reveal their private information, i.e., their
willingness to pay for the product. In the model of Section 4, we address the
third point by letting an entrepreneur choose not only her funding method
(crowdfunding or external funding) but also her organizational form (for-
profit or non-profit).
Before developing these models, we close this section by describing the
literature that could be used to study the above three sets of issues.
9

2.3 Related literature
As crowdfunding is a recent phenomenon, it is not a surprise that there
is virtually no literature at all on the topic. The little that exists con-
cerns the broader concept of crowdsourcing and can hardly be applied to
the specific case of crowdfunding. One of the very few academic articles on
crowdfunding is from Kappel (2009) that distinguishes ex post facto crowd-
funding (e.g., when a product is offered after financing is provided) from ex
ante crowdfunding (e.g., financial support for lobbying or political activi-
ties). Wojciechowski (2009) discusses donations in connection with projects
funded through crowdfunding. The author argues that social networks can
become a worthwhile model of money collection for many charity organi-
zations and NGOs. However, these two papers are of limited use for our
purpose as they both lie outside the field of industrial organization.
We have thus to look more broadly at the literature (in IO and elsewhere)
to find insights that could be used to model the specific features of crowd-
funding. We propose here a number of avenues. (TO BE COMPLETED)
2.3.1 For-profit vs. non-profit
To analyze the choice of organizational form, the so-called ‘contract failure
literature’ may provide useful insights. This literature is based on the view
that limiting monetary incentives of owners attracts more easily donations,
since it signals that the owners put a significant weight on the outcome and
less on monetary gains. For instance, Glaeser and Shleifer (2001) propose
a model where profit-driven organizations may be prone to focus too much
on profits at the expense of other dimensions such as quality of the product
or service provided. This in turn may not be desired from donors and
other sources aimed at fostering specific initiatives. Relatedly, Ghatak and
Mueller (2009) develop a theoretical framework of labor donation theory to
investigate under which conditions non-for-profit organizations can provide
a better alternative to motivated workers than other forms of organizations.
2.3.2 Choice of funding method
When crowdfunding is concerned purely from a financial perspective, it may
be useful to look at this branch of research that deals with bootstrap fi-
nance. Bootstrap finance consists of using alternative financing ways than
10

the traditional sources of external finance (e.g., bank loan, angel capital and
venture capital). Several studies provide evidence of the different forms of
alternatives used by bootstrapping entrepreneurs (see, Bhid´e (1992), Win-
borg and Landstrom (2001) and Ebben and Johnson (2006), just to cite a
few). Bhid´e (1992) shows that even among the Inc. 500 companies in the
US, most of them started by bootstrapping the company. Further financing
methods for startups companies are analyzed, for instance, by Cosh et al.
(2005), who examine a broader range of financing alternatives. Theoretical
considerations about the optimal timing between using internal and external
resources is provided by Schwienbacher (2007).
2.3.3 Customers as investors
When crowdfunding follows a threshold pledge approach (whereby all pledges
are voided unless a minimal amount is reached before some deadline), we
can see initial investors as privately contributing to a public good; through
their contribution, they indeed increase the probability that the good or
service will be put on the market. Useful insights can certainly be found in
the extensive literature in microeconomics that studies the private provision
of public goods (quote references). However, in contrast with what is usually
assumed in this literature, the good that is produced once the threshold is
reached is private in nature (there is no collective consumption).
A related strand of literature argues that individuals may provide public
goods due to social reputation, which induces pro-social behavior (B´enabou
and Tirole, 2006). Moreover, experimental economics studies indicate that
individuals become discouraged when faced with fines in case of underper-
formance or when treated unfair (Falk and Kosfeld, 2006), indicating that
monetary incentives may at times deter individuals to undertake initiatives
and behave altruistically.
3 Crowdfunding, pre-sale and menu pricing
In this section, we focus on crowdfunding experiences where consumers are
invited to pre-order the product. For the firm to be able to launch produc-
tion, the amount collected through pre-ordering must cover the fixed cost
of production. The firm prefers therefore that the consumers who pre-order
are those with a high willingness to pay for the product. However, a firm is
11

generally unable to identify these consumers. The firm must then use some
self-selecting device so as to induce high-paying consumers to reveal them-
selves. The sort of ‘community experience’ that web-based crowdfunding
offers may be a means by which the firm enhances the perceived quality
of the product for the consumers who agree to pre-order it. In this sense,
crowdfunding appears as a form of menu pricing (i.e., of second-degree price
discrimination). The trade-off we explore in this section is thus the follow-
ing: with respect to external funding, crowdfunding has the disadvantage
of delaying profits by one period and the advantage of offering an enhanced
experience to some consumers and, thereby, of allowing the firm to prac-
tice second-degree price discrimination and extract a larger share of the
consumer surplus.
Intuitively, we expect crowdfunding to become more attractive as the
discount factor increases (meaning that delaying profits becomes less costly)
and as the initial capital requirement decreases (so that pre-sales can cover
them). Our main result (see Proposition 1) gives a precise structure to this
intuition.
3.1 The model
Suppose a unit mass of consumers identified by θ, with θuniformly dis-
tributed on [0,1]. The parameter θdenotes a consumer’s taste for increase
in product’s quality. Consumers have unit demand (they buy one or zero
unit of the product). All consumers have a reservation utility rfor the
product; any increase from the basic quality is valued in proportion to the
taste parameter θ. Normalizing basic quality to zero, we have that if con-
sumer θbuys one unit of product of increased quality ssold at price p, her
net utility is r+θs −p.7. To ensure interior solutions at the pricing stage,
we assume:
Assumption 1. r < s < 2r.
The product is marketed by a monopolist. In this simple version of
the model, we consider the quality of the product, s, as exogenous.8For
7This problem was initially examined by Mussa and Rosen (1978). We use here the
results of the extended analysis of Bhargava and Choudary (2001).
8Naturally, we plan in future work to endogenize the choice of quality. In the spirit of
Glaeser and Schleifer (2001), we plan to contrast the quality choice of a for-profit and a
non-profit firm (as we do in Section 4).
12

simplicity, we set to zero the marginal cost of production. There is, however,
a fixed cost of production K > 0. The timing of the game is as follows. In
period zero, the firm chooses its funding mechanism—external funding or
crowdfunding—with the following implications.
•If the firm chooses external funding, then, in period 1, it sets a price p
for its product and incurs the fixed cost K; consumers decides to buy
or not and the game stops.
•On the other hand, if the firm chooses crowdfunding, then the game has
two more periods. In period 1, the firm sets p1, the price for consumers
who pre-order the product; the total revenue collected through pre-
orders is meant to cover the fixed cost of production. In period 2,
the firm sets two prices: pc, the price to be paid by those consumers
who have contributed to the financing of the firm, and pn, the price
to be paid by those consumers who have not. As for consumers, they
choose in period 1 whether to pre-order or not; in period 2, they decide
whether to purchase the product or not (as long as the product has
been put on the market, i.e., if total contributions in period 1 are at
least as large as K). It is assumed that contributors enjoy an increase in
the product quality equal to σ > 0; that is, a consumer who pre-order
the product perceives the quality of the product to be equal to s+σ;
this enhanced quality may come from different experiences resulting
from crowdfunding (early experience with the product, customization
of the product, sense of belonging to a group of ‘special consumers’).
We now consider the choice of prices under the two funding mechanisms.
We then compare optimal profits in the two cases and address the choice of
funding mechanism.
3.2 External funding
The case of external funding is straightforward. In period 1, the firm sets
a uniform price p. All consumers perceive that the product has quality s.
Hence, the indifferent consumer is such that r+θs−p≥0, or θ≥(p−r)/s ≡
ˆ
θ. As we assume a unit mass of consumers uniformly distributed on the unit
interval, we have that the quantity demanded is equal to q(p)=1−ˆ
θ= 1 −
(p−r)/s. From the first-order condition for profit-maximization, we easily
13

find the optimal price is p∗= (r+s)/2. It follows that ˆ
θ∗= (s−r)/2s,
which is positive according to Assumption 1. We can then compute the
optimal gross profit as p∗1−ˆ
θ∗= (r+s)2/(4s). The net profit under
external funding is thus equal to
πext =((r+s)2
4s−Kfor K < (r+s)2
4s
0 otherwise. . (1)
3.3 Crowdfunding
The crowdfunding case is more complicated to analyze for two reasons. First,
the firm tries to achieve a form of second-degree price discrimination; profit
is thus maximized under a set of incentive compatibility and participation
constraints. Second, in period 1 consumers who contemplate pre-ordering the
product must form expectations regarding the probability that the product
will indeed be put on the market in period 2. Consumers know that the
product will be produced only if pre-sales cover the fixed cost. They there-
fore anticipate that the larger the number of consumers who pre-order the
product, the more likely it is that the product will be produced.
3.3.1 Consumer choices
To model this, suppose that each consumer expects that a mass neof con-
sumers will choose to pre-order and pay the price p1set by the firm in
period 1.9We adopt the fulfilled-expectations approach: consumers base
their decision on their expectation the mass of contributors, and attention
is restricted on equilibria in which these expectations turn out to be cor-
rect (i.e., are rational; see Katz and Shapiro, 1985). Two cases have to be
distinguished. First, if ne= 0, then it is optimal for each consumer not to
contribute (because each consumer is infinitesimal and thus cannot on her
own make sure that the product will be put on the market; on the other
hand, even if the early contribution will be reimbursed, this will take some
time and there will thus be some loss for the consumer). As the initial ex-
pectation is realized, we have a fulfilled expectations equilibrium. Naturally,
crowdfunding is doomed to failure under such equilibrium. As crowdfunding
9This setting is clearly a simplification. In many crowdfunding experiences, consumers
(or more generally, donors) are invited to choose how much they want to contribute. We
ambition to relax this simplifying asumption in future work.
14

experience of this sort exist in reality, it seems natural to assume that firms
can find some ways to coordinate consumers so that this ‘bad’ equilibrium
is not selected.
The second case is the case of interest. For any ne>0, the firm can
set p1such as p1ne≥K. As there is no need to gather more capital then
needed, we have p1=K/ne. So, if consumer expect of positive mass of
contributors, they can be sure that the good will be produced. They also
realize that the lower their expectation, the larger the value of p1, i.e., the
contribution that will be asked by the firm.
To decide whether to pre-order or not, consumer θcompares her expected
utility in the two options (knowing that the product will be put on the
market anyway). If she contributes, she pays p1today and gets tomorrow a
product of enhanced quality (s+σ) that she will pay at price pc. Letting δ
denote the discount factor, we first make the following assumption:
Assumption 2. δσ < s.
According to Assumption 2, the discounted value of the increase in perceived
quality is lower than the original quality of the product.10 We can express
the expected utility when the consumer pre-orders as
Ue
c=−p1+δ(r+θ(s+σ)−pc) = −K
ne+δ(r+θ(s+σ)−pc).
If the consumer decides not to pre-order, she does not pay anything to-
day and she gets tomorrow a product of quality sat price pn. Hence, her
expected utility is
Ue
n=δ(r+θs −pn).
So, for a consumer to contribute, we must have
Ue
c≥Ue
n⇔δ(θσ +pn−pc)≥K
ne
⇔θ≥K
δσne−pn−pc
σ≡¯
θ(ne).
All consumers with a value of θlarger than ¯
θ(ne) prefer to pre-order. We ob-
serve thus that the mass of contributors increases as (i) the expected number
of contributors (ne) increases, (ii) the capital requirement (K) decreases, (iii)
the enhancement in quality (σ) resulting from pre-ordering increases, (iv)
10Under this assumption (which seems rather realistic), external funding makes produc-
tion profitable for a larger range of values of Kthan crowdfunding.
15

the difference between the price for non-contributors and for contributors
(pn−pc) increases. For the sake of the exposition, let us write ∆ ≡pn−pc.
For a given expected mass of contributors ne, the actual mass of contrib-
utors is thus equal to n= 1 −¯
θ(ne). We require fulfilled expectations at
equilibrium: n=ne. We must thus solve
n= 1 −K
δσn +∆
σ⇔σδn2−δ(σ+ ∆) n+K= 0.
The latter polynomial has two real roots as long as z≡δ2(σ+ ∆)2−4σδK >
0, which is equivalent to
∆>2rσK
δ−σ. (2)
Note that the RHS of the previous inequality is positive if K≥δσ/4 and
negative otherwise. Suppose for now that the latter condition is satisfied.
We will have to check below whether it is indeed the case. Then, the two
roots are
n=1
2σδ δ(σ+ ∆) ±qδ2(σ+ ∆)2−4σδK.
Intuitively, the actual mass of contributors should increases with (σ+ ∆),
which drives us to select the large root, i.e.
n=1
2σδ δ(σ+ ∆) + qδ2(σ+ ∆)2−4σδK.
3.3.2 Optimal prices
Suppose for now that n < 1. We have then that nconsumers pre-order
the product at price p1and buy it in period 2 at price pc. As for the
other consumers, they buy the product as long as r+θs −pn≥0, or
θ≥(pn−r)/s ≡ˆ
θ. As long as 0 <(pn−r)/s < 1−n, the firm’s profit
can be written as
π=p1n−K+δpcn+δpn1−n−pn−r
s
=δpn1−pn−r
s−δ(pn−pc)n.
Recalling that ∆ stands for the price difference pn−pc, we can express the
firm’s profit as
π=δpn1−pn−r
s−δ∆1
2σδ δ(σ+ ∆) + qδ2(σ+ ∆)2−4σδK.
16

It is easily found that the first-order condition with respect to pnyields
the optimal value p∗
n= (r+s)/2, which implies that ˆ
θ= (pn−r)/s =
(s−r)/2s.
The derivative of profit with respect to ∆ is
dπ
d∆=−1
2σδ(σ+ ∆) + qδ2(σ+ ∆)2−4σδK
+∆ 
δ+δ2(σ+ ∆)
qδ2(σ+ ∆)2−4σδK 

(3)
Recalling condition (2), we have to distinguish between two cases.
Case 1. K≥δσ/4.In this case, ∆ ≥0 under condition (2). Then, expres-
sion (3) is clearly negative, meaning that the optimal choice is the lowest
admissible value of ∆:
∆=2rσK
δ−σ.
As pn= (r+s)/2 and pc=pn−∆, we have
pc=r+s
2−2rσK
δ+σand π=δ(r+s)2
4s+δrσK
δ−2K.
Note that we still need to ensure that (pn−r)/s < 1−n, which is equivalent
to
s−r
2s<1−1
σrσK
δ⇔K < δσ (r+s)2
4s2.
If the latter condition is satisfied, it can be checked that a sufficient condition
for the equilibrium profit to be positive is σ < 2s. Otherwise, for larger
values of K, self-selection cannot be achieved and crowdfunding fails.
Case 2. K < δσ/4.Here, negative values of ∆ are compatible with
condition (2). To solve for dπ/d∆ = 0, we pose Z=δ2(σ+ ∆)2−4σδK
and we rewrite the first-order condition as:
δ(σ+ ∆) + √Z+ ∆ δ+δ2(σ+ ∆)
√Z= 0.
Developing, we find that the latter expression is equivalent to
√Z=4σδK −δ2(σ+ ∆) (σ+ 2∆)
δ(σ+ 2∆) .(4)
17

As long as the RHS is positive, we can take the square of the two sides of
the equality, replace Zby its value and solve for ∆ to get:
∆∗=4K−δσ
2δ.
Note that K < δσ/4 implies that ∆∗<0, i.e. that p∗
c> p∗
n: contributors
pay more than non-contributors in period 2.
We still need to check whether condition (2) is satisfied:
4K−δσ
2δ>2rσK
δ−σ⇔4K−δσ
2δ+σ2
>4σK
δ⇔(4K−σδ)2
4δ2>0,
which is indeed true. We also need to check that the RHS of expression (4),
as we assumed it. We compute
4σδK −δ2(σ+ ∆∗) (σ+ 2∆∗)
δ(σ+ 2∆∗)=−1
2(4K−σδ) = −δ∆∗
which is positive as we have shown above that ∆∗<0.
To proceed, note that
δ2(σ+ ∆∗)2−4σδK =(4K−δσ)2
4.
As K < δσ/4,
qδ2(σ+ ∆∗)2−4σδK =−1
2(4K−σδ) = −δ∆∗.
It follows that
n∗=1
2σδ (δ(σ+ ∆∗)−δ∆∗) = 1
2
Recall that we need
p∗
n−r
s<1−n⇔s−r
s<1
2⇔s < 2r,
which is guaranteed by Assumption 1.
We can now compute optimal profit:
π=δ(r+s)2
4s−δ∆∗1
2σδ (δ(σ+ ∆∗)−δ∆∗)
=δ(r+s)2
4s+δ
4−K.
What do consumers pay in this case? It is easily checked that contrib-
utors pay p1+δpc=δ
2(r+s+σ). Note that this is exactly the price that
18

the firm would set if it was only selling in period 1 a product of quality
(s+σ) to be delivered in period 2. Indeed, the indifferent consumer would
be identified by θ0such that −p+δ(r+θ0(s+σ)) = 0, which is equivalent
to θ0=1
s+σ1
δp−r. The firm maximizes π=δ(p(1 −θ0)). It is easy to
check that the optimal price is p=1
2δ(r+s+σ). It can also be checked
that the optimal profit is just equal to what the firm would achieve by set-
ting p1for contributors in period 1 and a price p2for non-contributors in
period 2 (contributors paying nothing in period 2).
Summary. Profit in the crowdfunding case is given by
πcrowd =






δ(r+s)2
4s+δ
4−Kfor K < δσ
4,
δ(r+s)2
4s+δqσK
δ−2Kfor δσ
4≤K < δσ (r+s)2
4s2,
0 for K≥δσ(r+s)2
4s2.
(5)
3.4 Choice of funding method
The trade-off for the firm between the two methods is the following: with
respect to external funding, crowdfunding has the disadvantage of delaying
profits by one period and the advantage of offering an enhanced experience to
some consumers and, thereby, of allowing the firm to practice second-degree
price discrimination and extract a larger share of the consumer surplus.
Comparing expressions (1) and (5), we can distinguish between four cases.
1. For very large values of the fixed cost, i.e., for K≥(r+s)2/(4s),
neither external funding nor crowdfunding allows the firm to enter the
market in a profitable way.
2. For large values of the fixed cost, i.e., for δσ (r+s)2/4s2≤K <
(r+s)2/(4s), only external funding allows the firm to enter profitably.
3. For intermediate values of the fixed cost, , i.e., for δσ/4≤K <
δσ (r+s)2/4s2, crowdfunding is preferred to external funding as
long as
πcrowd −πext =δrσK
δ−K−(1 −δ)(r+s)2
4s>0.
We observe that the latter expression increases with δand decreases
with Kfor K≥δσ/4. We expect thus crowdfunding to be preferred
19

for large enough δand for low enough K. More precisely, the condition
is equivalent to
−16s2K2+ 8s2σδs −(1 −δ) (r+s)2K−(1 −δ)2(r+s)4>0.
If δ < (r+s)2/σs + (r+s)2, then the latter polynomial admits
no real root and is always negative, meaning that external funding
is preferred. Otherwise, the polynomial admits two positive roots; to
be positive, Kmust be lie between the two roots. It can be shown
that the threshold δσ/4 lies between the two roots δσ/4. Hence, the
condition for crowdfunding to be preferred can be written as
K <
2σδs −(1 −δ) (r+s)2+ 2rsσδ sσδ −(1 −δ) (r+s)2
4s≡ˆ
K,
with ˆ
Kbeing larger than δσ (r+s)2/4s2for δlarge enough.11
4. For small values of the fixed cost, , i.e., for K < δσ/4, crowdfunding
is preferred to external funding as long as
πcrowd −πext =δ
4−(1 −δ)(r+s)2
4s>0⇔δ > (r+s)2
s+ (r+s)2≡¯
δ,
i.e. for a sufficiently large discount factor.
We collecting these results in the following proposition.
Proposition 1 In situations where a firm can use crowdfunding and pre-
sales to induce self-selection of high paying consumers, crowdfunding is pre-
ferred over external funding if the discount factor (δ) is large enough and
the fixed cost of production (K) is not too large. In particular, crowdfunding
is chosen for the following configurations of parameters:
(1) K < δσ
4and δ > (r+s)2
s+(r+s)2,
(2) δσ
4≤K < min nˆ
K, δσ(r+s)2
4s2oand δ > (r+s)2
σs+(r+s)2.
11For instance, if δ= 1, then ˆ
K=σ, which is larger than σ(r+s)2/`4s2´.
20

4 Crowdfunding, product information and non-
profit status
In the previous section, we considered crowdfunding as a mechanism through
which a firm is able to gather information about the willingness to pay of
its consumers. In this section, we continue to associate crowdfunding with
a flow of information but we reverse the direction of the flow: here, the firm
uses crowdfunding to increase consumer awareness and to disseminate infor-
mation about the product it plan to market. In other words, the firm is no
longer getting information from but giving information to the consumers.
Moreover, we try to provide some theoretical underpinning for the empirical
finding that crowdfunding initiatives that are structured as non-profit orga-
nizations tend to be significantly more successful than other organizational
forms, even after controlling for various project characteristics (Lambert and
Schwienbacher, 2010).
We study a model of horizontal differentiation between a firm with mar-
ket power and a competitive fringe. Before setting the quality and the price
of its product, the firm has first to choose its status (for-profit or non-profit)
and its funding method (external funding or crowdfunding). The main im-
plications of these two choices are as follows: (i) compared to the for-profit
status, the non-profit status is a commitment device to produce higher qual-
ity; (ii) compared to external funding, crowdfunding reveals to the consumer
their preference about the horizontal characteristic of the product. Com-
bining these two features, we establish (see Proposition 2) that non-profit
organizations are more likely to prefer crowdfunding over external funding
than for-profit organizations.
4.1 The model
Suppose that two types of products (indexed by 1 and 2) are located at the
extreme locations of the [0,1] interval. Letting lidenote the ‘location’ of
product i, we thus assume that li∈ {0,1}, i = 1,2. Consumer locations x
are uniformly distributed on the unit interval. Consumers incur a disutility
from travelling to the location of the product that is linear in distance. They
have mass 1. A consumer’s indirect utility is written as ri−τ|li−x| −piif
the consumer buys one unit of product i, where τmeasures how easily one
unit of a product of type 1 can be substituted by one unit of a product of
21

type 2. Additional units of a product do not increase a consumer’s utility.
Furthermore, a consumer is interested in exactly one of the products. The
willingness to pay ridiffers across product.
The product of type 2, located at 1, is in competitive supply (i.e., it is
sold at marginal costs). We can think of a large group of small firms (a
continuum, to be precise) that offer one unit each. These firms are hetero-
geneous in their costs and, in the aggregate, give rise to the cost function C.
We assume here that firms have constant marginal costs c. Since product
2 is in competitive supply, p2=c. As for the willingness to pay of the
consumers for product 2, we assume r2> c (otherwise, product 2 would not
be marketed); without loss of generality, we set r2= 1.
The product of type 1, located at 0, is sold by a single firm, noted 1.
Hence, firm 1 enjoys some degree of market power which is, however, limited
by the presence of the firms at the other location. Firm 1 has the possibility
to choose the quality, r1, of its product. For a quantity qand a quality r1,
firm 1’s cost function is given C(q, r1) = cq + (γ/2) r2
1. The marginal cost,
c, is thus assumed to be common to all firms. Without loss of generality, we
set c= 0.
There are two periods. In period 1, the entrepreneur managing firm 1
chooses the status and the funding mechanism of the firm. In terms of status,
the firm can be for-profit or non-profit. As for the funding mechanism, the
choice is between crowdfunding and external funding (which encompasses
usual sources of finance, such as own money, friends and family money,
business angels or government subsidy). We clarify the implications of these
choices below. In period 2, the entrepreneur sets the price and the quality
of product 1.
For-profit vs. non-profit. The status of the firm does not affect its
technological opportunities. The only impact is that under the non-profit
status, the entrepreneur is restricted in her ability to distribute profits to
herself. In particular, we make the following set of assumptions. As in
Glaeser and Shleifer (2001), we assume that regardless of the status of the
firm, the entrepreneur’s utility is an increasing function of the difference
between the quality of her product and the quality of the fringe product.
That is, the entrepreneur gets a higher (lower) utility if the quality r1of her
a product exceeds (falls short) of the quality of the fringe product (r2= 1).
22

This can be justified either by referring to some altruistic preference of the
entrepreneur (her desire to provide better quality than the competition), or
as a reduced form of some reputation mechanism that would be at work in
a richer model with asymmetric information and repeat purchases.12
If the firm is for-profit, the entrepreneur earns the firm’s profits as in-
come; she then maximizes the following quasi-linear utility function:
UF=pq −C(q, r1) + b(r1−r2),(6)
where b > 0 is the marginal utility of increasing the quality of the product.
In contrast, if the firm is non-profit, the entrepreneur is forced, because
of the non-distribution constraint, to consume profits as perquisites. We
assume that the entrepreneur strictly prefers cash to perquisites; her utility
from perquisites is thus modelled as a fraction 0 < d < 1 of the profits,
which leads to the following utility function
UN=d(pq −C(q, r1)) + b(r1−r2).(7)
Crowdfunding vs. external funding. Contrary to the previous sec-
tion, we assume here that the two funding methods are as costly for the
firm (there is a common fixed cost of capital K, which we set equal to zero
without any loss of generality). We make this simplifying assumption so
as to focus on one key aspect of crowdfunding, namely that it increases
the awareness of the product for the consumers with respect to external
funding. In particular, we assume that unless the firm chooses crowdfund-
ing, consumers ignore their exact location x(i.e., they ignore the disutility
that they face when purchasing one unit of either product). Crowdfund-
ing, through its informative advertising effect, reveals their preference to
the consumers. That is, crowdfunding provides information as to horizontal
attributes of the products (but not as to vertical attributes as we assume
that they are observable).
We now solve the two-stage decision problem, starting with the price-
quality choices.
4.2 Price-quality combinations
We consider in turn external funding and crowdfunding. For each funding
method, we contrast the entrepreneur’s choices for a for-profit and for a
12See Belleflamme and Peitz (2010, Chapter 12) for a review of such models.
23

non-profit firm.
4.2.1 Decisions under external funding
In this case, consumers ignore their exact location. Hence, their expected
disutility when buying either product is E(τ|li−x|) = τ/2 for li∈ {0,1}.
That is, consumers have, in expectation, the same disutility for the two
products. Hence, they all choose to buy the product of firm 1 as long as
r1−1
2τ−p≥1−1
2τ⇔p≤r1−1.
Clearly, whatever the status of the firm, it is in the entrepreneur’s best
interest to set p=r1−1≡pT(as long as r1≥1). At this price, all
consumers buy (i.e., q= 1) as long as their expected net utility is non-
negative: r1−1
2τ−(r1−1) ≥0 or
τ≤2,(8)
which we assume to be satisfied.
If the firm is non-profit, the entrepreneur chooses r1to maximize
d(r1−1) −(γ/2) r2
1+b(r1−1). The first-order condition yields d−dγr1+
b= 0. The optimal quality level is thus
r1=b+d
dγ ≡rN E ,
which is assumed to be larger than r2= 1 (we make the condition explicit
below). We can then compute the entrepreneur’s utility as
UNE =db+d
dγ −1−dγ
2b+d
dγ 2
+bb+d
dγ −1
=(b+d) (b+d−2dγ)
2dγ .(9)
If the firm is non-profit, we easily find the optimal quality and utility
by setting d= 1 in the above expressions (as the entrepreneur realizes the
profit as income). That is
rF E ≡b+ 1
γand
UF E =(b+ 1) (b+ 1 −2γ)
2γ.(10)
24

We observe that d < 1 implies that rNT > rF T :the entrepreneur delivers
a higher quality when the firm is non-profit rather than for-profit. This is
the result of Proposition 1 in Glaeser and Shleifer (2001). The intuition
is pretty clear: as a non-profit entrepreneur puts a relatively larger weight
on quality increases in her utility (as b/d > b), she is induced to produce a
higher quality. That is, the non-profit status can be seen as a commitment to
improved quality because the entrepreneur is limited in her ability to pocket
the profits. To guarantee positive utilities and prices in the two cases, we
assume
b+ 1 >2γ. (11)
Note that assumptions (8) and (11) define an open interval as long as
(b+ 1) /(2γ)> τ /2, which is equivalent to τγ < b + 1.
4.2.2 Decisions under crowdfunding
When the firm uses the ‘crowd’ to obtain its funding, it has to describe
the product and, as a result, to differentiate it with respect to the alterna-
tive products. This is modeled here by assuming that under crowdfunding,
consumers know their exact location on the Hotelling line. It follows that
consumer x’s purchasing decision solves maxi=1,2{ri−τ|li−x| − pi}. For
prices such that both products are sold, there is exactly one indifferent con-
sumer bxwho is defined by
r1−τbx−p=r2−τ(1 −bx) or, equivalently,
bx=1
2τ(τ+r1−1−p).
We check that bx≥0⇔p≤r1−1 + τand bx≤1⇔p≥r1−1−τ. The
demand of firm 1 consists of all consumers to the left of bxand thus, the
demand function is
Q1(p) = 




0 if p>r1−1 + τ,
1
2τ(τ+r1−1−p) if r1−1−τ≤p≤r1−1 + τ,
1 if p≤r1−1−τ.
Whatever the status of the firm, the price is chosen so as to maximize
pQ1(p). The first-order condition is τ+r1−1−2p= 0, which yields p=
1
2(τ+r1−1) ≡pC. We have an interior solution provided that pC≥r1−
1−τ, which is equivalent to 3τ≥r1−1. In this case, the identity of the
25

indifferent consumer is found as bx= (τ+r1−1) /(4τ). This consumer gets
a non-negative utility when purchasing either product as long as 3τ≤r1+3,
which is compatible with 3τ≥r1−1. If 3τ > r1+ 3, firm 1 becomes a
monopolist; the marginal consumer is located at ˜xsuch that r1−τ˜x−p= 0
or ˜x= (r1−p)/τ . The optimal price is then easily found as p=r1/2 and
˜x=r1/(2τ). Finally, if 3τ < r1−1, then the entrepreneur sets p=r1−1−τ
and all consumers buy from firm 1. We can then express profits at the
optimal price as
pCQ1(pC) = 






r2
1
4τif 3τ > r1+ 3,
(τ+r1−1)2
8τif r1−1≤3τ≤r1+ 3,
r1−1−τif 3τ < r1−1.
As for the choice of quality, the status of the firm matters. Assuming for
now that r1−1≤3τ≤r1+ 3, the entrepreneur of a non-profit firm faces
the following maximization problem:
max
r1
d (τ+r1−1)2
8τ−γ
2r2
1!+b(r1−1) .
The first-order condition gives
1
4τ(4bτ +dτ −d+r1(d−4dτγ)) = 0 ⇔r1=(4b+d)τ−d
d(4τγ −1) ≡rN C .
From our previous analysis, we expect the chosen quality to increase when
ddecreases. We therefore assume
4τγ > 1.(12)
The entrepreneur’s utility is then equal to
UNC =γ(τ−1)2d2−2τ b (4γ−1) d+ 4b2τ
2d(4τγ −1) .(13)
Note that we are in the conditions for an interior solution as long as rNC −1≤
3τ≤rNC + 3, which can be rewritten as
(4b+d)τ−d
d(4τγ −1) −1≤3τ≤(4b+d)τ−d
d(4τγ −1) + 3.
As above, the optimal quality and utility for a for-profit entrepreneur
is simply found by setting d= 1 in the previous expressions. We get
rF C ≡(4b+ 1) τ−1
4τγ −1and
26

UF C =γ(τ−1)2−2τ b (4γ−1) + 4b2τ
2 (4τγ −1) .(14)
We check that under assumption (12), the Glaeser-Schleifer result still
holds under crowdfunding: a non-profit entrepreneur delivers a higher qual-
ity than a for-profit entrepreneur:
rNC −rF C =(4b+d)τ−dr2
d(4τγ −1) −(4b+ 1) τ−r2
4τγ −1=4 (1 −d)bτ
d(4τγ −1) >0.
4.3 Choice of funding and status
We start by comparing the firm’s status under each funding mechanism.
Comparing expressions (9) and (10), we observe that the entrepreneur choos-
ing external funding prefers the non-profit status as long as
UNE > UF E ⇔1−d
2γd 2dγ −d+b2>0
⇔b2> d (1 −2γ).(15)
As, realistically, the non-profit status cannot always be chosen under exter-
nal funding, we posit that
γ < 1
2.(16)
As for crowdfunding, we compare expressions (13) and (14) , and find
that the entrepreneur prefers a non-profit over a for-profit status provided
that
UNC > UF C ⇔(1 −d)2dτ γ −dγ + 4b2τ−dτ 2γ
2d(4τγ −1) >0
⇔b2>1
4τ(τ−1)2dγ. (17)
The comparison of conditions (15) and (17) reveals that crowdfunding
is more likely to lead to the choice of the non-profit status than external
funding if
d(1 −2γ)>1
4τ(τ−1)2dγ ⇔γ < 4τ
6τ+τ2+ 1 ≡ˆγ.
We check that ˆγ < 1
2, meaning that either cases are possible under assump-
tion (16); we also check that γ < ˆγis compatible with assumption (12) (i.e.,
4τγ > 1) as long as τ > 0.527. We have thus established the following
result.
27

Proposition 2 In situations where crowdfunding is used to reveal their
preference to the consumers regarding the horizontal attribute of a product,
crowdfunding is more likely than external funding to lead to the choice of the
non-profit status if the cost of providing higher quality (γ) is small enough
and if the degree of horizontal product differentiation (τ) is large enough.
More precisely, this is so if
γ < 4τ
6τ+τ2+ 1 and τ > 0.527.
5 Concluding remarks
(To be written)
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