Liquid Capital: Comparing the Industrial Organization of the Blood and Sperm Donation Markets
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Wesleyan University The Honors College
Liquid Capital: Comparing the Industrial Organization of
the Blood and Sperm Donation Markets
by
Ella Sinfield
Class of 2019
A thesis submitted to the
faculty of Wesleyan University
in partial fulfillment of the requirements for the
Degree of Bachelor of Arts
with Departmental Honors in Economics
Middletown, Connecticut April, 2019Table of Contents
Acknowledgements…………………………………………………………………..1
Abstract……………………………………………………………………………….2
Introduction…………………………………………………………………………..3
Model 1: A Baseline Model for Fluid Donation…………………………………....5
The Markets for Blood and Sperm………………………………………………...14
Model 2.I: Re-conceiving the Fluid Donation Industry: Non-Profit and For-
Profit Agencies in Competition……………………………………..……………...21
Beta: The Business Stealing Effect on Firms' Equilibrium Quantity of
Collected Fluid…………………………………………………………….....24
Figure 1: The Effects of ω1 and β on Total Quantity………………...……....25
Omega1: The Nonprofit's Financial Constraint……………………………....26
Discussion……………………………………………………………………28
Who’s Your Donor? Identifying Donor Archetypes…………………………..…30
Model 2.II: Non-Cooperative Competition Based on Monetary and Non-
Monetary Incentives for "Donating" Fluid…………………………………….....38
The Case for Incentives…………………………………………………...…39
Opposition to Incentives……………………………………………………..40
Constructing the Model……………………………………………………....41
Business Stealing with Differentiated Donor Types……………….…….…..45
The Righteous Donor's Marginal Willingness to Donate Fluid, Given
Monetary Incentives…………………………….…………………….……...46
Figure 2: The Effects of ω and β on Total Quantity………………....……...48
1
Discussion………………………………………………………………...….49
Regulation: Juxtaposing the U.S. and Canada…………………………………....50
Model 2.III: Polar Donor Types on Non-Cooperative Competition with
Incentives…………………………………………………………………..………..57
Extension of the Model in Competitive Markets Where M2 is Banned……...60
Extensions of the Model in Monopolistic Markets Where M2 is Banned…....61
Figure 3: µ on the Quantity Differential Between Competitive and
Monopolistic Markets (With Varied Levels of Business Stealing β)…..........63
Discussion…………………………………………………...……………….64
The Effects of Prohibiting Donor Anonymity in the Model…………...…….65
Conclusion and Policy Recommendations……………………………………...…67
References…………………………………………………………………………...71Acknowledgements
I give many thanks to my two thesis advisors, Professor John Bonin and
Professor Christiaan Hogendorn. I met Professor Bonin when I took his Econ 110
class freshman year, and I believe that without his support during my time at
Wesleyan I might not be writing this thesis. I was lucky enough to work with
Professor Bonin during my first semester of thesis work, and his insights throughout
this process have been invaluable and eye-opening. Though I met Professor
Hogendorn only this year through his Industrial Organization course, he has been
hugely influential in my understanding and appreciation of economics. Professor
Hogendorn volunteered his time to be my advisor during my second semester of
writing, and I am incredibly thankful for his encouragement, technical savvy (whether
in Mathematica or LaTex), and imagination. I would also like to thank Professor
Rene Almeling for meeting with me at Yale to discuss her incredible work on egg and
sperm donation, Professor Gil Skillman for helping me talk through this paper, and
Professor Daniella Gandolfo for fostering my initial interest in “gifts and giving.”
From the Psychology department, I must truly thank Professor Royette
Tavernier for refining my research and academic writing skills. I consider myself
extremely lucky to know her, let alone to have worked in her Sleep and Psychosocial
Adjustment Lab at Wes.
Finally, I would like to thank my parents (Deanna and Paul), my brother
Liam, and the rest of my family for their support throughout my academic career and
for their frequent assurance that I would finish this thesis. We totally did it! And a big
thank you to all my people – you know who you are, and I love you lots.
1Abstract
Today, the blood and sperm donation markets are global, multi-billion dollar in-
dustries. Despite the altruistic rhetoric that commonly surrounds the donation of body
fluids, donors are regularly paid for their “gifts,” and recipients can face remarkably
high acquisition costs. For body fluid collection agencies, or ‘banks,’ which serve as
intermediaries between donors and recipients, the markets for blood and sperm are quite
robust. However, starkly different market outcomes have been seen to occur between
the two industries and between countries. In this thesis, I employ an industrial organi-
zation approach to examine the strategic interaction between fluid collection firms and
explore the efficiency of divergent regulatory regimes. I use the model of the blood
donation industry presented by Nagurney and Dutta (2018) as a baseline framework
for fluid donation, and sharpen new models for both industries based on my research
of both industries. Through investigation of the blood and sperm markets, average
donor characteristics, and varying regulatory approaches (using the United States and
Canada as illustrative examples), I am able to map the effects of several key parameters
on industry effectiveness. My results show that non-profit firms in competition should
provide super-optimal service levels to fluid donors in equilibrium. I also find that
as donors become more intense in their preferences toward incentives, the “business
stealing” effect that arises from competition between firms can mitigated by “product
differentiation” (appealing to different donor niches). However, donor neutrality can
benefit the market in alternative ways. These findings inform the policy recommen-
dations that the United States retain its competitive market structure and continue to
provide incentives for blood donation, but shift to a single-firm market which continues
to provide incentives for sperm donation.
2Introduction
When 48-year-old Washington social worker Cynthia Daily and her partner decided
to conceive a child via sperm donor in 2004, they were aware that their son might have
a few biological half-siblings. The couple even hoped that they would get to know these
individuals, in “an extended family of sorts for modern times.” So, after her son’s birth,
Daily searched her son’s donor number on an online database – only to find that her
son had over 150 half-siblings, all conceived using the sperm of a single donor (Mroz,
2011).
***
In May of 2018, 81-year-old Australian native James Harrison, “the man with
the golden arm,” donated blood for the last time. Physicians found that Harrison’s
blood contained rare antibodies that can be used to produce the medication anti-D im-
munoglobulin for rhesus disease, which can result in severe fetal complications. Thus,
he donated blood “every week for 60 years, saving over 2.4 million babies in the pro-
cess” (Vomiero, 2018).
***
Donating blood and donating sperm are two altruistic actions considered under the
umbrella of ‘giving the gift of life.’ As they should be – three lives can be saved with
one blood donation, and a single ejaculation (two to four vials of sperm) can produce
a pregnancy for a family that otherwise could not have conceived (Blood Needs, n.d.;
The Sperm Bank of California, n.d. b). Each “gift” comes with different emotional and
ethical complexities (taking the above anecdotes as thought-provoking examples), but
both are predominantly considered by society to be gifts.
Yet the commendable altruism present in these industries is tightly, perhaps un-
settlingly, intertwined with standard economic forces (Slonim, Wang, & Garbarino,
32014). Global technological innovation has allowed blood and sperm to be stored and
distributed by collection agencies or ‘banks,’ a term which aptly attaches financial con-
notations to these “body products” (Rosen, 2014). In the U.S., blood collection agen-
cies contract prices with hospitals for pints of blood and also often offer monetary or
in-kind incentives to attract donations (Slonim, Wang, & Garbarino, 2014). Likewise,
U.S. sperm donors are paid for donating, and individuals seeking donor insemination
can incur costs of thousands of dollars for a relatively simple procedure (Donor Insem-
ination, 2012). Today, the blood and sperm donation markets are global, multi-billion
dollar industries (Berry, 1991; Grand View Research, n.d.).
In this work, I examine both of these intriguing industries from the perspective
of industrial organization, of which game theory has become a standard formulation
(Bagwell & Wolinsky, 2002). The blood industry has been widely explored in the
field of economics, but rather narrowly in terms of IO, and the literature on sperm
donation stems primarily from the social sciences (i.e. sociology, anthropology, and
law) – quite distanced from quantitative methods in economics. An IO approach allows
me to understand the strategic interaction between fluid collection agencies and explore
the efficiency of different countries’ regulatory regimes.
In the outset of this paper, I present a brief outline of the blood industry to contextu-
alize a baseline framework for fluid donation, the game theoretical model of the blood
donation market presented by Anna Nagurney and Pritha Dutta (2018). Their frame-
work includes some insightful considerations for both the blood and sperm industries,
such as service-based competition between firms to capture donors. However, open
questions left in their model, such as the constant price of blood and firms’ maximiza-
tion of service level (rather than quantity of fluid), catalyze my further exploration of
the markets for blood and sperm.
From this point, my descriptive and theoretical analyses of these fluid markets in-
teract in a sort of conversation, wherein the new information gleaned from empirical re-
4search appears in new model iterations. I first examine the markets for blood and sperm
in the United States, finding important similarities and differences between the markets’
pricing strategies, firm organizational structures, and key challenges. This leads me to
reorganize firms’ utility functions and introduce for-profit entities into Model 2.I. Next,
I explore each industry’s “archetypal” donor, and note the importance of incentives to
donors. In Model 2.II, I allow firms to offer monetary and non-monetary incentives,
and vary donor attitudes toward incentives. Finally, I juxtapose the regulatory stances
of Canada and the United States to discern why countries might choose certain market
structures and why some countries see more “success” in blood and sperm collection.
This research motivates my reconstruction of donor preferences and theoretical com-
parison of Canada and the U.S. in Model 2.III.
Altogether, this economic exploration allows me to detail a new framework for
thinking about blood and sperm donation,1 which integrates empirical and experimen-
tal findings. Additionally, I reflect upon current market regulations and construct future
policy recommendations considering the efficiency and ethics of blood and sperm do-
nation.
Model 1: A Baseline Model for Fluid Donation
Each year, 32,000 pints of blood are used in the United States for transfusions and
rapidly advancing medical procedures (Blood Facts - Providence, n.d.). Every two
seconds, someone is in need of blood, and 4.5 million Americans annually require
a transfusion (Blood Facts - Community, n.d.). The magnitude and criticality of the
blood donation market, together with its current mechanisms for coordinating supply
and demand, make it an intriguing topic for economics research.
1 My models may also be applicable to the markets for cord blood and breast milk, though these
industries fall outside of the scope of this paper. Future research should consider if the parameters
included in my models are relevant to these markets.
5The market for blood in the U.S. is mostly controlled by the American Red Cross
(a nonprofit, charitable organization), though other nonprofits (such as United Blood
Services) also operate in the space (Slonim, Wang, and Garbarino, 2014). As the use
of altruistic rhetoric in the market suggests, the United States collects blood largely
from voluntary unpaid donors (World Blood Donor Day, n.d.). Donors who do receive
incentives are paid in flat rates (e.g., gift cards and lottery tickets) or receive in-kind
payments (e.g., t-shirts and pins), which do not change in response to shifts in total
supply. Paid and unpaid donors are both often targeted through media campaigns and
outreach.
In terms of costs incurred by blood banks, most relate to recruiting donors, testing
and processing blood (screening for disease and separating it into component parts,
like plasma), and paying staff (Toner, 2011; On the Edge News, 2017). Additional
costs must come from equipment, maintaining permanent donation properties, setting
up temporary donation sites, and donor-facing costs like incentives and media. It is
estimated that the Red Cross operates on an annual budget of approximately $1.7 billion
(McQueen, n.d.).
The source of revenue in the blood market is the sale of donated blood to hospitals
for patient use. Contracted prices vary based on “the hospital, the region, and the
usage [of blood],” and appear to last for periods of several months at a time (McClurg,
2002). Blood collection agencies often frame this cost as purely for reimbursement (On
the Edge News, 2017), such that any increase in the price of blood is correlated with
increases in testing, for example. Notably, it would seem that hospital demand must be
relatively inelastic, as they must have a steady stream of donated blood to successfully
function and can expect reasonable reimbursement by patients and their insurance.
Despite the attention paid to the blood donation market by economists, few mathe-
matical frameworks for the market currently exist. A few authors have developed for-
mulae for thinking about donor responses to incentives, including Goette and Stutzer
6(2008) and Costa-Font, Jofre-Bonet, and Yen (2013). Empirical models of charitable
markets in general, such as by Andreoni (1990) and Bryant et al. (2003), provide valu-
able insight into donor behavior and nonprofit attraction strategies, but these are not
tailored specifically to the blood industry.
One novel representation of the blood donation market comes from Anna Nagur-
ney and Pritha Dutta (in press in Omega, The International Journal of Management
Science, 2018), who construct a game theory model for donations to blood collection
agencies. Nagurney and Dutta’s framework is established under non-cooperative qual-
ity competition, in which blood collection agencies seek to maximize blood donations
by competing on the quality level of their establishments and by “maximiz[ing] their
transaction utilities” (Nagurney & Dutta, 2018). As per a standard non-cooperative
Nash equilibrium model, firms set the competitive variable of quality (conceptualized
as service level) simultaneously. Nagurney and Dutta’s exploration of the industry is
rooted in the literature on supply chain management and is extremely complicated in
notation.
This section serves a dual purpose, in that I will both modify the authors’ existing
model for the purposes of simplification and clarity, and appraise the strength of the
underlying assumptions of Nagurney and Dutta’s paper. As will be explored further,
my investigation of their model is the starting point for establishing my own models
in the following sections. For instance, I find that the equilibrium of their competitive
model is socially inefficient, and adjust their framework so that it is more in line with
standard economic literature.
The model given in this section primarily differs from that of the aforementioned
authors threefold: (1) it is simplified to one “region of blood collection” rather than
supply chain management across regions, (2) the utility of firms for providing blood
collection services (corporate “warm glow,” in a sense) is denoted by a single vari-
able (ω), and (3) the notation in the donor supply functions is slightly altered to better
7highlight “business stealing” effects.
I consider two identical firms, and my adapted variables are defined as follows (in
terms of firm 1 for simplicity, as they are identical for firm 2):
S1 = the quality of service provided by firm 1
Nagurney and Dutta define service quality level as encapsulating “operational char-
acteristics” including the cleanliness and accessibility of the facility and the treatment
of donors by staff. In this model, firms will simultaneously choose their service levels
as the competitive variable.
c1 (S1 ) = the total cost of firm 1’s blood collection
ω1 S1 = firm’s 1’s transactional utility
Q1 (S1 ) = the volume of blood collected by firm 1 (conceptualized within a time
frame of approximately one month)
P1 = the price associated with firm 1’s blood collection activity (i.e., to cover the cost
of supplies, storage, staff, testing, etc.) (Slonim, Wang, & Garbarino, 2014). Nagurney
and Dutta assume that price is constant and not a choice variable in this model. In the
discussion following this model, I consider the implications of this assumption.
I maintain the optimization problem established by Nagurney and Dutta, that each
organization seeks to maximize its transaction utility U. The donor supply functions of
firm 1 and its competitor firm 2 are:
Q1 (S1 ) = S1 − β1 S2 + γ1
Q2 (S2 ) = S2 − β2 S1 + γ2
I slightly alter the authors’ donor supply functions by placing the β coefficient on
the service level of the firm’s competitor (rather than its own). Note that this sets up a
system of competition in service quality between the firms where there is the potential
for “business stealing” of donors based on relative service levels (0 < β1 < 1 ; 0 < β2
8< 1). In other words, β represents the degree to which a change in one firm’s service
level affects its competitor’s strategic choice of service level.
The firms’ cost functions are written as:
c1 (S1 ) = ψ1 S12
c2 (S2 ) = ψ2 S22
I now present the optimization problem established by Nagurney and Dutta in which
each organization seeks to maximize its “transaction utility” U. Firms maximize rev-
enue minus costs plus an extra intrinsic utility term ωi Si that reflects their nonprofit
charitable motivation to provide service, subject to their respective service levels.
Firm 1:
U1 = P1 Q1 (S1 ) + ω1 S1 − c1 (S1 )
Firm 2:
U2 = P2 Q2 (S2 ) + ω2 S2 − c2 (S2 )
Deriving the first order conditions of each utility function and then solving them
simultaneously for the Nash equilibrium quality levels yields the below expressions:
ω1 + β1 P1
S1∗ =
2ψ1
ω2 + β2 P2
S2∗ =
2ψ2
A few interesting insights can be drawn from this model’s equilibrium outcome.
Perhaps most immediately noticeable, the chosen quality levels have no interdepen-
dence in an oligopoly sense. In classic non-cooperative equilibria, firms’ strategic
choices are bound by the choices of their competitor, and thus neither will deviate.
9Yet in this model the quality level chosen by each firm is entirely independent of its
competitor.
Next, as the utility of each firm for providing blood collection services (ω) in-
creases, the quality of service offered by the firms will likewise increase. Put simply,
firms who like to provide quality service do. While appearing straightforward, I chal-
lenge the authors’ assertion that blood collection agencies are motivated to maximize
quality of service rather than quantity (pints of whole blood). I agree that the underly-
ing mission of organizations like the American Red Cross can be vague – its mission
statement reads: “The American Red Cross prevents and alleviates human suffering in
the face of emergencies by mobilizing the power of volunteers and the generosity of
donors” (American Red Cross, n.d.) – yet within the blood collection space, it seems
peculiar to model agencies’ decision making based on anything other than motivation
to supply society with high quantity. Per contra, this assertion could apply to the sperm
industry; one might imagine that sperm banks’ overall mission is to provide the best
service possible to clients looking to start a family.
The equilibrium also exhibits that increasing a firm’s service level increases its col-
lected quantity of blood. Increasing the price of blood, P, increases the service level,
which is logical in the sense of providing increased funding for staff, accessibility, and
cleanliness. Lastly, the inverse relationship between ψ and S signifies firms’ essential
trade-off between service level and cost. These assumptions seem fair for the blood
market, but further exploration is needed to determine if increased service level in the
sperm industry truly drives in a higher quantity of donated semen.
Interestingly, Nagurney and Dutta do not explore the economic efficiency of their
model of the blood market. To explore this question, I extend the model to understand
whether the two firms in competition are behaving differently than would a monopolist
that operated both firms.
To begin, I add the utility functions of firm 1 and firm 2 to get total monopolist
10utility:
UM = ω1 S1 − ψ1 S12 + P1 (S1 )[γ1 + S1 − β1 S2 ] + ω2 S2 − ψ2 S22 + P2 (S2 )[γ2 − β2 S1 + S2 ]
The first order conditions of monopolist utility with respect to S1 and S2 are:
∂UM
= ω1 + P1 − β2 P2 − 2ψ1 S1 = 0
∂ S1
∂UM
= ω2 + P2 − β1 P1 − 2ψ2 S2 = 0
∂ S2
These can be rearranged to form the monopoly equilibrium service levels:
∗ ω1 + P1 − β2 P2
S1M =
2ψ1
∗ ω2 + P2 − β1 P1
S2M =
2ψ2
To compare the pints of blood collected in the monopoly situation versus the au-
thors’ duopoly, I add together the blood collection functions Q1 + Q2 and evaluate them
at the equilibrium quality levels derived for the duopoly model (S1 , S2 ) and monopoly
model (S1M , S2M ).
ω1 + P1 β2 (ω1 + P1 ) ω2 + P2 β1 (ω2 + P2 )
Q∗duop = γ1 + γ2 + − + −
2ψ1 2ψ1 2ψ2 2ψ2
ω1 + P1 − β2 P2 β2 (ω1 + P1 − β2 P2 ) ω2 − β1 P1 + P2 β1 (ω2 − β1 P1 + P2 )
Q∗monop = γ1 +γ2 + − + −
2ψ1 2ψ1 2ψ2 2ψ2
11The difference in quantity collected is:
ψ1 (1 − β1 )P1 + ψ2 (1 − β2 )P2
Q∗duop − Q∗monop = (1)
2ψ1 ψ2
This logic can be repeated to understand the difference in social welfare between
the monopoly and duopoly systems. Leaving aside donors’ benefit from donating, and
assuming that blood price P correctly represents the social value of the blood, the social
benefit of a firm’s operation is PQ(S) − c(S). I evaluate the social welfare functions of
the monopoly and duopoly cases at their respective service level equilibria and solve
for the difference:
β1 ω1 P1 β12 P12 β2 ω1 P2 β22 P22
∗ ∗
SWduop − SWmonop =− + + + (2)
2ψ2 4ψ2 2ψ1 4ψ1
The two difference equations above (1 & 2) clearly illustrate that, in this model,
two firms in competition are behaving differently than would a monopolist in the same
scenario.
Focusing on the quantity differential (1), it is clear that the expression is positive
if the β values (which represent the influence of competitor service level on firms’
own quantity of blood collected) are less than one. If β1 and β2 were greater than
one, the amount of blood collected by the American Red Cross, for instance, would
be more responsive to the service level provided by the United Blood Services than to
the level of its own services, which seems implausible. Assuming that the β values
are less than one, the blood donation functions point to an over-provision of service
level by duopolists due to increased competition. Because the difference between the
equilibrium service levels in a duopoly state versus a monopoly state is positive (S1 −
S1M > O; S2 − S2M > O), I can interpret the increased service level in the duopoly
situation as the effects of business stealing.
The phenomenon of business stealing, in which an action is taken by a firm to
12abstract consumers from competition rather than attract new consumers, has been pre-
viously documented within the nonprofit and medical care spaces. Tay (2003) dis-
cusses how competition between hospitals on the basis of adopting new technologies
could lead to “wasteful duplication of costly facilities...if business stealing effects are
large.” Aldashev and Verdier (2009) analyze business stealing as a negative externality
of fundraising by NGOs and identify the potential for “overproduction” of fundrais-
ing in equilibrium. In the blood donation industry, it follows that service-level-based
competition would produce similar effects.
Curiously, in Nagurney and Dutta’s model, the increased service level produced
by duopoly competition does not lead to any lives saved. The authors keep the price
of blood (P) constant, indicating a horizontal supply line, which prevents consumer
surplus, and the equilibrium quantity of blood able to be utilized by recipients, from
growing due to increased service levels. I examine whether this is truly the case in the
blood and/or sperm industries below.
In terms of social welfare differential (2)2 , it is straightforward that the social wel-
fare derived in the duopoly scenario is lower than in a monopoly. While the market is
expanded and a higher quality of service is offered in the duopoly state, much of the
increased quality goes into wasteful business stealing, which runs up the cost of provid-
ing such high quality. If P1 and P2 correctly correspond to the marginal social benefits
of blood, the duopolist’s cost of maintaining its service quality is too high for optimal
social benefit.
So, given the market structure outlined by Nagurney and Dutta, how do we move
forward in affirming an accurate framework which could apply to both the blood and
sperm industries? First, I will reframe the exploration in a way that is more consistent
with standard economic theory by re-conceptualizing firms’ optimization problems and
using a single price of fluid in the market to signal “product” homogeneity. Second, I
2 Reminding the reader that SW excludes the direct consumer benefit of the increased service level.
13will retain the authors’ conception of business stealing in the market, as this is a foun-
dational observation to their paper and consistent with findings in other nonprofit and
medical care spaces. Third, I will transition to discussing the implications of nonprofit
and for-profit competition in this space, to best guide discussion about both markets
for fluid. I begin by detailing the markets for blood and sperm to understand which
drivers are the most significant to include in a theoretical framework. Do the facts on
the ground match that which has been modeled?
The Markets for Blood and Sperm
“If you give blood even two hours after an event, the people who are going to die of
bleeding are already dead by the time it’s ready.” (Cara, 2017)
In the United States, the blood market is dominated by three nonprofit organiza-
tions: the American Red Cross, the American Association of Blood Banks (in which
United Blood Services is a member), and the Armed Services Blood Program (which
provides blood products to “service members, veterans, and their families”) (Berry,
1991; Slonim, Wang, & Garbarino, 2014; Armed Services Blood Program, n.d.). In
fact, to my knowledge, no (openly) for-profit blood collection agencies exist in the
U.S. In economic theory regarding the existence of nonprofits, the basic argument is
that such institutions are better equipped to provide social, collectively-beneficial ser-
vices than governments (Anheier, 2005), like blood. Despite the industry creating bil-
lions of dollars in revenue, it appears that the altruistic rhetoric surrounding the blood
market has prevented for-profit agencies from widely operating. It should be noted that
for-profit blood banking is currently legal in the United States (Florida Senate Interim
Report, 2009).
The contemporary economic literature on blood donation effectively investigates
the market’s constraints and challenges, far beyond just identifying the current price of
blood. An in-depth review by Slonim, Wang, and Garbarino (2014) addresses many of
14the current realities of the blood industry by reviewing its development through history.
The authors describe how the industry evolved from “thin one-to-one ‘marriage mar-
kets,’ in which each recipient needed a personal blood donor, to thick, impersonalized,
diffuse markets,” which increased the number of possible blood transfusions but also
created rifts between aggregate supply and demand (Slonim, Wang, and Garbarino,
2014). Namely, the U.S. blood market experiences periods of over-supply, such as
when a large number of people donate blood immediately after a natural disaster, and
under-supply, as during the Christian holiday season (Slonim, Wang, and Garbarino,
2014). Following are few reasons for which such imbalances occur.
For one, as explored in Model 1, the United States collects blood largely from
voluntary, unpaid donors (World Blood Donor Day, n.d.). Thus, there is no market
“price” visible to donors with which to gauge demand for blood; price does not indi-
cate when to optimally donate. According to Starr (2002), huge supply spikes followed
the 9/11 attacks on the World Trade Center as citizens anticipated an increased need
for donor blood. However, Slonim, Wang, and Garbarino estimate that, after the disas-
ter, “100,000 to 300,000 units [of blood were] eventually discarded (plus the time and
equipment wasted collecting these units), for an estimated minimum cost of $21 [to]
63 million” (2014). Though demand for blood had been satiated, no price signals were
available to alert potential donors to hold off .
Another factor that contributes to demand and supply imbalance in the blood in-
dustry is its limited shelf life – up to 35 days, for whole blood (Blood Components,
n.d.). Even with the technology to separate blood into its component parts (Blood
Components, n.d.), blood collection agencies may not be in positions to fully mitigate
a divergent market. For instance, plasma, “the liquid portion of blood,” can last up to a
year when frozen (Donor FAQ, n.d.). However, “centrifuge and filtration capacity con-
straints,” coupled with a lower incidence of plasma donation compared to whole blood
donation, limit the effectiveness of this option (Slonim, Wang, and Garbarino, 2014;
15Types of Blood Donations, n.d.).3
A paper by Greinacher and colleagues (2017) also shows that demographic changes
from population aging and birth rates can affect blood supply, as changes in medical
practices and technologies can shift demand.
Slonim, Wang, and Garbarino additionally provide insight into how blood service
agencies and economists can (and do) address inefficiencies in the blood market. First,
the authors suggest the continued use of small, non-monetary incentives to assure a
steady supply of new and repeat donors, citing seminal authors such as Lacetera, Macis,
and Slonim (2012) and Titmuss (1971). The validity of this suggestion will be teased
apart later in this work, specifically when incentives are introduced into Model 2.II.
Secondly, blood services already utilize media, telemarketing, and donor registries to
more precisely target donors who will respond during times of blood shortage, per-
haps in their own communities (Slonim, Wang, and Garbarino, 2014). The authors
even conducted their own experiment to underscore the theory that “registr[ies] in-
creas[e] donations during shortages and increas[e] donor welfare by inviting donations
when the shadow value donating is higher to the supplier” (Slonim, Wang, and Gar-
barino, 2014). Powerfully, even despite issues coordinating the demand and supply of
blood, the United States is nearly 100% self-sufficient in its supply of blood (Institute
of Medicine, 1995; World Health Organization, 2016).
Along with the aforementioned review, James Andreoni’s 1990 paper on “impure
altruism” and “warm glow giving” sets an important foundation for modeling the in-
dustry. In his work, Andreoni describes blood as a public good, and discusses the mo-
tivations for donating blood, which range from pure altruism (caring only for the good
of the community) to pure egoism (caring only for the “warm glow” self-assurance
associated with doing an altruistic action) (Andreoni, 1990). The author implies that
a model incorporating impure altruism, a combination of the aforementioned motiva-
3 Plasma donation requires a significantly longer time commitment than whole blood donation, at 2.5
to 3 hours versus 1 hour.
16tional extremes, would more accurately capture market phenomena (Andreoni, 1990).
One open question left by Nagurney and Dutta’s model is why the price of blood
(paid by hospitals to cover the cost of blood collection agencies’ operation) is held
constant in their model. While I was initially hesitant to accept this assumption, it is
actually very defensible in the short term. According to Slonim, Wang, and Garbarino
(2014), blood prices are contracted between collection agencies and hospitals for set
periods before prices are reassessed, and thus they rarely change due to short-run shifts
in supply. It is true that a range of prices for collected blood exist within the market;
in 2010, “average prices...ranged from $154 to $211 per unit” (Slonim, Wang, and
Garbarino, 2014; Toner et al., 2011; Shander et al., 2010; Dreaper, 2010). Yet, for a
given firm, it is justifiable to hold price constant in the model.
Altogether, economic literature on the market for blood points to a few key chal-
lenges and potential resolutions. Imbalances in supply and demand are exacerbated
by the limited shelf life of collected blood, and blood banks might turn to offering in-
centives or increasing media outreach as anticipatory measures. Further, the notion of
“impure altruism” in the market sets the stage for variance in donor motivations, and
the reality of contractual pricing backs Nagurney and Dutta’s assumption of constant
price.
“Now [fatherhood] can involve nothing more than a financially strapped college
student masturbating into a cup for fifty dollars and writing a vaguely caring letter to
an offspring he will never see or care about.” (Haimes, 1993)
The market for sperm is the subject of far less economic attention, particularly due
to its modernity, but there is evidence that similar occurrences are present for sperm
as for blood. The first commercial sperm bank opened its doors about 40 years after
the first blood bank, in the early 1970s (California Cryobank, n.d.; AABB, n.d.), and
the industry arguably gained critical socio-economic interest in the late 1990s. As one
17might expect, the main issues that have been explored in regard to gamete donation per-
tain to the legality, ethics, and familial implications of the practice – which continue to
be contentious. Rene Almeling and Diane Tober, two foundational voices in the discus-
sion of commodification in the egg and sperm markets, explore some of the following
thought-provoking questions in their research: How are the value of bodily goods de-
termined? In what ways do “gendered expectations” of donors interplay with notions
of gift-giving, fair compensation, and donor-recipient matchmaking? And, importantly,
how are different bodies valued? (Almeling, 2009; Tober, 2001). These insights are in-
dispensable to our current understanding of the sperm market, and lay the groundwork
for realistic economic modeling, which until now appears untried.
Like the blood market, the sperm market has evolved from one-to-one matching
of donors with recipients to part of the clinical, multi-billion dollar fertility industry
we see today. At present, roughly 75,000 children are born annually as a result of
sperm donation in the United States (Xytex, 2014), and by 2025, the sperm market is
expected to grow to nearly $5 billion globally (Grand View Research, n.d.), a figure
which might surprise the unknowing economist. Importantly, the United States is the
world’s largest exporter of sperm, at least partly due to loose regulations on the industry
which have earned the U.S. market the appellation “legal Wild West” (Jarvis, 2013).
This to say that sperm banks in the U.S. “operate in a free market regulated by profit-
driven, cost–benefit considerations” (Pietrzak, 2013; Spar, 2006). From donation to
processing to receipt, the market for sperm in the United States is worthy of economic
scrutiny.
The process of sperm donation in the U.S. is deceivingly complex. After a screen-
ing process of “8 weeks to 6 months depending on the sperm bank to which the man
is applying” – during which questionnaires, subjective ‘fitness’ evaluations and sev-
eral health tests are administered – those cleared are finally allowed to donate (What
Does Sperm Donation Involve?, n.d.). It is estimated that only 5% of applicants meet
18all of the conditions (What Does Sperm Donation Involve?, n.d.). All men are paid
the same rate of about $100 per viable sample (Almeling, 2007), and because of the
lengthy screening process, most sperm collection agencies require donors to deliver se-
men weekly for one year (Taylor, 2019). Semen lacking a high enough sperm count is
discarded without compensation (Almeling, 2007). Therefore unlike blood donation,
which could seem like a one-off altruistic act, sperm donation might feel more like
employment (Almeling, 2007).
After the donated semen is collected, vials are frozen in liquid nitrogen and stored at
a collection facility (Taylor, 2019). At this point, banks fabricate an imbalance between
supply and demand, in that a “limited ‘inventory’ of sperm vials from each donor”
are kept at any given time (Almeling, 2007). This phenomenon appears to serve two
distinct purposes: to encourage genetic diversity within the population utilizing donor
sperm4 , and to differentiate their “goods” to justify oligopolistic (if not monopolistic)
pricing. The high demand that exists in the industry is best exemplified by banks’
common prescription that recipients choose multiple donors from their “catalogue” in
case one should become unavailable (Almeling, 2007; Almeling, 2011). Indeed, after a
successful match is made between donor and recipient, an individual procuring semen
from the Sperm Bank of California should expect to pay up to $200 for registration,
between $600 and $680 for the donor sperm itself, and over $500 for storage and ship-
ping (The Sperm Bank of California, n.d. b). Important to note is that while some steps
in fertility treatment are covered by insurance, “the cost of actual sperm always comes
out of pocket” (Malooly, 2016).
So to what are the true costs of donated sperm owed? First, at least part of the
cost must cover labor, equipment, payments to donors, and other reasonable associated
costs. Second, rapidly advancing technology, combined with additional test require-
4 While a valuable intention, recipients are not actually required to report their births to the sperm
collection facility which delivered the semen. Rene Almeling has estimated that less than 40% of births
from donor sperm are recorded by banks, leaving no paper trail of exactly how many babies are conceived
using donated sperm (Almeling, 2011; Smoot, 2018)
19ments, allow sperm collection agencies to intensify what has been referred to as genetic
“quality control” (Malooly, 2016). This no doubt hikes up costs. Third, donor profiles,
which are the primary tools used by recipients to choose donors and thus key features of
a sperm agency’s “service level,” can be tedious to assure and assemble. Sperm banks
have been seen to recruit donors near college campuses (Borg, 2015), and take time and
effort to assure that donors’ presentations are of the greatest appeal possible to prospec-
tive parents. Fourth, optional costs surround the level of knowledge the recipient can
gather about the donor, usually manifesting as a flat rate to see donor baby photos,
extended profile information, and/or audio messages (Seattle Sperm Bank, n.d.). Yet
prices are not fully cost-based. A cardinal feature of the sperm market is that the price
of sperm paid by recipients outweighs the cost; in 2017, it was estimated that only 1 in
the over 500 sperm banks in the United States operated as a nonprofit (Tribe, 2017).
When examining pricing in the sperm market, my perusal of the literature suggests
that the price of sperm is subject to nationwide competition, and that individual sperm
banks can be modeled as price takers. While donors are more geographically bound in
donating sperm – should they have to donate once a week for a year, they will stay close
to home – recipients are able to “shop around” between sperm banks and have donor
sperm delivered (R. Almeling, personal communication, April 2, 2019). It does not
appear that sperm collection agencies hike up prices based on the “quality” of the donor
but rather only on the amount of information provided about him (Fairfax Cryobank,
2019). With the number of sperm banks currently in operation in the United States and
globally, I believe that the sperm industry can be envisaged as pricing competitively
and with stable prices in the short run.
With this parallel analysis of the blood and sperm industries in mind, I present a new
model of a market for body fluid which preserves the strongest assumptions present in
Nagurney and Dutta’s model (such as business stealing) but examines nonprofit and
for-profit competition with re-imagined firm optimization problems.
20Model 2.I: Re-conceiving the Fluid Donation Industry:
Nonprofit and For-Profit Agencies in Competition
I now present a reorganized version of the previous model that allows me to analyze
the different strategies and outcomes that arise from competition between nonprofit and
for-profit entities.
The markets for body fluid in the United States are marked by diversity in compo-
sition and strategic decision-making, with the sperm industry dominated by for-profits
entities and the blood industry by nonprofits (which sometimes appear to act like for-
profits). In the blood market, it is not clear that nonprofit organizations would always
produce more socially beneficial outcomes than for-profit entities in the industry. Even
with financial donors and government subsidies, nonprofits conceivably face tougher
financial constraints than profit maximizing firms, thereby restricting the amount of
blood collected and service level provided within a given cost structure. Thus, blood
collection nonprofits in competition may make strategic decisions in order to “secur[e]
the fee-based and donative revenues necessary to support the work of [their] organiza-
tion” (McCambridge, 2018) but that may not be directly in line with their firm’s mission
of blood collection. For-profit firms in the U.S. sperm industry are subject to far less
regulatory scrutiny than firms in the blood industry, and can therefore take advantage
of the free market as they see fit.
This section aims to intuitively alter the previous model based on the open questions
it raised, and use this new model to understand the specific circumstances in which
nonprofit and for-profit firms can provide more social benefit to the blood industry.
In keeping with Nagurney and Dutta’s framework, I retain P as a constant value (in
the given time period), though I choose not to differentiate between the prices of fluid
collected by firm 1 and firm 2. In this analysis, I use a single P to denote a singular
price of fluid in the market, asserting that the two firms produce homogeneous products
like in standard non-cooperative competition. This is without loss of generality as long
21as the prices are fixed.
Let firm 1 represent a nonprofit fluid collection agency and firm 2 a for-profit
agency.
The system of fluid donation functions for these firms is:
Q1 (S1 ) = S1 − β S2
Q2 (S2 ) = S2 − β S1
As before, the cost functions are:
c1 (S1 ) = ψS12
c2 (S2 ) = ψS22
In keeping with other economic literature on nonprofits, including Richard Stein-
berg’s (1986) work on revealed objective functions, I choose to have nonprofit firms
maximize a weighted average of quantity (their objective) and revenue minus cost (their
budget). I expect that the more financially constrained a nonprofit becomes, the more it
will have to focus on revenue minus cost (RMC). Let ω be the weight that represents the
significance of RMC to a fluid donation organization’s overall utility. A for-profit firm
(firm 2 in this model) would set ω2 equal to 1 (deriving 100% of utility from profit),
and a nonprofit firm (firm 1) might weight profit as necessary to fund operating costs,
but as much as possible maximize the collection of fluid. Once again, firms maximize
U subject to service level.
Firm 1 (nonprofit):
U1 = (1 − ω1 )Q1 (S1 ) + ω1 [P ∗ Q1 − c1 (S1 )]
22Firm 2 (for-profit):
U2 = PQ2 (S2 ) − c2 (S2 )
Lastly, I establish consumer surplus simply as:
1
CS = (A − P) (Q1 (S1 ) + Q2 (S2 ))
2
This function considers the fluid in question a homogeneous good, such that fluid
collected by either firm holds the same marginal social benefit. It also assumes a linear
demand curve with price intercept A.
Repeating the logic outlined in the previous section, I solve the reaction functions
of each firm simultaneously to find the firms’ equilibrium quality levels:
1 1
S1∗ = ( + P − 1)
2ψ ω1
P
S2∗ =
2ψ
A higher price of fluid allows both firms to produce higher levels of service, and a
higher cost of service restricts both firms’ service levels. Interestingly, for the nonprofit
(firm 1), a higher ω (higher significance of RMC to utility) causes a decrease in the
service level it provides.
Although the two firms find their optimal service levels independently of one an-
other, the fluid donation functions lock them into an interdependent relationship when
it comes to fluid quantity. Evaluating firms’ quantities at the equilibrium service levels
yields:
1 1
Q∗1 = S1∗ − β S2∗ = − 1 + P(1 − β )
2ψ ω1
23
1 1
Q∗2 = S2∗ − β S1∗ = P − β ( + 1 − P)
2ψ ω1
The total quantity of fluid in equilibrium is thus:
∗ 1 1−β
Qtotal = (S1∗ + S2∗ )(1 − β ) = (2P + − β − 1)
2ψ ω1
Comparing statics in the nonprofit versus for-profit quantity equilibria reveals the
influence of business stealing and the nonprofit’s weight on RMC.
Beta: The Business Stealing Effect on Firms’ Equilibrium Quantities of Col-
lected Fluid
The effects of β on the equilibrium quantities this fluid donation market are:
∂ Q∗1 P
=− (< 0)
∂β 2ψ
∂ Q∗2 P − 1 1
= −
∂β 2ψ 2ψω1
∗
∂ Qtotal 1 1
=− − (< 0) (3)
∂β 2ψ 2ψω1
From these expressions, it becomes clear that increasing β reduces overall fluid
quantity in the market. A rising β indicates that firms’ efforts to provide quality service
go more towards taking donors from competition than expanding the overall donor
pool.
24Figure 1: The Effects of ω1 and β on Total Quantity5
Figure 1 illustrates the effects of increasing β on the total quantity of fluid, as ω1
varies. Total quantity decreases drastically as ω1 increases from 0 to 0.1, but this oc-
currence is mitigated when the business stealing effect is less prevalent (β approaches
0).
I turn now to the effects of β on equilibrium consumer and total surplus, which are
as follows:
1 1
CS∗ = ∗
(A − P) (Qtotal ) = (A − P)(S1∗ + S2∗ − β S1∗ − β S2∗ ) (4)
2 2
1
T S∗ = P(Qtotal
∗
) + (A − P)(Qtotal ∗
) − ψS1∗ 2 − ψS2∗ 2
2
1
= P(S1∗ + S2∗ − β S1∗ − β S2∗ ) + (A − P)(S1∗ + S2∗ − β S1∗ − β S2∗ ) − ψS1∗ 2 − ψS2∗ 2 (5)
2
Expressions 3, 4, and 5 demonstrate that an increase in β is unambiguously negative
in this model of a fluid donation market. The ideal β would be zero, in which case the
5 Figure
1 uses the market calibrated values of P = 210.74 and A = 300 (Toner et al., 2011; Palmer,
2014), and assumes ψ = 1 for simplicity.
25quantity of fluid collected by any given firm would be completely dependent on its own
service level and independent of the effects of competition. The results of this analysis
of β are in line with Model 1’s outcome that a monopoly will achieve higher welfare
than a duopoly.
Omega1 : The Nonprofit’s Financial Constraint
The effects of the nonprofit’s financial constraint on the equilibrium quantities are:
∂ Q∗1 1
=− (< 0) (6)
∂ ω1 2ψω12
∂ Q∗2 β
= (> 0) (7)
∂ ω1 2ψω12
∗
∂ Qtotal β −1
= (< 0) (8)
∂ ω1 2ψω12
For the nonprofit firm (firm 1), equilibrium quantity is decreasing in ω1 because the
nonprofit weights the cost of service level more as ω1 rises. However, for the for-profit
firm (firm 2), ω1 also factors into its optimal quantity. A rise in ω1 (representative of a
more financially constrained nonprofit) will lead to a greater quantity of fluid collected
by the for-profit firm. This is strictly a result of the business stealing effect in the fluid
donation functions and not from a change in the service level offered by the for-profit
firm.
Adding up the effects of ω1 on each individual firm’s quantity (6 and 7) as in ex-
pression 8, one can see that the increase in service level offered by the for-profit is
not enough to compensate for the decrease in S1 . Therefore the total quantity of fluid
collected is reduced when the nonprofit becomes more financially constrained.
The effects on the surplus functions of the nonprofit’s weight on RMC (ω1 ) are:
26∂CS∗ 1 ∂ Q∗ 1 β −1
= (A − P) total = (A − P) (< 0) (9)
∂ ω1 2 ∂ ω1 2 2ψω12
∗
∂ T S∗ ∂ S∗ ∂ Qtotal
1
= −2ψS1 1 + P + (A − P)
∂ ω1 ∂ ω1 ∂ ω1 2
1 + (P − 1)ω1 β − 1 1
= + P + (A − P) (10)
2ψω13 2ψω12 2
Consumer surplus clearly decreases in ω1 , but the sign of the first derivative of total
surplus is indeterminant, so I take its second derivative:
∂ 2 T S∗
3 + 3(P − 1)ω1 β − 1 1
=− − P + (A − P) (< 0)
∂ ω12 2ψω14 ψω13 2
Increasing the financial constraint on the nonprofit firm (ω1 ) has intriguingly varied
effects in this model. First, the total quantity of fluid collected suffers as ω1 increases
(8) due to the firm weighting its cost of service more heavily. Secondly, as ω1 increases,
firms decrease total spending on fluid collection, collecting less fluid and decreasing
consumer surplus (9). However, when ω1 rises and the nonprofit becomes more finan-
cially constrained, the firms internalize more of the total costs incurred, which increases
total surplus (10).
The fact that the total surplus is concave in ω1 indicates that there is indeed a so-
cially optimal value for ω1 . There exists a level of financial constraint for the non-profit
that would most benefit this market (i.e. resulting in the optimal balance between fluid
collected and costs incurred). This motivates the following questions: what is the opti-
mal ω1 ? Is it less than 1, such that a nonprofit is underweighting RMC compared to its
for-profit competitor?
To address these queries, I evaluate the derivative of T S with respect to ω1 at ω1 = 1.
There are three possible outcomes. If the derivative of T S is 0 at ω1 = 1, I can interpret
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