Content uploaded by Oliver Fabel

Author content

All content in this area was uploaded by Oliver Fabel on Jul 21, 2014

Content may be subject to copyright.

Rechts-, Wirtschafts- und

Verwaltungswissenschaftliche

Sektion

Fachbereich

Wirtschaftswissenschaften

Diskussionspapiere der DFG-

Forschergruppe (Nr.: 3468269275):

Heterogene Arbeit: Positive und Normative

Aspekte der Qualifikationsstruktur der Arbeit

Oliver Fabel

Spin-offs of Entrepreneurial Firms :

An O-Ring Approach

Mai 2003

Diskussionspapier Nr. 03/03

http://www.ub.uni-konstanz.de/kops/volltexte/2003/1002/

Diskussionspapier der Forschergruppe (Nr.: 3468269275) “Heterogene Arbeit: Positive und Normative

Aspekte der Qualifikationsstruktur der Arbeit“

Nr. 03/03, Mai 2003

Spin-offs of Entrepreneurial Firms : An O-Ring Approach

Abstract:

The O-Ring theory provides a framework to analyse the emergence of firms organized as partnerships. The owner-

managers of such entrepreneurial firms can benefit from ability matching within their production teams. However, they

must also bear the project risk. Risk-aversion then induces a second-best solution. At the same time, integrated firms

managed on behalf of risk-neutral residual-claimants face information and/or enforcement problems. Hence, they

cannot organize ability-matched teams. It is shown that there exists an equilibrium such that groups of individuals

sharing a superior ability level will found entrepreneurial firms. Low-quality individuals will be employed by managed

firms which hire randomly.

The paper constitutes a significantly revised version of the study formerly entitled “The Emergence of a New Economy:

An O-Ring Approach”, Department of Economics, University of Konstanz, Discussion Paper Series I – 314.

JEL Classification : D2, L2, M2

Keywords : O-Ring Theory; Ability Matching; Entrepreneurial Firms; Managed Firms

Download/Reference : http://www.ub.uni-konstanz.de/kops/volltexte/2003/1002/

Oliver Fabel

Universität Konstanz

Fach D 144

78457 Konstanz

Germany

mail : oliver.fabel@uni-konstanz.de

phone : +49-7531-88-2992

fax : +49-7531-88-4456

1 Motivation

While there exists a variety of de¯nitions of entrepreneurship, Bull and

Willard (1995) note two common features. According to the Knightian

school of thought, the entrepreneur bears the risk associated with an un-

certain business environment. At the same time, the Schumpeterian view

emphasizes the function of the entrepreneur to implement "new combina-

tions". Beginning with Cooper and Bruno (1977) and Cooper (1985), a

number of authors have then already focussed on the "incubator" role of

the place of employment prior to founding a new ¯rm. In this respect, the

recent emergence of the so-called "New Economy" - typically referring to

¯rm foundations in the computer, information and communications, and

bio-technology industries - appears to provide a prime example.

Hence, according to Bhid¶e's (2000, p. 54) survey of the 1989 Inc. 500

companies, 71% of the respective start-ups are founded by individuals who

"replicated or modi¯ed an idea encountered during their previous employ-

ment". Superior technological knowledge can therefore not explain the

emergence of such new ¯rms. Yet, Rajan and Zingales (2000, 2001a) empha-

size that the nature of the "new combinations" has changed. In particular,

the new technologies induce a fundamental shift of power from ¯nancial to

human capital. The innovations originate from human capital rather than

from inanimate assets. Thus, the allocation of the decision rights within the

¯rm becomes the prime issue. Corporate venturing for new opportunities

then results in a subdivision of the corporate physical assets.

Following the same basic argument, Baily and Lawrence (2001) conclude

that the emergence of the "New Economy" re°ects outsourcing decisions of

human capital-intensive productions. Bhid¶e (2000, p. 94) observes that such

spin-o®s are typically led by former high-pro¯le employees. Hence, 83% of

the founders in his survey at least hold a four-year college degree. While

¯nancial innovations have made this development possible, the recent expe-

rience of ¯nancial volatility now adversely a®ects the "New Economy" ¯rms

[Baily and Lawrence (2001)]. Reintegration constitutes a means to overcome

these problems. Moreover, according to Holmstr¿m and Kaplan (2001), the

process of disintegration generally terminates once the critical assets have

been identi¯ed. Reintegration via mergers and acquisitions then follows

again. Thus, even successful spin-o®s are viewed as transitory phenomena.

Yet, there exist limits to vertical control associated with (re-)integration.

Prat (2002) shows that °at hierarchies with ability-matched teams are dom-

inant in production environments characterized by positive complementari-

ties between specialized tasks. Moreover, °at hierarchies with "up-or-out"-

promotion schemes for experienced managers provide "incentives [...] to

protect, rather than steal, the source of organizational rents" [Rajan and

Zingales (2001b, p. 805)]. The perspective to become owners themselves

limits the exploitation risk and, therefore, enhances the incentives to spe-

1

cialize for young managers. Then, Bhid¶e (2000, p. 139-140, 367-368) again

reports the particular importance of such team work in corporate ventures.

The two examples provided by Prat (2002) further demonstrate the piv-

otal role of adequate recruiting. In fact, "unusual judgement or perceptive-

ness" in employee selection characterizes the successful entrepreneur [Bhid¶e

(2000, p. 108)]. Case studies show that - during the growth phase following

the immediate start-up period - recruiting experienced managers from es-

tablished ¯rms constitutes a key success factor [Bhid¶e (2000, p. 282-288)].

At the same time, corporate policies in well-established ¯rms to "recruit

individuals who will ¯t their culture and norms to promote cooperation and

team work [...] limit their ability to employ the best individual for a given

task [...]" [Bhid¶e (2000, p. 324)]. Hence, entrepreneurial spin-o®s constitute

a persistent response to the established corporations' failure in organizing

team-work in human capital-intensive industries.

Within the new spin-o®s, stock ownership or stock option plans then

serve as selection devices [Bhid¶e (2000, p. 87, 200)]. Rajan and Zingales

(2001b, p. 832) add that ownership must be wide-spread throughout these

new ¯rms. Concentrated control rights would again increase the threat of ex-

propriation for new team members. Thus, the incentives to specialize would

be reduced. According to Audretsch and Thurik (2001), ownership-like

management incentive schemes characterize "entrepreneurial" ¯rms. Fur-

ther, the change from "managed" to "entrepreneurial" ¯rms constitutes the

single most important characteristic associated with the emergence of the

"New Economy". In fact, the past two decades have witnessed a signi¯cant

increase in managerial stock ownership [Holderness et al. (1999)].

Following the Knightian view of entrepreneurship, Kihlstrom and La®ont

(1979, 1983) already demonstrate the existence of a contract equilibrium.

Less risk-averse individuals become risk-taking entrepreneurs who provide

insurance for their more risk-averse employees. Yet, the recent experience

of "New Economy" spin-o®s sheds doubts on the self-selection of individ-

uals as entrepreneurs, respectively employees according to their degree of

risk-aversion. Thus, the increased necessity to compensate poor employee

stock performance in cash has induced additional ¯nancial problems for the

"New Economy" ¯rms [Zingheim and Schuster (2000)]. Moreover, this de-

velopment gives rise to motivation problems for the manager-owners who

formerly received preferential treatment as high-potential employees [Wein-

berg (2001)]. Hence, partnership-like incentive schemes limit the scope of

spin-o®s. Individuals who - either as high-pro¯le employees in established

corporations, or as potential entrepreneurs - are equally risk-averse will de-

mand a compensating risk-premium in order to join a ¯rm in which incen-

tives are provided via ownership.

The current study focuses on the trade-o® between the bene¯ts of ability-

matching and the costs of partnership-like compensation schemes in entrepre-

neurial spin-o®s. It applies the O-Ring production theory introduced by

2

Kremer (1993)

1

. On ¯rst sight, the O-Ring theory only constitutes a partic-

ular example of positive complementarities in organizing team-work. Yet,

while previous work has focussed on the relationship between asset com-

plementarity and the internal organization of ¯rms, the current study ana-

lyzes entrepreneurial activity in terms of a labor market equilibrium. It is

therefore more closely related to Gromb and Scharfstein (2002) and Landier

(2001). However, both studies analyze informational equilibria. Failed ¯rm

founders are not stigmatized whereas project failure within a ¯rm provides

an informative signal concerning employee quality. In contrast, the O-Ring

framework identi¯es individual abilities with probabilities of failing in task-

performance. Thus, the bene¯ts of ability-matching are directly linked to

reductions in project-risk.

The remainder of the study is organized as follows. The next section in-

troduces the basic analytical framework. Section 3 investigates the e®ects of

¯rm organization and risk-aversion given exogenous alternative employment

opportunities. It is shown that the ¯rst-best solution can be implemented by

partnerships of risk-neutral individuals. However, partnerships of risk-averse

individuals induce ine±cient input choices. Section 4 then demonstrates the

existence and characteristics of a competitive industry equilibrium with en-

dogenous separation of entrepreneurial and managed ¯rms. Matched groups

of high-ability individuals found partnerships. Low-ability individuals will

seek employment in managed ¯rms which recruit randomly while o®ering

certain income opportunities. The ¯nal section summarizes and discusses

the results with particular reference to the perceived "volatility" of "New

Economy" ¯rms.

2 The basic O-Ring framework

The following theoretical framework modi¯es the basic O-Ring model in-

troduced by Kremer (1993) only marginally. Thus, consider the expected

revenue function

R = pF (k; n)

"

n

Y

i=1

q

i

#

n (1)

where k refers to physical capital input and n denotes the number of

tasks involved in a particular ¯rm's production. For analytic convenience,

the output price p is normalized to equal unity.

Further, q

i

2 [q

L

; q

H

], with 0 < q

L

< q

H

< 1 and i = 1; :::; n, denotes

the ability of the employee, respectively team member assigned to task i.

Ability directly corresponds to the individual probability of perfect task

1

The term "O-Ring theory" refers to the Challenger-accident which is blamed on the

malfunctioning of a simple o-ring. By analogy, the weakest link in a production chain

determines the team's productivity.

3

performance. More precisely, if the individual assigned to task i malper-

forms, the team as a whole cannot produce positive output. This occurs

with probability [1 ¡

Q

n

i=1

q

i

]. Further, the probability q

i

constitutes an

individual characteristic of the particular team member assigned to task i.

Thus, (1) re°ects a typical team production function. The output of

the team depends on the performance of each team member. In fact, given

the O-Ring framework, the productivity of the team is always governed by

the lowest-quality employee hired. Only the fact that output is completely

destroyed upon malperformance of a single team member may be considered

as an extreme assumption. This approach therefore constitutes a particular

variant of the positive complementarities in production discussed by Prat

(2002)

2

.

Intuitively, F (k; n) then de¯nes output per team member given that all

members perform perfectly. It increases with physical capital employed and

the number of tasks involved in production. Hence, increasing n implies a

technological change towards the production of a more sophisticated variant

of the industry's good, or service. For convenience, let F (k; n) = [k]

®

[n]

(1¡®)

in the following.

Spin-o®s typically produce services which replace a formerly integrated

production. Thus, new bio-technology ¯rms often constitute R&D spin-

o®s founded and controlled by former employees of a pharmaceutical ¯rm.

Also, "New Economy" ICT ¯rms customize standard accounting software,

prepare Internet presentations, or optimize server-client networks for "Old

Economy" ¯rms. In principle these services can be - and, in less sophisticated

variants, are still - produced in integrated ¯rms as well.

The analysis therefore considers a particular labor market for profes-

sional specialists. In equilibrium, they are either employees of integrated

¯rms, or partners in entrepreneurial spin-o®s. For simplicity, abilities are

distributed uniformly over the interval [q

L

; q

H

]. Thus, N(q) = ¹n = 0 mem-

bers of the pool of professionals share the ability q. The analysis abstracts

from explicitly considering the labor-leisure trade-o®. Given voluntary par-

ticipation, all individuals supply one unit of labor inelastically.

Throughout the analysis draws on the following concept of a competitive

industry equilibrium:

De¯nition: If the competition of ¯rms for professionals of di®erent qual-

ity induces an allocation such that

a) the residual expected pro¯t in all expected pro¯t-maximizing ¯rms equals

zero,

2

Positive complementarities can be associated with super-modular revenue functions.

However, the more general concept of super-modularity does not require that the revenue

function is at least twice di®erentiable. Compare the discussion in Prat (2002).

4

b) and all individuals of a given quality q 2 [q

L

; q

H

] obtain an identical

expected utility level either as members of a partnership maximizing

the expected utility of their partners, or being employed by an expected

pro¯t-maximizing ¯rm,

this allocation is said to constitute a competitive industry equilibrium.

Given that the two types of ¯rms - partnerships and expected pro¯t-

maximizing ¯rms - coexist, a separating competitive industry equilibrium

must further satisfy that

c) (i) no current member of a partnership prefers to be employed by an

expected pro¯t-maximizing ¯rm, and (ii) no group of current employees

of expected pro¯t-maximizing ¯rms prefers to found a new partnership.

The next section serves to prepare the equilibrium analysis by investi-

gating the optimal input decisions associated with ¯rm type. Only for this

purpose, let V = 0 then denote an exogenous reservation income associated

with alternative employment. Also, all ¯rms are able to select individual

workers to organize their production teams. Thus, abilities are publicly

observable and the ¯rms' recruitment decisions can be perfectly enforced.

These assumptions allow to isolate the e®ects of ¯rm organization and risk-

aversion on the e±ciency of input choices. They will be removed in section

4. The separating reservation income is then determined endogenously in

labor market equilibrium.

3 Firm organization and risk-aversion

3.1 Expected pro¯t-maximizing ¯rms

In order to construct a benchmark case for further analysis, consider the

standard expected pro¯t-maximizing ¯rm. Its residual claimant solves

Max

(fq

i

g;n;k)

¼(fq

i

g ; k; n) = R (fq

i

g ; n; k) ¡

n

X

i=1

w(q

i

) ¡ rk (2)

where w(q

i

), with i = 1; ::; n, denotes the wage income o®ered to the

employee assigned to task i. The expression fq

i

g then refers to the ability-

pro¯le of the ¯rm. Also, r is the rental rate of capital in a perfectly com-

petitive capital market.

It can now be shown:

Proposition 1 Suppose the reservation wage V is su±ciently low to allow

for positive production. Also, there exist only expected pro¯t-maximizing

¯rms in the industry.

5

(a) Then, with observable individual abilities, there exists a competitive

industry equilibrium such that all ¯rms employ a single ability-type only.

Moreover, the corresponding identical ability level of the team members de-

termines a unique optimal team size and capital input level for each ¯rm.

The optimal team size increases in the team members' identical ability level.

The shares of revenue devoted to repaying capital and rewarding labor are

given by the production elasticities ®, respectively (1 ¡ ®).

(b) The allocation implemented by the competitive industry equilibrium

is e±cient.

Proof. To begin with, note that, given (2), an expected pro¯t-maximizing

¯rm will not be induced to change its current ability pro¯le, if

@¼(fq

i

g ; k; n)

@q

i

= 0 = (3)

F (k; n)

2

4

Y

j6=i

q

j

3

5

n ¡

dw(q

i

)

dq

i

; 8i = 1; ::; n

Now, assume that, in equilibrium, ¯rms employ a single ability-type

only. The expected pro¯t of a ¯rm hiring employees of ability q can then be

obtained as

¼(q) = F (k; n)q

n

n ¡ w(q)n ¡ rk (4)

If an interior optimum exists, it is characterized by the ¯rst-order con-

ditions

®k

(®¡1)

n

(1¡®)

q

n

n = r (5)

and

[2 ¡ ® + log(q)n] k

®

n

(1¡®)

q

n

= w(q) (6)

Given that only expected pro¯t-maximizing ¯rms exist in equilibrium,

condition b) of the de¯nition of the competitive industry equilibrium re-

quires the existence of a wage-schedule which unambiguously assigns a wage-

payment w(q) to all individuals of ability q. If production teams are homo-

geneous, the optimality of the recruiting decisions according to (3) implies

that this schedule must satisfy

F (k; n)q

(n¡1)

n =

dw(q)

dq

(7)

Then, if the ¯rms' equilibrium choices of capital input and team size

actually satisfy the ¯rst-order conditions (5) and (6), rearranging condition

(5) reveals that

k

¤

=

µ

®q

n

¤

r

¶

1

1¡®

(n

¤

)

2¡®

1¡®

(8)

6

with superscripts "¤" indicating optimal values. Inserting from (8) into

(7) yields

dw

¤

(q)

dq

=

³

®

r

´

®

1¡®

(n

¤

)

1

1¡®

q

³

n

¤

1¡®

¡1

´

n

¤

=) w

¤

(q) = (1 ¡ ®)

³

®

r

´

®

1¡®

(n

¤

)

1

1¡®

q

³

n

¤

1¡®

´

+ c (9)

The constant of integration c must equal zero. In the limit q = q

L

! 0, it

re°ects the wage o®ered when organizing teams consisting of professionals

with zero quality. However, such teams would produce zero output with

certainty. Thus, they cannot o®er positive wage-income.

With c = 0, (9) then implies

n

¤

w

¤

(q) = (1 ¡ ®)(k

¤

)

®

(n

¤

)

(1¡®)

q

n

¤

n

¤

= (1 ¡ ®)R

¤

(10)

since ®

h

2¡®

1¡®

i

+ (1 ¡ ®) =

1

(1¡®)

. This proves that the total wage-bill

in each ¯rm equals the share (1 ¡ ®) of revenue. Moreover, according to

(5), the rental payment for capital rk

¤

amounts to the share ® of revenue in

each of these ¯rms. Thus, as required by condition a) of the de¯nition of a

competitive industry equilibrium, residual expected pro¯ts equal zero.

Further, inserting from (10) into (6) implies

1

n

¤

= ¡ log(q) (11)

Thus, the optimal team size is increasing in the ability level of the team

members. Interpreting this result, note that the function nq

n

attains a

unique maximum for

1

n

¤

= ¡ log(q).

Next, investigating the second-order conditions for the ¯rm's optimiza-

tion problem, reveals that

@

2

¼

¤

(q)

@k@k

= ® (® ¡ 1) (k

¤

)

(®¡2)

(n

¤

)

(1¡®)

q

n

¤

n

¤

=

¡ (1 ¡ ®) r

k

¤

< 0 (12)

@

2

¼

¤

(q)

@k@n

= (1 ¡ ®) ®(k

¤

)

(®¡1)

(n

¤

)

(1¡®)

q

n

¤

=

(1 ¡ ®)r

n

¤

> 0 (13)

@

2

¼

¤

(q)

@n@n

= ¡(k

¤

)

®

(n

¤

)

¡®

q

n

¤

=

¡rk

¤

(n

¤

)

2

µ

1 + ® (1 ¡ ®)

®

¶

< 0 (14)

upon utilizing (11) and (5). Thus,

¯

¯

¯

¯

@

2

¼

¤

(q)

@k@k

@

2

¼

¤

(q)

@k@n

@

2

¼

¤

(q)

@k@n

@

2

¼

¤

(q)

@n@n

¯

¯

¯

¯

=

r

2

(1 ¡ ®)

(n

¤

)

2

®

> 0 (15)

7

Given the proposed characterization of the industry equilibrium, (n

¤

; k

¤

)

thus constitute unique optimal choices for ¯rms employing homogeneous

teams consisting of type-q individuals.

Production will actually take place in ¯rms characterized by team ability

q such that

w

¤

(q) = V (16)

or some q 2 [q

L

; q

H

]. By virtue of (9) w

¤

(q) is monotonically increasing in

q. Hence, positive production in this industry can be assured by assuming

w

¤

(q

H

) > V = w

¤

(q

L

). Then, q

¤

2 [q

L

; q

H

[ - de¯ned by w

¤

(q

¤

) = V

- characterizes the competitive labor market equilibrium. All professionals

exhibiting abilities q = q

¤

will be employed in the industry, while individuals

of quality q < q

¤

will prefer the alternative employment.

So far, it has still be assumed that, in the competitive industry equi-

librium, the ¯rms select teams which are homogeneous with respect to the

team members' abilities. However, note that the increasing wage-schedule

derived in (9) now also implies that (3) actually characterizes an optimal

choice of the i ¡ th team member's ability level.

Intuitively, since the LHS of (3) is monotonically increasing in

h

Q

j6=i

q

j

i

,

¯rms which have hired the highest-quality employees for the ¯rst (n ¡ 1)

tasks, will always bid most in order to ¯ll the n-th position in the team. This

implies that a ¯rm which has decided to recruit the top-quality employee

for one task will recruit only such top-qualities for all tasks.

Similarly, a ¯rm which has decided to begin hiring by recruiting some

medium-quality professional cannot successfully compete for higher-quality

individuals when ¯lling other positions. However, it will succeed in attract-

ing other employees of the same quality when competing with ¯rms which

have started hiring lower-quality employees.

Thus, given the wage schedule w

¤

(q) provided in (9), the ¯rms' optimal

recruitment decisions described by (3) imply that each ¯rm will employ a

single ability type only. Then, (n

¤

(q); k

¤

(q)) as characterized by (8) and (11)

constitute the corresponding unique expected pro¯t-maximizing choices in

¯rms with teams consisting of individuals with identical ability q. Hence,

the competitive industry equilibrium introduced in part a) of Proposition 1

exists.

For expositional reasons, the proof that this equilibrium implements an

e±cient allocation is relegated to the Appendix.

3

3

Recall that, by assumption, condition c) de¯ning a separating competitive industry

equilibrium does not apply to the case made in Proposition 1. While the proof of the

proposition is then constructive, it has also been particularly organized to allow for the

subsequent use of the ¯rst-order conditions for the expected pro¯t-maximing ¯rm's opti-

mization problem. Thus, there may be other, and certainly more rigorous ways to prove

Proposition 1.

8

Obviously, the e±ciency-property of this competitive equilibrium moti-

vates its further use as a benchmark case. When referring to this solution,

the input choices (k

¤

(q); n

¤

(q)) will be denoted ¯rst-best in the following.

In addition to the characteristic features noted in Proposition 1, also

recall that larger teams of superior ability produce more sophisticated vari-

ants of the industry's commodity or service. Hence, there exists a multitude

of ¯rms o®ering services of di®erent sophistication in competitive industry

equilibrium. According to (9), small di®erences in team abilities then yield

rather large income di®erentials across ¯rms. At the same time, there is no

wage-di®erentiation within the ¯rm.

3.2 Risk-neutral partnerships

Contrasting with the assumption of pro¯t maximization utilized above, spin-

o®s typically constitute entrepreneurial ¯rms. If not organized as formal

partnerships, they distribute a large fraction of their economic pro¯t among

their employees via stock or stock option plans. Hence, it is appropriate to

assume that such ¯rms are self-managed by the members of the production

team. Then, given that individuals are risk-neutral, they rather maximize

surplus per team member. Thus, they solve

Max

(fq

i

g;n;k)

R (fq

i

g ; n; k) ¡ rk

n

(17)

Note, however, that

d

2

[R (fq

i

g ; n; k) =n]

dq

i

d

h

Q

j6=i

q

j

i

> 0 (18)

as well. Hence, consider two professionals each founding such a part-

nership ¯rm and one characterized by higher ability than the other. The

superior ability founder will always be able to o®er a more attractive part-

nership for other high-ability professionals. This remains to be true as the

production teams grow by attracting even more partners. In labor mar-

ket equilibrium entrepreneurial ¯rms will therefore also consist of partners

sharing an identical ability level.

Replacing [

Q

n

i=1

q

i

] by q

n

when solving (17), di®erentiating with respect

to capital k restates (5). The ¯rst-order condition with respect to the num-

ber of tasks n further reveals

(1 ¡ ®)k

®

n

¡®

q

n

+ k

®

n

(1¡®)

q

n

log(q) +

rk

n

2

= 0

=) [1 + nlog(q)] = 0 (19)

9

upon substituting from (5). Again, the optimal choice of technology

yields team size n

¤

(q). Obviously, this also implies that the capital de-

manded by the ¯rms is given by k

¤

(q). The second-order su±cient conditions

can be obtained as shown in (12) to (15) above.

Recall that the total wage bill in the pro¯t maximizing case always equals

the share (1 ¡ ®) of expected revenue. With risk-neutral team members,

the wage for employees in such ¯rms is thus equal to the expected surplus

net of capital rental payments. Obviously, this exactly coincides with the

individual expected income generated in an entrepreneurial ¯rm. Hence,

given the results above, the ability level q

¤

also satis¯es

(1 ¡ ®) [k

¤

(q

¤

)=n

¤

(q

¤

)]

®

h

(q

¤

)

n

¤

(q

¤

)

n

¤

(q

¤

)

i

= V (20)

Thus, without further proof, it follows:

Proposition 2 Again, assume that individual abilities are observable. How-

ever, suppose that there exist only ¯rms organized as partnerships of risk-

neutral individuals in the competitive industry equilibrium. Then, this equi-

librium can be characterized as derived in Proposition 1 for the case when

there exist only expected pro¯t-maximizing ¯rms.

Given the particular O-Ring team production function (1), this equiva-

lence result should be obvious. Rewarding factor inputs according to their

marginal revenue implies that expected residual pro¯ts equal zero. With

risk-neutral individuals, the institutional structure of the ¯rm only deter-

mines the means to distribute income. It does not a®ect the realized income

distribution.

Further, recalling that the distribution of abilities over the pool of pro-

fessionals is uniform, there exist

R

1

q

¤

h

¹n

n

¤

(q)

i

dq of such ¯rms in industry equi-

librium. Due to (11) and (19) ¯rm size increases with team quality. Thus,

the number of ¯rms characterized by a particular team quality increases

with decreasing team quality. It follows that small increases in the reserva-

tion income V induce the closing of a rather large number of ¯rms in the

industry

4

.

3.3 Partnerships of risk-averse individuals

Let the members of the industry's pools of professionals now be risk-averse.

Hence, they maximize their expected utility. Instantaneous preferences are

4

Alternatively, suppose that the pdf of abilities is single-peaked. Given normally or

log-normally distributed abilities - as often assumed - this result is even reinforced as long

as the industry attracts professionals with above-average abilities. Moreover, in this case

a small increase of V also induces a rather signi¯cant migration of professionals from the

industry into alternative occupations.

10

characterized by a utility function U(y), with U

0

(y) > 0 and U

00

(y) < 0 for

incomes y > 0. Of course, assuming that there only exist managed ¯rms

which maximize expected pro¯ts, all results of section 3.1 can be retained.

However, the manager-owners of entrepreneurial ¯rms will maximize

EU =

"

n

Y

i=1

q

i

#

U(Y + F (k; n) ¡

rk

n

) +

Ã

1 ¡

"

n

Y

i=1

q

i

#!

U(Y ¡

rk

n

) (21)

Introducing exogenous income Y > 0 in (21), the analysis will exclusively

focus on interior solutions. Such solutions can be ensured by assuming that

U(y) satis¯es the usual Inada-conditions.

If it is ever bene¯cial to found such ¯rms, they will consist of teams of

individuals characterized by identical abilities again. This follows from the

fact that @EU=@

h

Q

j6=i

q

j

i

> 0 for F(k; n) > 0. Thus, high-ability individu-

als will always ¯nd it more attractive to join partnerships already consisting

of higher-quality team members in the ¯rst (n¡1) tasks. Replacing [

Q

n

i=1

q

i

]

by q

n

in (21) then yields the ¯rst-order conditions

q

~n

U

0

(Y + F (

~

k; ~n) ¡

r

~

k

~n

)

h

®

~

k

(®¡1)

~n

(1¡®)

¡

r

~n

i

= (1 ¡ q

~n

)U

0

(Y ¡

r

~

k

~n

)

r

~n

(22)

and

¡q

~n

log(q)

"

U(Y + F (

~

k; ~n) ¡

r

~

k

~n

) ¡ U(Y ¡

r

~

k

~n

)

#

= q

~n

U

0

(Y + F (

~

k; ~n) ¡

r

~

k

~n

)

"

(1 ¡ ®)

~

k

®

~n

¡®

+

r

~

k

~n

2

#

(23)

+(1 ¡ q

~n

)U

0

(Y ¡

r

~

k

~n

)

r

~

k

~n

2

where (

~

k; ~n) denote the respective optimal choices in this case.

Substituting from (22) into (23) implies

¡log(q)

U(Y + F (

~

k; ~n) ¡

r

~

k

~n

) ¡ U(Y ¡

r

~

k

~n

)

U

0

(Y + F (

~

k; ~n) ¡

r

~

k

~n

)

=

~

k

®

~n

¡®

(24)

Concavity then implies that

¡log(q)~n < 1 (25)

Thus, partnerships managed by risk-averse team members are ceteris

paribus smaller than risk-neutral partnerships. Rearranging (22) it also

follows

11

~

k

(®¡1)

~n

(1¡®)

~nq

~n

=

r

®

"

q

~n

+ (1 ¡ q

~n

)

U

0

(Y ¡

r

~

k

~n

)

U

0

(Y + F (

~

k; ~n) ¡

r

~

k

~n

)

#

(26)

Substituting for r from (5) above,

~

k

(®¡1)

~n

(1¡®)

~nq

~n

= (k

¤

)

(®¡1)

(n

¤

)

(1¡®)

n

¤

q

n

¤

"

q

~n

+ (1 ¡ q

~n

)

U

0

(Y ¡

r

~

k

~n

)

U

0

(Y + F (

~

k; ~n) ¡

r

~

k

~n

)

#

(27)

Recall from Proposition 1 that, for a given team ability level q, nq

n

is

maximized by setting n = n

¤

. Thus, n

¤

q

n

¤

> ~nq

~n

, 8q 2 [q

L

; q

H

]. Risk-averse

partners not only require an expected income su±cient to cover their share

of capital costs. In addition, they must be compensated for risk associated

with paying the capital rental costs even if production fails. Consequently,

the cost of attracting partners is higher than in the risk-neutral case. This

implies that the size of the production team falls short of maximizing the

expected team output.

Also, due to decreasing marginal utilities, the last term in the RHS of

(27) is greater than one. Thus, n

¤

> ~n implies (k

¤

=n

¤

) > (

~

k=~n) and k

¤

>

~

k.

Let ~y(q) then denote the certainty equivalent income of such risk-averse part-

ners self-managing a ¯rm of team quality q. Hence, ~y(q) = U

¡1

(EU(q; ~n;

~

k)).

De¯ning ~w(q) = ~y(q) ¡ Y as the respective certainty equivalent return to

participating in the partnership, it is also immediately clear that

~w(q) <

~

k

®

~n

(1¡®)

q

~n

¡

r

~

k

~n

(28)

< (k

¤

)

®

(n

¤

)

(1¡®)

q

n

¤

¡

rk

¤

n

¤

= w

¤

(q)

for all q 2 [q

L

; q

H

]. The second inequality follows from the allocative

distortions associated with maximizing expected utility.

Finally, note that

@EU(q; ~n;

~

k)

@q

= ~nq

(~n¡1)

"

U(Y + F (

~

k; ~n) ¡

r

~

k

~n

) ¡ U(Y ¡

r

~

k

~n

)

#

> 0 (29)

for all q > 0. Again, assume that there exists q = ~q 2 [q

L

; q

H

[ such that

EU(~q; ~n(~q);

~

k(~q)) = U(Y + V ). Then, production will take place. However,

only individuals of ability q = ~q will actually found entrepreneurial ¯rms.

The inequalities (28) then yield ~q > q

¤

.

Summarizing the analysis, it therefore follows:

12

Proposition 3 Ceteris paribus, risk-aversion induces less ¯rms founded as

partnerships in competitive industry equilibrium. The ¯rms actually founded

produce less sophisticated services with ine±ciently small teams. Moreover,

capital input and capital per team member is ine±ciently low.

Else, the equilibrium with risk-averse partnerships shares the proper-

ties derived above already. Small variations in team quality again induce

large expected income di®erentials between the partnerships. Also, a small

increase in the relative attractiveness of alternative jobs induces a rather

large reduction of the number of ¯rms in the industry. Due to smaller ¯rm

sizes, the latter e®ect is even reinforced by introducing risk-aversion.

4 Endogenous separation of managed and entre-

preneurial ¯