Small Business Economics (2008) 30:111 126 Ó Springer 2007
DOI 10.1007/s11187-006-9023-0
Entrepreneurship in the Theory
of the Firm Philip E. Auerswald
ABSTRACT. This paper develops micro-economic founda- for a theory of entrepreneurship and growth,
tions for a theory of entrepreneurship and growth, focusing
focusing on innovation and opportunity as
on innovation and opportunity as intermediate linkages be-
intermediate linkages between the two.1 While I
tween the two. Expanding upon points of tangency between
will use the generic term   entrepreneurs 
Schumpeter and Coase, the paper argues that transactions
throughout this paper, I am primarily concerned
costs are the glue that holds together entrepreneurial   new
combinations.  Technological/organizational complexity of with the Schumpeterian notion of the entrepre-
production is defined as the extent to which a technical deci-
neur as an innovator, as contrasted with the
sion by one unit within the firm affects the productive effi-
Kirznerian (alternately, neo-Austrian) notion of
ciency of other units. Where decreasing transactions costs tend
the entrepreneur as the seeker of arbitrage
to pull incumbent organizations apart, the possession of diffi-
opportunities, or the Knightian (alternately,
cult to imitate production practices by the same organizations
keeps them together. The dissolution of incumbent firms neoclassical) notion of the entrepreneur as the
creates opportunities for entrepreneurs; the prospect of
bearer of risk.2
Schumpeterian rents provides the incentive to realize those
The relationship between entrepreneurship
opportunities.
and growth is the subject of a growing literature.
Acs and Audretsch (1987, 1990) and Audretsch
KEY WORDS: complexity, entrepreneurship, growth,
intrafirm externalities, opportunity, production recipes, (1995), set the stage by providing empirical
spillovers, theory of the firm.
evidence of the significant role of small firms in
generating technological innovations. Acs
JEL CLASSIFICATIONS: D20, D21, D23, L26, O14,
(1992) went further to sketch multiple pathways
O30, O31.
by which entrepreneurial activity drives eco-
nomic growth. Schmitz (1989) offered a formal
model of this process in which the entrepreneur
1. Introduction
is represented as an imitator of incumbents.
More recently, Acs and Armington (2004)
Growth theory is built upon the neoclassical
empirically assessed the role of entrepreneurs in
theory of the firm. An attempt to understand the
promoting knowledge spillovers and growth at
relationship between entrepreneurship and
the scale of a city. Acs and Varga (2005) and Stel
growth therefore naturally begins with the
et al. (2004) both employed data from the
question: Where does entrepreneurship 
Global Entrepreneurship Monitor (GEM)
particularly Schumpeterian entrepreneurship 
project to study the relationship between entre-
fit into the theory of the firm? This paper is an
preneurship and growth at the scale of the
effort to develop micro-economic foundations
nation. Michelacci (2003) and Acs et al. (2006)
explored the role of entrepreneurs as knowledge
  implementors  or   filters,  respectively, and
Final version accepted on October 2006 the manner in which those functions drive eco-
nomic growth. Weitzman (1998) and Michelacci
Philip E. Auerswald
(2003) presented models in which the ultimate
School of Public Policy
limits to growth will lie not in the generation of
George Mason University
inventions and new fundamental knowledge that
Fairfax, VA,
  spills overs  from one part of the economy to
22030-4444, USA
E-mail: [e-mail] another, but rather in the availability of
112 Philip E. Auerswald
Schumpeterian entrepreneurs to guide the con- of   a large number of parts that interact in non-
version of those inventions and new knowledge simple ways ... [such that] given the properties of
into practice through innovation. the parts and the laws of their interaction, it is
Where these recent papers (with the exception not a trivial matter to infer the properties of the
of Weitzman, 1998) have taken the macroeco- whole.  In the same spirit, I define the techno-
nomic literature as the point of the departure,3 I logical/organizational complexity of production
start with role of the entrepreneur in the theory as the extent to which a technical decision by
of the firm, and sketch potential causal path- one unit within the firm affects the productive
ways   from the ground up.  In a spirit similar efficiency of other units. The modeling structure
to Foss and Klein (2005), I argue that a sub- is based upon Kauffman and Levin s (1987)
stantial and instructive overlap exists between NK model of   fitness landscapes,  applied pre-
the respective theories of the firm of Schumpeter viously to production theory, organizational
(1912) and Coase (1937) as each relates to theory, and industrial economics but until now
entrepreneurship. I argue that the two theories not to the study of entrepreneurship.6 I conjec-
considered jointly are consistent with a charac- ture that the complexity of production affects
terization of entrepreneurs as seekers of solu- firm learning and imitation  and thus the
tions of hard combinatorial problems  creators magnitude of Schumpeterian profits  in two
of   new combinations  in a world where only a related ways. Both incumbents and new entrants
few of all possible combinations improve on faced with more complex production tasks have
existing practice.4 a relatively difficult time finding improvements
To link the Coasean theory of firm to entre- to current methods. At the same time, those
preneurship (and ultimately to growth), I need firms that do find   solutions  to difficult pro-
to be able to differentiate formally the sort of duction problems are not easily imitated, as
  hard problems  that I claim are solved by small errors in   copying  by entrants will result
entrepreneurs from easy problems whose reso- in large changes in outcomes (measured in terms
lution does not create opportunity for of efficiency). In this way the magnitude of
Schumpeterian profits. Informally, this is a technological complexity is a core parameter in
familiar distinction. Both academics and policy- the economy, determining the magnitude of
makers routinely differentiate two sorts of incentives to convert inventions into innova-
opportunity entrepreneurship:   high-tech,  tions, and thus the link between entrepreneur-
presumably involving innovation, and   low- ship and growth via opportunity.
tech,  involving only the application of known The organization of the paper is as follows.
and little-changing techniques.5 However, the In Section 2, I briefly describe points of
terms   high-tech  and   low-tech  can be con- tangency between Coase (1937, 1960) and
fusing. A local print shop might be considered a Schumpeter (1912) relating to entrepreneurship
  high-tech  firm to the extent that its activities in the theory of the firm. In Section 3, I
integrally involve the use of complicated tech- introduce the production recipes model of
nologies. However, the organization itself is not technological innovation. In Section 4, I
complex, and its practices are easily imitated. describe two limiting cases of innovation:
Viewed from the standpoint of economic imitation of an incumbent by a   spin-off  firm
fundamentals, the problem solved by a print and   innovation-by-doing.  I differentiate both
shop owner is a simple one as compared with from invention. In Section 5, I conclude by
those solved by an aircraft manufacturer, a describing three directions for empirical work
biotech firm, or a large retail operation (such as suggested by the paper: constructing theoreti-
Wal-Mart). cally derived measures of technological/
My approach therefore is not to focus on the organizational complexity to differentiate
technology in use within a firm, but rather on   high-tech  from   low-tech  firms and indus-
the technological/organizational complexity of tries; better understanding the respective
the firm taken as a whole. Simon (1969, p. 195) dynamics of   high-tech  and   low-tech 
describes complex systems as being constituted industries; and studying the manner in which
Entrepreneurship in the Theory of the Firm 113
the internal structure of firms is endogenously There is a combination when transactions
determined in the process of market compe- which were previously organised by two or
tition, alternately creating and eliminating more entrepreneurs become organised by one.
possibilities for new firm formation and growth. This becomes integration when it involves the
organisation of transactions which were pre-
viously carried out between the entrepreneurs
2. Linking Schumpeterian and Coasean theories
on a market. A firm can expand in either or
of the firm
both of these ways.
According to Coase (1937, p. 390), the task of
Coasean entrepreneurs thus create   new
theorists of the firm is   to attempt to discover
combinations,  in the Schumpeterian sense,
why a firm emerges at all in a specialized
by either organizing within a new firm activities
exchange economy.  At the outset, a link to
previously carried out by different firms, or
entrepreneurship is suggested: asking why   a
expanding the scope of an existing firm to incor-
firm  emerges in a market economy is, after all,
porate activities previously related through the
not very different from asking why or under
market.
what circumstances a new firm emerges. Coase s
answer focuses on the cost of using the price
system to organize production7 as compared
with the alternative of managing transactions
3. Production recipes and intrafirm externalities
within a newly created firm:
What is the nature of these   new combinations 
that entrepreneurs create? They are combina-
Outside the firm, price movements direct
tions of particular activities that jointly consti-
production, which is coordinated through a
tute the organization as a whole    routines  in
series of exchange transactions on the mar-
the language of Nelson and Winter (1982),10
ket. Within a firm these market transactions
  organizational capabilities  in the language of
are eliminated, and in place of the compli-
Chandler (1990, 1992),11 and   production
cated market structure with exchange
recipes  in the language of Winter (1968) and
transactions is substituted the entrepreneur-
Auerswald et al. (2000).12
coordinator, who directs production. (Coase,
In this paper, I employ   recipes  as the term
1937, p. 388)
of choice to relate the entrepreneurial creation
of new combinations to production theory:13
For a given production activity, if the cost of
creating a new firm is lower than that of using
creating new combinations()
the price system, an entrepreneurial opportunity
creating new production recipes:
exists. If an entrepreneur acts to realize this
opportunity, s/he will create a new firm. The Formally, denote the recipe by x. The recipe x
scope of the firm will be determined by the costs is comprised of a set of N distinct activities each
of relevant transactions.8 Where further oppor- carried out in a particular way:
tunities exist, the entrepreneur will expand the
xź�x1;. . .;xi;. . .;xN�;
number of transactions within the firm, enlarg-
ing span of control, to realize economies of wherexi represents the instructions for activity i.14
scope:   As more transactions are organized by Any recipe that has been tried is associated
an entrepreneur, it would appear that the with a particular level of organizational capital
transactions would tend to be either different in h. As in Prescott and Visscher (1980), organi-
kind or in different places.  9 In the process of zational capital refers to   information as an
expanding the scope of the firm, the entrepre- asset of the firm   the sum of the knowledge,
neur diversifies the firm s activities. much of it likely tacit, involved in produc-
Coase (1937, p. 397) uses the terms   combi- tion.15 Organizational capital collapses the
nation  and   integration,  respectively, to refer details of the firm s internal activities into a
to horizontal and vertical mergers: single number. It is the direct analog of   fit-
114 Philip E. Auerswald
ness  in an evolutionary model. In a linear treatment consistent with the above discussion of
specification, the value of organizational capi- Coase (1937, 1960), e would be determined
tal is given as h endogenously by a dynamic process of entrepre-
neurial entry and exit that would create distinct
N
X
technological/organizational types at the firm
h�x�ź hi; i�xi�;
level. Different firms in the same industry may be
iź1
characterized by different magnitudes of intra-
where hi, -i (xi) is the contribution to organiza-
firm externalities. To focus attention on the
tional capita of activity xi when carried out in a
manner in which different levels of technological/
particular way, conditional on the manner in
organization complexity affect opportunity and
which the other activities (represented by the
growth, in this paper I assume that e is exogenous
superscript   )i  ) are carried out.16
 determined by the engineering and other tech-
To emphasize: The organizational capital
nical principles underlying production in a given
represented in a given activity depends on the
industry. With this assumption the parameter e
chosen instructions for that activity and possibly
can serve to distinguishing one industry from
on the instructions for some (but not necessarily
another. Three types of industries are possible:
all) of the other activities. Why? Coase (1960)
provides the motivation: when entrepreneurs act
" e =1 (zero intrafirm externalities). One limit-
to create or expand a firm in the manner described
ing case is that in which there are no intrafirm
above they   internalize externalities,  incorpo-
externalities: A change in the production
rating into the firm precisely those activities for
method employed by one of the N production
which contracts are difficult to negotiate, for
units within the firm affects the efficiency only
example due to multiple contingencies or high
of that single unit. Each unit is   linked  to
degrees of intrinsic uncertainty. This is critical. If
exactly one unit: itself. The average level of
the firm s internal resources can be allocated more
interconnection of the firm s production units,
effectively through the market, then no function
e, therefore is equal to 1.
exists for the   entrepreneur-coordinator  to
" 1whom Coase refers; presumably in a competitive
e such that 1 < e Ł N characterize production
environment he will earn zero return for his
over a range of industries where a change in
efforts.
the production method by one of the N pro-
The internalization of externalities, which is
duction units in the firm affects the efficiency
the premise of the existence of the firm to begin
of that unit, as well as some, but not all, of
with, means that distinct units of the firm brought
the other N)1 production units. In this range
together by the entrepreneur are inter-dependent.
of industries the level of complexity of
Finding the optimal configuration of a firm s
production (the average linkage of the firm s
activities is much like finding the solution to a
production units) is increasing in e. The argu-
Rubik s cube puzzle: the creation, expansion, and
ment above suggests that most industries fall
management of the firm is made difficult by the
in this category.
fact that modification to the practices of one unit
" e = N (total intrafirm inter-connection). The
will affect the effectiveness of other units. Indeed,
limiting value e = N represents the case of
if one particular unit of a firm is not linked to any
maximal complexity: a change in the produc-
other via such   intrafirm externalities,  then we
tion method by one of the N production units
can reasonably wonder why that unit is part of the
within the firm affects not only that unit, but
firm to begin with (rather than, for example,
all of the other production units as well.
acting as an outside contractor). Entrepreneurs
and firm managers are thus typically charged with
Figure 1, derived from Ulrich and Pearson
solving complex coordination problems.17
(1998), provides an example. Here the activities in
Specifically, denote by e the magnitude of in- an enterprise producing coffee makers are iden-
trafirm externalities within a firm. This is the key
tified as assembly, sheet metal cutting, and plastic
parameter in the paper.18 In a more complete
moulding. As there are three activities, N=3. The
Entrepreneurship in the Theory of the Firm 115
even if the knowledge is codified: while codified
knowledge may be non-rivalrous, in most cases it
is either excludable (patents, documents pro-
tected by trade secret) or not directly applicable to
production (basic research papers). The excep-
tional cases of published, unprotected   designs 
are not likely to offer significant opportunities for
Schumpeterian entrepreneurs unless combined
with other information in novel, and not easily
imitable, ways.20 Furthermore, patent protection
is available to innovators in all industries, yet
significant inter-industry differences exist in the
extent to which patents allow for persistence of
profits. As Henderson et al. (1999) observe:
Figure 1. An example of intrafirm externalities: N =3,
e =2.
[R]apid imitation of new drugs is difficult in
pharmaceuticals for a number of reasons. One
nature of the linkages between the activities is
of these is that pharmaceuticals has historically
illustrated in the figure. While here conjectured,
been one of the few industries where patents
they are potentially discoverable by empirical
provide solid protection against imitation.
study. In this example, the manner in which sheet
Because small variants in a molecule s structure
metal cutting and plastic molding take place both
can drastically alter its pharmacological prop-
have an effect on the efficiency of assembly. This
erties, potential imitators often find it hard to
accounts for two intrafirm external effects, or
work around the patent. Although other firms
linkages. The manner in which assembly take
might undertake research in the same thera-
place does not affect efficiency outcomes for sheet
peutic class as an innovator, the probability of
metal cutting. However, in this example, assem-
their finding another compound with the same
bly does affect plastic moulding  for example,
therapeutic properties that did not infringe on
because of physical proximity of machinery. This
the original patent could be quite small.
is a third intrafirm linkage. By definition, each
activity is   connected  to itself, which adds three
With regard to codified knowledge that is par-
more intrafirm linkages. The total number of in-
tially excludable, a critical issue is the extent to
trafirm linkages is six. Consequently, e, the aver-
which partial imitation, or copying, preserves
age number of intrafirm external effects, or
the quality of the original. In many, perhaps the
6
linkages, is ;or 2.
majority, of economically important contexts it
3
will not.
4. Two limiting cases of innovation In this light, consider the actions of a new
entrant in a sub-industry defined around a single
4.1. Imitation
good with well-defined, uniform characteristics.
I have detailed above how the existence of The new entrant can either
intrafirm externalities is directly implied by Coase
(1937, 1960)  the fundamental framework in " imperfectly imitate the incumbent, inadver-
economics for understanding the theory of the tently altering a certain number, denoted by
firm. The presence of intrafirm externalities sug- d, of the N activities in the incumbent s pro-
gests that the transfer from one firm to another of duction recipe;
knowledge regarding production  the essence of " differentiate itself by innovating new approaches
the concept of   instructions  that is the core of to d of the N activities in the recipe; or
Romer (1986, 1990)  is far more likely to be " undertake some combination of both ap-
costly and subject to errors than it is to   spill- proaches, leading to changes in d of the N
over  costlessly between firms.19 The same is true activities in the recipe.
116 Philip E. Auerswald
i
The parameter d is thus the measure of either the where the u  s are i.i.d. random variables drawn
extent of imperfections in imitation, the scope from a distribution g (u) with mean l which is
of search using existing practice as a point of common knowledge to all firms.
reference, or a combination of both. Which of The first term on the RHS of equation 1
these three options holds is less significant than represents the component of the spin-off firm s
the observation that, in most cases, the entre- initial stock of organizational capital (or effi-
preneurial new entrant will be either unwilling ciency) that is unaffected by the imperfect
or unable to copy perfectly an incumbent s imitation. This unaffected component roughly
N e
production recipe. In the case where d is sys- represents a fraction of the firm s total effi-
N
tematically large relative to N, there is little ciency level. Note that the fraction of the firm s
transferability of knowledge from the incumbent efficiency that is unaffected by the imperfect
to the new entrant for the trivial reason that the imitation is decreasing in the complexity of
entrant essentially ignores or is unable to grasp production.
the existing organizational knowledge in the The second term on the RHS of equation 1
industry. represents the contribution to the spin-off firm s
Without ruling out the possibility of   radical stock of organizational capital (or efficiency) of
innovators  aggressively seeking dramatically the e units that are affected by imitation. I model
new solutions to the problem of production, I the contribution to the firm s efficiency of the
focus here on the limiting case in which the new affected components simply as the summation of
entrant is very nearly able to copy the produc- e independent and identically distributed ran-
tion method of the incumbent firm: the new dom variables. Implicit in this construction is
entrant seeking to copy an incumbent modifies the view that firms experience as random events
exactly one out of the N activities in the shocks to efficiency at the level of the production
incumbent s production recipe. Let us refer to unit (that is, at the organizational scale that lies
this limiting case as that of an entrepreneurial below that of the firm as a whole) resulting from
  spin-off  firm. The results that hold for the incremental changes in production methods.21
spin-off firm highlight the central role in The higher the value of e, the lower the cor-
the model of intrafirm externalities  that is, of relation between the incumbent s stock of
the complexity of production  and thus provide organizational capital and that of the nearly
a point of reference for understanding the perfectly imitating start-up firm. Consequently
behavior of other entrepreneurial new entrants. the higher the value of e, the greater the diffi-
The spin-off enters the industry with a cultly (ease) of finding an improvement to a high
production recipe that is very close to that of the (low) efficiency production method. Impor-
incumbent. However, due to the presence of in- tantly, the organizational capital of the spin-off
trafirm externalities, the organizational capital of firm may be greater, equal to, or less than the
the spin-off may be very distant from the organization capital of the firm being imitated.
incumbent s. The spin-off s modification of the In other words, it is possible for the   imitator 
instructions for a single operating unit will affect to surpass the leader. The likelihood that this
the performance of exactly e other units within will occur is a function both of the leader s
the firm. The organizational capital level associ- organizational capital, and of e, the level of
ated with the spin-off firm s production recipe intrafirm externalities.
thus takes on the following stochastic form:
hspin offź 4.2. Innovation by doing
t
e
1X
Having defined recipes and intrafirm externalities,
�N e�
/i
hincumbent
t
N I need only to specify a process by which exper-
N
iź1
|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}
�
|fflfflfflffl{zfflfflfflffl}
imentation occurs in order to complete a
unaffected by imitation
affected by imitation
micro-economic representation of technological/
�1� organizational innovation.
Entrepreneurship in the Theory of the Firm 117
At any time period t,22 some subset of the N parameter on learning by an incumbent firm.
teams comprising an incumbent firm informally The correlation between ht (current organiza-
experiments with a change to its method of tional capital) and htlbd (the organizational cap-
production for a given activity. This change ital associated with the production experiment)
results in a   trial  production recipe. An depends on e, the magnitude of intrafirm exter-
nalities (i.e., the complexity of the production
incumbent firm s managers can pay ctlbd to a
process) in the following manner:
quality control manager to learn htlbd, the overall
efficiency of the firm given the trial method of
�N e�
ht
production.23 In the absence of supervision, the
N
|fflfflfflfflfflffl{zfflfflfflfflfflffl}
hlbdź
t
experiment is dropped and forgotten. In the
lbd unaffected by time t lbd
presence of supervision, the firm learns h . In
t
�3�
the next time period it can either maintain it s
e
1X
current method of production (and thus current
/i
N
efficiency level, ht), or adopt the newly tried iź1
�
|fflfflfflffl{zfflfflfflffl}
method (thus achieving efficiency htlbd). The firm
affected by time t lbd
will make the choice that gives it the highest
where as before, the ui s are i.i.d. random
level of efficiency at any time, thus
variables drawn from a distribution g (u) with
mean l which is common knowledge to all
max ht;hlbd withlearning  supervision  ;
t
ht�1ź
firms. Equation 3 formally expresses the effect
ht without.
on learning of the presence of intrafirm exter-
�2�
nalities. Roughly speaking, the higher the value
In Figure 2, I present a timeline summarizing of e, the lower the correlation between current
the sequence of events in the learning process efficiency and the efficiency associated with a
within a single period. production experiment. Consequently the higher
Where the parameter d above indicated the the value of e, the greater the difficultly (ease) of
extent to which imitation is imperfect, the finding an improvement to a high (low) effi-
parameter e (intrafirm externalities) indicates the ciency production method. I present the formal
extent to which any modification of the firm s proposition in Appendix C.
existing production recipes will have broad im- In the sample learning curves and simulation
pacts on the firm s organizational capital. Where results presented in Figures 3 5, g (u) =
the incumbent firm can reasonably be expected Uniform[0, 1] (l = 0.5). Figure 3 presents
to   imitate  itself more effectively than an means and standard deviations of learning
entrepreneurial new entrant, it cannot escape the rates24 computed from 12 sets of 20 separate
technological/organizational fundamentals that simulated learning curves. Each set represents
are represented by the parameter e. For this one industry, characterized by its own value of
reason, a symmetry exists between the effect of e. The figure shows that mean simulated learn-
the parameter e on the effectiveness of imitation ing rates decline as the complexity of production
by a spin-off firm, and the effect of the same in an industry increases.
production experiment occurs
firm begins time t with efficiency �t firm begins time t+1 with efficiency �t+1
t t+1
firm decides whether or not firm chooses production method
to evaluate production experiment
for time t+1
during time period t
Figure 2. Sequence of events in a single time period.
118 Philip E. Auerswald
25
20
15
10
5
0
10 20 30 40 50 60 70 80 90 100
e (intrafirm externalities)
Figure 3. Percent improvement in efficiency after experience is doubled, e (magnitude of intrafirm externalities) varied. (N = 100,
g (u) = Uniform[0, 1], l = 0.5.) From Auerswald et al. (2000).
1
Figures 4 and 5 display simulation results for (on the order of ). To the extent that N is large,
N
single realizations of learning curves generated learning will appear to be nearly deterministic as
from an innovation by doing process. In indus- small efficiency gains cumulate in a regular
tries where production is simple (e = 1), the manner over an extended period of time.
efficiency of any given production method is In contrast, in the limiting case for industries
highly correlated with that of   similar  where production is maximally complex (e = N),
production methods  precisely, production similar production methods are wholly uncorre-
methods that differ only with respect to the lated with one another in terms of efficiency.
approach taken by one of the N production Figure 5 illustrates: with parameters set at
units. Figure 4 illustrates: a representative e = 100, n = 100, improvements are rare and
learning curve (e =1, N = 100) is smooth and gains minimal. Any change to the production
initially steep, but evidences sharply diminishing method leads to an entirely new efficiency level.
returns. Small changes in the production meth- The resulting   learning  process is highly dis-
od lead to small changes in productive efficiency jointed. Though extreme in the context of a model
e=1, N=100, g(phi)=Uniform[0,1], mu=0.5
100
95
90
85
80
75
70
65
60
55
50
45
100 200 300 400 500 600 700 800 900 1000
time (t)
Figure 4. Industry with simple production process (e = 1): typical firm learning curve.
% efficiency improvement (after doubling experience)
productive efficiency (theta)
Entrepreneurship in the Theory of the Firm 119
e=100, N=100, g(phi)=Uniform[0,1], mu=0.5
100
95
90
85
80
75
70
65
60
55
50
45
100 200 300 400 500 600 700 800 900 1000
time (t)
Figure 5. Maximally complex production (e = 100): typical firm learning curve.
of firm learning with intrafirm externalities, this that each operating units in a typical firm
limiting case is the default in most of the firm interacts directly with approximately 5% of the
learning literature in economics as exemplified by other operating units. The resulting process of
the classic papers of Evenson and Kislev (1976) firm learning is relatively irregular but none-
and Telser (1982). theless results in significant efficiency gains over
The simulated learning curve displayed in time, with a doubling in output expected to
Figure 6 illustrates the innovation by doing result in a cost reduction of approximately 20%.
process in an industry characterized by pro-
duction of intermediate complexity (e =5,
4.3. Differentiating invention from innovation
N = 100). Auerswald et al. (2000) calibrate a
generalized innovation by doing model to the A production recipes model offers one approach
quantitative and qualitative features of a modal for clearly distinguishing between genuine
empirically observed learning curve.25 They find novelty (which is rare) and innovation through
that, in the typical manufacturing industry, the creation of new combinations (which is
parameter values corresponding to intermediate relatively common, and occurs along a poten-
complexity yield the best fit. The implication is tially measurable spectrum26). Contributors to
e=5, N=100, g(phi)=Uniform[0,1], mu=0.5
100
95
90
85
80
75
70
65
60
55
50
45
100 200 300 400 500 600 700 800 900 1000
time (t)
Figure 6. Industry with moderately complex production process (e = 5): typical firm learning curve.
productive efficiency (theta)
productive efficiency (theta)
120 Philip E. Auerswald
literatures on entrepreneurship and technical (as elsewhere) would seem to suggest that a theo-
change have long distinguished   imitation  from retically based consensus exists as to its meaning.
  innovation.  27 A common presumption is that In fact, no such consensus exists. The literature
Schumpeterian entrepreneurs are innovators, contains several conventions. One is to focus on
not imitators.28 However, the more fundamental research intensity  for example, employing aver-
distinction is that between invention (alternately, age levels of R&D as a percentage of sales to
  novelty  ) and innovation (or the   mechanism  differentiate high-tech from low-tech industries.
by which novelty is transmitted).29 While this approach has some intuitive appeal, it is
In the production recipes model, invention not at all clear that research inputs are the right
corresponds to the creation of new activities  measure: traditional manufacturing industries
fundamentally new building blocks from which such as chemicals that exhibit relatively high R&D
  combinations  are derived. In a cooking anal- to sales ratios may not be significantly more   high-
ogy, the activities could be stirring, baking, roll- tech  than financial and other service industries
ing, slicing, and so forth. Excluding newly added that do not. An alternative is to employ as a
elements, the set of activities is widely known. measure the intensity of investment in information
Recipes are combinations of these activities. technology. This measure has the advantage of
In contrast,   innovation  is the creation of recognizing the potential for service industries to
new recipes from a fixed set of activities. Just as be   high-tech  and is a reasonable proxy for
software engineers routinely combine tested industry-wide changes in transactions costs.
segments of code (in existing programming However, again, a theoretical rationale is lacking.
languages!) rather than constructing complex A production recipes model offers an
programs entirely de novo, entrepreneurs approach for formally differentiating   high-
routinely combine existing activities rather than tech  from   low-tech  firms that is theoretically
inventing fundamentally new categories of grounded. Recipes as described in this paper
economic action.30 are neither purely technological nor purely
organizational. They are both. An example
illustrates why this is important. Weitzman
5. Conclusion
(1996) eloquently describes the manner in which
In this paper I have proposed a firm-level the   hybridization of ideas  played a central role
representation of the innovation process. I in Edison s invention of the   electric candle; 
began by emphasizing the manner in which along the same lines he elsewhere has observed
transactions costs define opportunities for the that   once you have nuclear power and you have
creation by entrepreneurs of technological/ a submarine, it is almost inevitable you re going
organizational   new combinations.  I argued to have a nuclear submarine.  32 Yet the devel-
that transactions costs are the glue that holds opment of the first nuclear submarine also
together entrepreneurial new combinations. required radical changes in the Navy itself. What
Knowledge intensive entrepreneurial firms come is more, implementing those radical changes
into existence when transactions costs are rela- required nearly dictatorial coordination on the
tively high, not when they are low or zero. part of the project s champion, Admiral Hyman
Furthermore, when transactions costs decrease Rickover.33 Although the combination of
in some parts of the economy relative to   nuclear  and   submarine  may, in some long-
others, we expect to observe reconfigurations of term, statistical sense have been   inevitable, 
economic activity and the subsequent entry and realizing the potential of that particular combi-
exit of Coaseanially affected firms.31 nation at a singular point in time required the
As with any theory, this paper s primary vision and determination of an entrepreneur 
intended contribution is to frame future empir- one capable of creating new technological
ical study. The paper suggests three primary and organizational combinations.34 Due to its
directions for further research. combined technological and organizational
The first concerns measurement. The ubiquity complexity, the creation of a nuclear Navy was a
of the term   high-tech  in the research literature legitimately   high-tech  activity. In general, a
Entrepreneurship in the Theory of the Firm 121
rich research agenda exists in the use of measures A third research agenda  the one with the
derived from the internal organization of firms  most potential significance for the study of
for example, the intrafirm externalities (e) in this entrepreneurship  would involve treating the
paper  as a way of differentiating   high-tech  magnitude of intrafirm externalities as an
from   low-tech  firms. endogenous variable and studying its determi-
A second research agenda would explore nants, importantly including transactions costs.
implications for industrial organization, partic- Unsurprisingly, the internal structure of firms is
ularly the manner in which   high-tech  (tech- a topic that has been explored more thoroughly
nologically/organizationally complex) and   low- in the management literature than in economics.
tech  (technologically/organizationally simple) Even in management, there has been little study
industries exhibit different patterns of entry, of the effect of transactions costs on technological/
exit, and evolution. The definitions presented in organizational complexity and on the process of
this paper seem to suggest that in industries entry and exit. A notable exception is the paper
where production processes are simple, we by Brynjolfsson et al. (1994), who find evidence
would expect profits to converge rapidly to zero, that investments in information technology at
particular when imitation is possible. In indus- the scale of an industry lead to a decrease in
tries where production processes are more average firm size. Evans and Wurster (1999)
complex, persistent Schumpeterian profits may present a more general argument, describing the
accrue to surviving firms. Schumpeterian profits, manner in which changes in transactions costs
and thus entrepreneurial opportunity, conse- brought about by the Internet are driving
quently may be greatest industries in the early organizational change across multiple indus-
stages of industries where technology is of tries. Rivkin (2000) explores the implications for
intermediate complexity  that is, where learning management strategy, describing how complex
is rapid enough to confer competitive advan- strategies resist imitation.
tage, but imitation is sufficiently uncertain to Where decreasing transactions costs pull
deter later entry. incumbent organizations apart, the possession
A more complete model would take the of difficult to imitate production recipes by the
demand side seriously, recognizing that the bulk same organizations keeps them together. The
of process innovation and a considerable dissolution of incumbent firms creates oppor-
amount of entrepreneurship involves making tunities for entrepreneurs; the prospect of
incremental changes to existing recipes, moti- Schumpeterian rents provides the incentive to
vated by direct engagement in the marketplace. realize those opportunities. The two factors are
Many of the firms that have in recent years in tension. In developed economies, competi-
forced significant market transformations (from tiveness at the national scale is a function of
Ebay to Napster) are engaged in the same sort of innovation and adaptability: the possession of
market, as opposed to technology, based capabilities that are difficult to imitate and the
opportunity exploitation that has been the norm ability to capitalize rapidly on opportunities
for most economic history. Furthermore, as created by technological change.35 For this
Henderson and Clark (1990) argued some time reason, a representation of the innovation pro-
ago (in different terms), there is no strong rela- cess that accounts for transactions costs and
tionship between the magnitude of change to a technological/organizational complexity is a
recipe and the resultant market impact: small pre-requisite for a formal theory of entrepre-
modifications to recipes and/or in the associated neurship and growth.
  product architecture  can result in dramatic
dislocations in the marketplace. Conversely, as
Acknowledgements
Christensen (1997) famously documented for the
case of the disk-drive industry, recipes that in- I thank Karl Shell, Stuart Kauffman, and
volve high levels of technological complexity Jose� Lobo for their contributions to this paper via
may create products which are essentially prior joint work. Zoltan Acs provided invaluable
commoditized in the marketplace. guidance in thinking through the argument as
122 Philip E. Auerswald
presented. Appendices A and B are drawn from for i, j = 1,...,N. Since the choice of the setting
Auerswald et al. (2000). All errors are my own. for the ith activity always affects the costs for the
ith activity, we have
eiź1
i
Appendix A. The technology landscape
for i = 1,...,N. The number ei of activities with
as a realization of a random field
costs affected by activity i is given by
We assume that the unit labor cost of activity i,
N
X
ui (x), is a random variable whose distribution
eiź ei
j
function is defined on R�:Consider two distinct
jź1
recipes, x and xó. The random variables ui (x)
for i = 1,..., N, while the number ei of activities
and ui(xó) are not necessarily independent. In
that affect the costs of activity i is given by
fact, ui depends on the instructions, xi, for
activity i and possibly on (some of) the instruc-
N
X
tions for the other activities, x)i. (With minor
eiź eij
abuse of notation, one could then have denoted jź1
the unit labor costs of activity i by ui (xi; x)i), or
for i = 1,..., N. Define Ei, the set of activities
more simply, ui (x).) We assume that the labor
cost-relevant to activity i, by
requirements are additive; hence we have
Eiź j2f1;. . .;Ngjejź1
N i
X
/�x�ź /i�x�;
for i = 1,..., N.
iź1
In general, each activity could be cost-affected
where u (x) is the unit cost of production
activity is cost-affected by (e)1) other activities,
employing recipex. Forxfixed,u(x) is a random
so that we have
variable. If x is allowed to vary over the set of all
#Eiźeiźe
possible recipes, W, then u (x) isarandom field. A
random field is a slight generalization of a sto- for i = 1,..., N, where e2f1;. . .;Ng:
chastic process to allow the argument (in this case
x) to be a vector (as opposed to being a scalar such
as   time  ). For the special case in which N =1,u
Appendix C. Complexity, learning, and imitation
(x) is then an ordinary stochastic process. We
denote by hi, -i (x) the realization of the random
Consider the firm s expectation regarding htlbd,
variable ui (x). The realization of the random
given by
PN
variable u (x) is h�x�ź hi; i�x�:If x varies
iź1
�N e� e
overW, the family of realizationsh(x) is called the
E hlbdjht 1;e ź ht 1� l: �4�
t
N N
landscape (of the random field u(x)). A landscape
is thus a generalization to the case with N > 1 of a With some departure from mathematical preci-
  history  (of a stochastic process).36 sion, I take the partial derivative equation 3 with
respect to e (which is integer valued) to express
the effect of e on E (htlbd):
Appendix B. Formal definition of intrafirm
@ E hlbd
l ht 1
t
ź :
externalities
@e N
A bit more notation is required to get the Consequently
concept of production recipes into the model.
@ E hlbd 0 ifht 1l;
t
Define the connectivity indicator eji by
�5�
0 otherwise.
8 @e
1 if the choice of setting for activityiaffects
<
This rough result reinforces the intuition behind
eiź the labor requirement for activityj
j
:0
part (iii) of proposition 1 below: the higher the
otherwise
Entrepreneurship in the Theory of the Firm 123
level of intrafirm externalities, the greater the Notes
1
likelihood that a relatively efficient firm will be
Expanding upon Acs (1992), Wennekers and Thurik
difficult to  imitate,  even by a well-informed
(1999) describe a set of phenomena linking entrepreneur-
ship to growth, including: creation of new markets; newness
spin-off firm.
through start-ups; invention and innovation; variety and
In order to formally express this relationship,
selection of ideas; markets and competition; disequilibrium;
I express the probability that htlbd is lower than
and replacement of obsolete enteprises.
2
some number z as
The definition offered by Carree and Thurik (2003)
Zz
provides a more comprehensive expression of what I in-
tend:   Entrepreneurship is the manifest ability to will-
Pr hlbd zjht 1;e źHzjht 1;e�ź h�zjht 1;e�dz
�
t
ingness of individuals, on their own, in teams, within and
0
outside existing organizations to perceive and create new
economic opportunities (new products, new production
where H (z|" ) denotes the cumulative density
methods, new organizational schemes, and new product
function and h (z|" ) denotes the probability
market combinations), and to introduce their ideas in the
density function. H(ht |ht-1, e) represents the
market, in the face of uncertainty and other obstacles, but
probability of failure of a firm to find an making decisions on the location, form, and use of re-
sources and institutions. 
improvement on method ht-1 in a single trial. We
3
In particular, Romer (1986, 1990) and Aghion and
can write the firm s expectation of its productive
Howitt (1992).
efficiency in the next period precisely as 4
Reiter and Sherman (1962), Kauffman (1988), Weitz-
E�htjht 1;e�źhtH�htjht 1;e�
man (1996, 1998).
5
Examples of low-tech entrepreneurship might include
Z1
dry-cleaning, landscaping, or copying services. The limit-
� zh zjhi;t 1;e dz: �6�
ing case is that of franchise operations, in which tech-
hi;t niques are fully codified.Note that both high- and low-
tech opportunity entrepreneurship are distinct from
The following proposition specifies some prop-   necessity entrepreneurship,  in which self-employment
results from an absence of alternative employment
erties of the distribution H (z | ht, e).
opportunities. See Acs (2006).
6
Applications of the NK-model to industrial economics
Proposition 1 (Properties of the Distribution of
and organizational theory include Levinthal (1997),
Outcomes from Imitation) H (z|ht-1; e) is (i)
Auerswald (1999), Kauffman et al. (2000), Rivkin (2000),
stochastically nondecreasing in ht-1 for e < N;
and Auerswald et al. (2000). In the model that follows, my
(ii) not a function of ht-1 for e = N; (iii) sto- parameter N is directly analogous to N in the NK-model,
and my parameter e is directly analogous to K + 1 in the
chastically non-decreasing in e for ht-1 > l, and
NK-model.
stochastically non-increasing in e for ht-1 < l.
7
Coase (1937):   The main reason why it is profitable to
establish a firm would seem to be that there is a cost to
Proof.
using the price mechanism. The most obvious cost of
 organizing production though the price mechanism is that
i. If e < N, neighboring production methods are
of discovering what the relevant price are.  The boundary
of the firm is where an entrepreneurial   span of control 
correlated: a fraction (N)e)/N of the activities of
(Lucas 1978) ends and market transactions begin.
any one neighbor variant of xt-1 will be in the
8
The scale of the firm will be determined by standard
same states as the corresponding activities in
issues pertaining to competition, market structure, and
xt-1.37 Consequently, for e < N, H (z | ht)1, e)
economies of scale.
9
will shift to theright with increasing ht)1.
Coase (1937, p. 397). See also Lucas (1978).
10
ii. When e = N the correlation between neigh- Nelson (1995, pp. 68 69) describes   routines  as fol-
lows:   [F]irms can be regarded as... the incubators and
boring production methods is 0. Therefore
carriers of  technologies and other practices that determine
h�zjht 1;eźN�źh�zjeźN�:
 what they do and  how productively in particular
circumstances. Winter and I have used the term  routines to
iii. e parametrizes the correlation between htlbd
denote these. 
11
and ht-1. If ht-1 > l, increasing e moves h (" ) to
Chandler s (1992, p. 86) definition of   organizational
capabilities  builds upon the routines of Nelson and Win-
the left, towards the unconditional distribution
ter, emphasizing the coordination of productive activities
h (z | e = N). If h < l, increasing e moves h
t-1
within the firm:
(" ) to the right, again towards h (z | e = N). (
124 Philip E. Auerswald
[L]earned routines are those involved in functional activi- Legal restrictions  in particular, patent protection and
ties those of production, distribution and marketing, trade secret law  clearly are important. However, as
obtaining supplies, improving existing products and pro- emphasized long ago by (Mansfield, 1961, 1963), even in the
cesses, and the developing of new ones. Even more important absence of legal barriers, the adoption of new technology is
are those routines acquired to coordinate these several difficult and expensive. See also Mansfield et al. (1981) and
functional activities... The resulting organizational capabil- Jovanovic (1995).
20
ities permit the enterprise to be more than the sum of its parts. The phenomenon of   orphan drugs  is illustrative.
21
They give it a life of its own above and beyond those of the
Here the model bears some similarity to the less
individuals involved. The individuals come and go, the
purposive approaches of Simon and Bonini (1958),
organization remains.
Hopenhayn (1992), and Atkeson and Kehoe (1997). How-
ever, where purely stochastic shocks in these papers occur at
12
Schumpeter emphasizes that production itself is a
the scale of the firm as a whole, here they occur of the scale
fundamentally combinatoric phenomenon.   Technologi- of the production unit.
22
cally as well as economically considered,  Schumpeter
Presumably, the time required to produce one   batch 
wrote in the first chapter of The Theory of Economic
of output.
23
Development,   production  creates nothing in the physical
In the case of a   pure  learning-by-doing model,
sense. In both cases it can only influence or control things
ctlbd =0.
24
and processes, or  forces. ... [T]o produce means to combine
Specifically, the percentage increase in efficiency real-
the things and forces within our reach. Every method of
ized from a doubling of experience (e.g., going from the first
production signifies some definite combination.  (Schum- full month to the second full month of production).
25
peter, 1912 [1961], p. 14). Echoing Shumpeter (1912) and
See summary in Argote and Epple (1990).
26
anticipating Weitzman (1998), Kuznets (1962) opens the
For the theory on this point, see Appendix C.
27
famed Richard Nelson edited volume on The Rate and
Related is the distinction made by Cohen and Levinthal
Direction of Inventive Activity by proposing that an inven-
(1989) between learning (R&D directed as using existing
tion be defined as   a new combination of available
information) and innovation (R&D directed at creating new
knowledge concerning properties of the material universe. 
information).
13
28
The   recipe  metaphor finds a parallel expression in
For example, Carree and Thurik (2003) comment that
Romer (1996) who observes that   non-rival ideas can be
  Schmitz (1989) was the first to present an endogenous
used to rearrange things, for example, when one follows a
growth model that relates entrepreneurial activity and
recipe and transforms noxious olives into tasty and
economic growth. However, his entrepreneurs are [rela-
healthful olive oil. Economic growth arises from the dis-
tively]  passive ... because their role is restricted to that of
covery of new recipes and the transformation of things from
 imitation.  
29
low to high value configurations. 
A recently discovered paper by Schumpeter empha-
14
In particular, we assume that xi satisfies
sizes this point:   How does novelty come about? Why do
some people happen to paint in a different way than they
xi2f1;. . .;sg
learned to and how is this new way of painting transferred
for i = 1,...,N, where s is a positive integer. Hence, for a given
to other painters and the public? What is on the one hand
product, the number of recipes is finite and given by
the  energy, if we may say so, and on the other hand
the  mechanism of this process?  (Schumpeter, 2005, pp.
113 114) While Schumpter (2005) does not link novelty to
#Xźsn:
invention, such a connection seems reasonable in light of
15
the his observation that   [w]e find novel phenomena in
Prescott and Visscher (1980, p. 446):   Information is an
the economy as in any other social domain, and there
asset to the firm, for it affects the production possibilities set
is no difference between novelty in the economy and
and is produced jointly with output. 
16
elsewhere. 
See appendix A, draw from Auerswald et al. (2000), for
30
Schumpeter (1912):   As a rule, the new combinations
a formal description of the manner in which realizations of
must draw the necessary means of production from some
organizational capital define a technology   landscape  in
old combinations... development consists primarily in
the sense of Kauffman and Levin (1987).
17
employing existing resources in a different way, in doing
A classic paper by Reiter and Sherman (1962) entitled
new things with them.  As described by Kauffman (1988)
  Allocating Indivisible Resources Affording External
and Weitzman (1996, 1998), the assumption of a fixed set of
Economies or Diseconomies,  anticipates recent work (e.g.,
activities imposes only a weak limit on the search space for
Weitzman 1998; Auerswald et al., 2000) on the firm as a
innovators, as the number possible recipes that can be
solver of hard combinatorial optimization problems.
18
derived from even a modest number of activities is hyper-
The e here is directly analogous to the K in the
astronomical.
NK-model. The parameter e can take on integral values
31
See the seminal studies of industry dynamics by Dunne
between 1 and N. See appendix B for a formal definition of
et al. (1988, 1989) and Davis and Haltiwanger (1992).
this variable.
19
Whether the returns from such Coasian/Schumpeterian
A number of factors determine the extent of transfer-
disruptions accrue to firms or consumers depends on the
ability of technical knowledge from one firm to another.
Entrepreneurship in the Theory of the Firm 125
magnitude of technological/organizational complexity Acs, Z. and A. Varga, 2005, �Entrepreneurship, Agglomeration,
within the industies in question. See Nordhaus (2004). and Technological Change�, Small Business Economics
32
Comments at the   Between Invention and Innovation  24, 323 334.
workshop held at the Kennedy School of Government, Aghion, P. and P. Howitt, 1992, �A Model of Growth Through
Harvard, on May 2, 2001. Creative Destruction�, Econometrica 60(2), 323 351.
33
The first nuclear-powered submarine was the U.S. Argote, L. and D. Epple, 1990, �Learning Curves in Manufac-
turing�, Science 247, 920 924.
Nautilus, completed in 1954. Rickover is often referred to
as the   father of the nuclear Navy.  The inter-relation- Arthur, W. B., 1989, �Competing Technologies, Increasing
ship of technological and organizational innovations Returns and Lock-in by Historical Events�, Economic
required to achieve this milestone is detailed in Rockwell Journal 99, 116 131.
Atkeson, A. and P. Kehoe, 1997,  Industry Evolution and
(1995).
34
Whether individual will or inexorable   forces  of his- Transition: A Neoclassical Benchmark , in Working Paper
6005, NBER.
tory cause events to occur in a particular manner is a very
Audretsch, D., 1995, Innovation and Industry Evolution, MIT
old question, dating in a modern form to 19th century
Press.
debates over the philosophy of history involving Hegel,
Auerswald, P. E., 1999, Organizational Learning, Intrafirm
Marx, Nietszche, and Tolstoy (who proposes a sensible
Externalities and Industry Evolution, University of
resolution in the epilog to War and Peace). In economics,
Washington Ph.D. thesis.
the debate has been taken up by Nelson and Winter (1982),
Auerswald, P. E., S. Kauffman, J. Lobo and K. Shell, 2000,
Arthur (1989) and others who emphasize the critical role of
�The Production Recipes Approach to Modeling Techno-
evolution,   path dependence  and historical accident over
logical Innovation: An Application to Learning by Doing�,
the determinism of conventional economic models.
Journal of Economic Dynamics and Control 24, 389 450.
Schumpeter (2005) anticipates those discussions.
35
Brynjolfsson, E., T. Malone, V. Gurbaxani and A. Kambil,
As Krugman (1994) pointed out a decade ago, it is easy
1994, �Does Information Technology Lead to Smaller
to exagerate the imporance of innovation in developing
Firms?�, Management Science 40(12), 1628 1644.
countries (notably China), where the accumulation of
Carree, M. and A. Thurik, 2003,  The Impact of Entrepre-
quality-adjusted conventional factors of production
neurship on Economic Growth , in Z. Acs and D. Audretsch
remains the primary driver of growth.
36
See Durrett (1991, especially Chapter 2). The relation- (eds.), Handbook of Entrepreneurship Research, Springer.
Chandler, A. D., 1990, Scale and Scope: The Dynamics of
ship between random field models and models based on
Industrial Capitalism, Belknap/Harvard University Press.
realizations of random fields (i.e., landscape models) is
Chandler, A. D., 1992, �Organizational Capabilities and the
discussed in Stadler and Happel (1995). For previous
Economic History of the Industrial Enterprise�, Journal of
applications of random fields and landscape models to
Economic Perspectives 6(3), 79 100.
economics, see e.g., Follmer (1974), Kauffman (1988), and
�
Christensen, C. M., 1997, The Innovator s Dilema: When New
Durlauf (1993).
37
Technologies Cause Great Firms to Fail, Boston: Harvard
As above, organizational capital is function of the
Business School Press.
particular state of the production recipe:
Coase, R., 1937, �The Nature of the Firm�, Economica 4, 386 405.
ht 1źh�xt 1�:
Coase, R., 1960, �The Problem of Social Cost�, Journal of Law
and Economics 3, 1 44.
Cohen, W. A. and D. A. Levinthal, 1989, �Innovation and
Learning: The Two Faces of R&D�, Economic Journal
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