Bruno S. Frey
Small Business Economics
19: 69–80, 2002.
2002 Kluwer Academic Publishers. Printed in the Netherlands.
ABSTRACT. The paper presents a model of the entrepre-
neur as an undertaker of new combinations of ideas.
Technology is seen as a set of ideas in a metric technology
space where new knowledge is created by the combination of
older ideas in the spirit of Schumpeter (1934), Weitzman
(1998) and Olsson (2000). Given some intuitive assumptions,
we demonstrate that technological progress generated by the
convex combination of ideas is constrained by five factors:
First, the combinatory process eventually leads to the
exhaustion of technological opportunity. Second, the cost of
combining ideas increases with the technological distance
between the originating ideas. Third, profits are maximized
when ideas are combined that are technologically close.
Fourth, the technology set is constrained by a social possi-
bility set of socially acceptable ideas. Fifth, the boundaries
implied by the ruling technological paradigm limit the scope
for eternal recombinant growth.
It is often acknowledged that entrepreneurial
activity is not easily included in standard
economic models. The nature of the entrepreneur
is in many ways at odds with the rational,
well-informed capitalist in the theory of the
firm and with the routinized, large-scale R&D
processes modeled in endogenous growth
theory. Nevertheless, technological creativity is
generally regarded as a fundamental determinant
of economic progress.
In this paper, we follow
in the spirit of Schumpeter (1934), Weitzman
(1998) and Olsson (2000) in viewing the entre-
preneur as an undertaker of new combinations of
ideas. In our formal model, binary pairings are
carried out in a metric technology space where
ideas are separated by technological distance.
Convex combinations of ideas at the technological
frontier lead to the expansion of the technology
set. The process is constrained by (i) technolog-
ical opportunity, (ii) the costs of combination, and
(iii) the revenues of combination, (iv) the institu-
tional framework, and (v) the ruling technolog-
The notion of innovations as a result of new
combinations is described in Schumpeter (1934).
In Schumpeter’s own words, “The carrying out of
new combinations means, therefore, simply the
different employment of the economic system’s
existing supplies of productive means . . .”
(Schumpeter, 1934, p. 68). All economic devel-
opment is the result of such new combinations.
This combination process is very different from
the dynamic analysis of orthodox microeconomic
theory since the former involves “. . . spontaneous
and discontinuous change . . ./and/disturbance of
equilibrium, which forever alters and displaces the
equilibrium state previously existing.” (p. 64).
Schumpeter distinguishes between five different
kinds of new combinations: The introductions of
(i) a new good, (ii) a new method of production,
(iii) a new market, (iv) new source of supply of
intermediate goods, and (v) a new organization.
Any person who carries out new combinations is
defined as an entrepreneur.
Weitzman’s (1998) starting point is the pro-
duction functions for new knowledge in modern
growth theory. Like Schmookler (1966), Weitzman
uses combinatorial mathematics to describe the
Final version accepted on May 30, 2001
Department of Economics
Box 640, 405 30, Göteborg
Bruno S. Frey
Institute for Empirical Economic Research
University of Zürich