1036 THE ECONOMIC JOURNAL IDECEMBER well as some features implicit in Mansfield-type models, such as imperfect nformation and as ymmetric technological knowledge.d IIL A SELF-ORGANISATION MODEL OF THE DIFFUSION OF INNOVATIONS AND THE TRANSITION BETWEEN TECHNOLOGICAL JECTORIES In two previous papers, one of the present authors(Silverberg, I984; I987 attempted to demonstrate the relevance to economic theory of the self- organisatio proach to dynamic modelling pioneered by Eigen, Haken Prigogine and others. In essence the argument proceeds from the observation that in complex interdependent dynamical systems unfolding in historical, i c irreversible time, economic agents, who have to make decisions today the correctness of which will only be revealed considerably later, are confronted with irreducible uncertainty and holistic interactions between each other and with aggregate variables. The a priori assumption of an'equilibrium'solutic to this problem to which all agents ex ante can subscribe and which makes their actions consistent and in some sense dynamically stable is a leap of methodological faith. Instead we proposed employing some of the recently developed methods of evolutionary modelling to show how the interaction of diverse capabilities, expectations and strategies with the thereby emerging selective pressures can drive a capitalistic economy certain definite patterns of development Drawing on a dynamic model of market competition with embodied technical progress investigated in Silverberg(I987), we embed the question of diffusion into the larger one of the transition of an industry between two technological trajectories. Choice of technique is no longer a choice between two pieces of equipment with given(but perhaps imperfectly known characteristics, but now involves skills in using them which can be endogenously built up by learning by doing or by profiting from the experience of others, as well as expectations about future developments along the various competing trajectories. As we shall see, the diversity in firms'capabilities and expectations is an irreducible element driving the diffusion process In the sectoral approach taken here industry-level demand is taken as given and growing some exponential rate. Firms command some market share of his demand at any given time, but market shares may change over time as a dynamic response with a characteristic, time constant(reflecting the'freeness of competition and such factors as brand loyalty, information processing and search delays and costs, etc. )to disparities in the relative competitiveness of firm This concept, so dear to close observers of the business scene, has to our knowledge evaded incorporation into a systematic economic theory until now 4 A more detailed discussion of the empirical basis of the hypotheses entering into the model presented below can be found in Dosi et al.(I tional modelling Haken(1983), Nicolis and Prigogine(1977) and Prigogine(1976)
INNOVATION AND DIFFUSION The evolution of market structure is governed in our approach by an equation relating the rate of change of a firms market share to the difference between its competitiveness (defined below)and average industry competitivene averaged over all competing firms in an industry, weighted by their market shares). This equation is formally identical to the equation first introduced into mathematical biology by R. A. Fisher in 1930 and more recently applied in a variety of contexts and studied in considerable mathematical detail by Eigen (1971), Eigen and Schuster(1979), Ebeling and Feistel (I982), Hofbauer and Sigmund(I984), and Sigmund (1986). Our use of this equation differs from most biological applications, however, in that the competitiveness parameters ather than being constants or simple functions of the other variables themselves change over time in complex ways in response to the strategies pursued by firms and feedbacks from the rest of the system. In a systems theoretic sense this equation may be regarded as the fundamental mathematical description of competitive processes. It is worth emphasising the difference between our approach and standard theoretical conceptualisations of com- petition. The latter generally identify the circumstances under which no lative competitive shifts or profits can be realised(impossibility of arbitrage uniform rate of profit, etc )and then assume that the system must always be in or near this state If we denote by fi the market share in percentage of real orders of the ith firm, by Er its competitiveness and by (e>the average competitiveness of all firms in the industry(=EfE, then the evolution of market shares is governed by the following equation =A(E-〈E》 le define the competitiveness parameter as a linear combination of terms reflecting relative price and delivery delay differentials E=-InPe-Alo dd, where Pr is the market price of the ith firm and dd, its current delivery Silverberg (1987) presents a basic dynamic structure for dealing with strategic investment in the face of uncertainty with respect to the future course of embodied technical progress, overall demand and changes in relative competitiveness. In this framework, entrepreneurs are seen as being fully change, so that their decisions, particularly concerning fixed investment, take ccount of and try to anticipate these developments. Decision-making is incorporated on the one hand in certain robust rules of thumb(for the most part feedback rules dealing with oligopolistic pricing and production policies) and' animal spirits in the form of decision rules governing replacement policy the payback period method)and expansion of capacity ('estimates'or guesses of future demand growth corrected by experience). Technical change here to mark
THE ECONOMIC IOURNAI DECEMBER is embodied in vintages, and the resulting capital stocks are not assumed to start in, and in general need not converge to steady-state distributions The capital stock(measured in units of productive capacity) of each firm is represented as an aggregation over nondecaying vintages between the current period t and the scrapping date T(t) K()=K(4,)dr where k,(t, t)is gross investment at time t(in capacity units) K(4,t)=k(,n)if T(o)<t<t and o otherwise This aggregate capital stock may be a composite of different technologies as well as different vintages of a single technological trajectory. A payback calculation is performed by each firm with its desired payback period(which may differ between firms) to determine a desired scrapping date for its capital stock Tar(t) by solving P(D)/(c(a)-c(0)]=b, here P(t)is the price of new capital equipment per unit capacity, c(... )is the unit operating cost at time t of the vintage in question, and b, is the target payback period of the ith firm The actual scrapping date adjusts to this desired date via a first-order catch p procedur T=z max [Au(la-1),o where zu is a rationing parameter between o and I(the ratio of current cash How to desired gross investment) which may arise if the ith firm, due to financial constraints, is not able to finance its desired investment programme fully (otherwise it is I). The amount of capacity scrapped as a result of this decision(as well as a possible desire to reduce overall capacity)is S=kt, T)T Net expansion (or contraction) of capacity is governed by a desired rate r for each fir technologically obsolete equipment should beemingly'self-evident' rules have been applied to decide when 7 In the economics literatu ced by new cquipment, One calls for an old vintage to replacement when unit variable costs exceed the price attained per unit of output. A substantial specialised literature exists, however, dealing with optimal replacement beginning with Terborgh(Terborgh, 1949;see also Smith, 1961). Under suitable assumptions about the rate of future technical progress this leads to the so-called square root rule. k criterion is a reasonable approximation to in this ru calculations to be widely For a discussion of optimal replacement in the evolutionary framework emp ere see Silverberg (987)