# An age structured demographic theory of technological change

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## Abstract

At the heart of technology transitions lie complex processes of social and industrial dynamics. The quantitative study of sustainability transitions requires modelling work, which necessitates a theory of technology substitution. Many, if not most, contemporary modelling approaches for future technology pathways overlook most aspects of transitions theory, for instance dimensions of heterogenous investor choices, dynamic rates of diffusion and the profile of transitions. A significant body of literature however exists that demonstrates how transitions follow *S*-shaped diffusion curves or Lotka-Volterra systems of equations. This framework is used *ex-post* since timescales can only be reliably obtained in cases where the transitions have already occurred, precluding its use for studying cases of interest where nascent innovations in protective niches await favourable conditions for their diffusion. In principle, scaling parameters of transitions can, however, be derived from knowledge of industrial dynamics, technology turnover rates and technology characteristics. In this context, this paper presents a theory framework for evaluating the parameterisation of *S*-shaped diffusion curves for use in simulation models of technology transitions without the involvement of historical data fitting, making use of standard demography theory applied to technology at the unit level. The classic Lotka-Volterra competition system emerges from first principles from demography theory, its timescales explained in terms of technology lifetimes and industrial dynamics. The theory is placed in the context of the multi-level perspective on technology transitions, where innovation and the diffusion of new socio-technical regimes take a prominent place, as well as discrete choice theory, the primary theoretical framework for introducing agent diversity.

## Keywords

Technology transitions Lotka-Volterra Replicator dynamics Evolutionary economics Discrete choice theory## JEL Classification

O330## Notes

### Acknowledgments

I would like to acknowledge the students who have been attending the Energy Systems Modelling seminars held at 4CMR in 2013, in particular A. Lam, P. Salas and E. Oughton, with whom the discussions on technology and evolutionary economics led to the development and enhancement of this theory. I would furthermore like to thank participants to the International Conference on Sustainability Transition 2013 for providing valuable feedback, in particular K. Safarzynska for critical comments, as well as two anonymous referees for their recommendations. This research was funded by the UK Engineering and Physical Sciences Research Council, fellowship number EP/K007254/1.

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