American Institute of Mathematical Sciences

Advanced
December  2014, 19(10): 3299-3317. doi: 10.3934/dcdsb.2014.19.3299

The dynamics of technological change under constraints: Adopters and resources

M. Núñez-López 1, , J. X. Velasco-Hernández 2, and  P. A. Marquet 3,

1. 

Departamento de Matemáticas Aplicadas y Sistemas, DMAS, Universidad Autónoma Metropolitana, Cuajimalpa, Av. Vasco de Quiroga 4871, Col. Santa Fe Cuajimalpa, Cuajimalpa de Morelos, 05300, México, D.F., Mexico
2. 

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Boulevard Juriquilla No. 3001, Juriquilla, 76230, Mexico
3. 

Departamento de Ecología, Facultad de Ciencias Biológicas, Pontificia Universidad Católica de Chile, Casilla 114-D, Santiago 6513677, Chile

Received  July 2013 Revised  April 2014 Published  October 2014

We present a mathematical model for a technology cycle that centers its attention on the coexistence mechanisms of competing technologies. We use a biological analogy to couple the adoption of a technology with the provision of financial resources. In our model financial resources are limited and provided at a constant rate. There are two variants analyzed in this work, the first considers the so-called internal innovation and the second introduces external innovation. We make use of the adaptive dynamics framework to explain the persistence of closely related technologies as opposed to the usual competitive exclusion of all but one dominant technology. For internal innovation the existence of a resource remanent in the full adoption case does not always lead to competitive exclusion; otherwise with the external innovation the resident technology can not be displaced. The paper illustrates the persistence of closely related technologies and the competitive exclusion in renewable energy technologies and TV sets respectively.
Keywords: technology adoption, Innovation diffusion, coexistence., adaptive dynamics, technology cycle.
Mathematics Subject Classification: Primary: 37C25, 37C75; Secondary: 91B42, 92D2.
Citation: M. Núñez-López, J. X. Velasco-Hernández, P. A. Marquet. The dynamics of technological change under constraints: Adopters and resources. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3299-3317. doi: 10.3934/dcdsb.2014.19.3299
References:
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[2]

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G. Dosi, Technological paradigms and technological trajectories, Research Policy, 11 (1982), 147-162. doi: 10.1016/0048-7333(82)90016-6.  Google Scholar

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G. George, Slack resources and the performance of privately held firms, Academy of Management Journal, 48 (2005), 661-676. doi: 10.5465/AMJ.2005.17843944.  Google Scholar

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A. Grübler, Technology and Global Change, The Press Syndicate of the University of Cambridge, Cambridge, UK, 1998. Google Scholar

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A. B. Jaffe, M. Trajtenberg, S. Michael and Fogarty, Knowledge spillovers and patent citations: Evidence from a survey of inventors, American Economic Review, 90 (2000), 215-218. doi: 10.1257/aer.90.2.215.  Google Scholar

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A. B. Jaffe and M. Trajtenberg, Patents, Citations, and Innovations: A Window on the Knowledge Economy, The MIT Press Cambridge, Massachusetts, 2002. Google Scholar

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N. Jonard and M. Yildizoglu, Interaction of local interactions: Localized learning and network externalities, in The Economics of Networks: Interaction and Behaviours, Springer Berlin, (1998), 189-204. doi: 10.1007/978-3-642-72260-8_8.  Google Scholar

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J. E. Keymer, M. A. Fuentes and P. A. Marquet, Diversity emerging: From competitive exclusion to neutral coexistence in ecosystems, Theoretical Ecology, 5 (2012), 457-463. doi: 10.1007/s12080-011-0138-9.  Google Scholar

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[26]

C. Marchetti, Society as a learning system: Discovery, invention and innovation cycles revisited, Technol. Forecast. Soc. Chang., 18 (1980), 267-282. doi: 10.1016/0040-1625(80)90090-6.  Google Scholar

[27]

T. Modis, Predictions: Societys Telltale Signature Reveals the Past and Forecasts the Future, Simon and Scuster, New York, 1992. Google Scholar

[28]

A. Nair and D. Ahlstrom, Delayed creative destruction and the coexistence of technologies, J. Eng. Technol. Manage, 20 (2003), 345-365. doi: 10.1016/j.jengtecman.2003.08.003.  Google Scholar

[29]

R. Nelson and S. Winter, In search of a useful theory of innovation, Research Policy, 6 (1977), 36-76. doi: 10.1016/0048-7333(77)90029-4.  Google Scholar

[30]

, Overview of the OECD Activities on Climate Change and the Main Policy. Tackling Climate Change and Growing the Economy, OECD Report,, 2010. Available from: , ().   Google Scholar

[31]

F. Phillips, On S-curves and tipping points, Technol. Forecast. Soc. Chang., 74 (2007), 715-730. doi: 10.1016/j.techfore.2006.11.006.  Google Scholar

[32]

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[33]

S.-J. Lee, D.-J. Lee and H.-S. Oh, Technological forecasting at the Korean stock market: A dynamic competition analysis using Lotka-Volterra model, Technol. Forecast. Soc. Chang., 72 (2005), 1044-1057. Google Scholar

[34]

J. Shot and F. W. Geels, Niches in evolutionary theories of technical change. A critical survey of the literature, Industrial and Corporate Change, 17 (2007), 605-622. doi: 10.1007/s00191-007-0057-5.  Google Scholar

[35]

G. Silverberg, G. Dosi and L. Orsenigo, Innovation, diversity and diffusion: A self-organisation model, The Economic Journal, 98 (1988), 1032-1054. doi: 10.2307/2233718.  Google Scholar

[36]

A. Stirling, On the Economics and Analysis of Diversity, SPRU Electronic Working Paper Series, 28 (1998). Google Scholar

[37]

J. Tan and M. W. Peng, Organizational slack and firm performance during economic transitions: Two studies from an emerging economy, Strategic Management Journal, 24 (2003), 1249-1263. doi: 10.1002/smj.351.  Google Scholar

[38]

M. L. Tushman and P. Anderson, Technological discontinuities and organizational environments, Administrative Science Quartely, 31 (1986), 439-465. doi: 10.2307/2392832.  Google Scholar

[39]

C. Watanabe, R. Kondo, N. Ouchi and A. Wei, The dynamics of adaptation and evolutionary branching, Physical Review Letters, 78 (1997), 2024-2027. Google Scholar

[40]

C. Watanabe, R. Kondo and A. Nagamatsu, Policy options for the diffusion orbit of competitive innovations: An application of Lotka-Volterra equations to Japan's transition from analog to digital TV broadcasting, Management Science, 23 (2003), 437-445. doi: 10.1016/S0166-4972(02)00004-4.  Google Scholar

[41]

C. Watanabe, R. Kondo, N. Ouchi and A. Wei, A substitution orbit model of competitive innovations, Technol. Forecast. Soc. Chang., 71 (2004), 365-390. doi: 10.1016/S0040-1625(02)00351-7.  Google Scholar

[42]

H. P. Young, Innovation Diffusion in Heterogeneous Populations: Contagion, Social Influence and Social Learning, SFI Working Papers,, 2007., ().   Google Scholar

show all references

References:
[1]

P. Anderson and M. L. Tushman, Technological discontinuities and dominant design: A cycle model of technological change, Administrative Science Quartely, 35 (1990), 604-633. Google Scholar

[2]

F. Bass, A new product growth model for consumer durables, Management Science, 50 (2004), 1825-1832. doi: 10.1287/mnsc.1040.0264.  Google Scholar

[3]

W. E. Bijker and T. P. Pinch, The Social Construction of Technological Systems: New Directions in the Sociology and History of Technology, MIT Press, New York, 1989. Google Scholar

[4]

C. M. Christensen, The Innovators Dilemma: When New Technologies Cause Great Firms to Fail, Harvard Business School Press Boston, MA, 1989. Google Scholar

[5]

C. W. Clark, Mathematical Bioeconomics: The Optimal Management of Environmental Resources, John Wiley and Sons, 1990.  Google Scholar

[6]

D. T. Coe, E. Helpman and A. W. Hoffmaister, North-South R & D spillovers, The Economic Journal, 107 (1997), 134-149. doi: 10.3386/w5048.  Google Scholar

[7]

F. Dercole, U. Dieckmann, M. Obersteiner and S. Rinaldi, Adaptive dynamics and technological change, Technovation, 28 (2008), 335-348. doi: 10.1016/j.technovation.2007.11.004.  Google Scholar

[8]

T. Devezas and J. Corredine, The biological determinants of long-wave behavior in socioeconomic growth and development, Technol. Forecast. Soc. Chang., 68 (2001), 1-57. doi: 10.1016/S0040-1625(01)00136-6.  Google Scholar

[9]

U. Dieckmann and R. Law, The dynamical theory of coevolution: A derivation from stochastic ecological processes, J. Math. Biol., 34 (1996), 579-612. doi: 10.1007/BF02409751.  Google Scholar

[10]

O. Diekmann, A beginners guide to adaptive dynamics, Mathematical Modelling of Population Dynamics, Banach Center Publications, Polish Academy of Sciences, Warszawa, 63 (2004), 47-86.  Google Scholar

[11]

G. Dosi, Technological paradigms and technological trajectories, Research Policy, 11 (1982), 147-162. doi: 10.1016/0048-7333(82)90016-6.  Google Scholar

[12]

J. Fisher and R. Pry, A simple substitution model of technological change, Technol. Forecast. Soc. Chang., 3 (1971), 75-88. doi: 10.1016/S0040-1625(71)80005-7.  Google Scholar

[13]

C. Freeman and C. Pérez, Structural Crises of Adjustment, Business Cycles and Investment Behaviour, in Technical Change and Economic Theory (eds. Dosi et. al.), Pinter Publishers, U.K., 1998. Google Scholar

[14]

G. George, Slack resources and the performance of privately held firms, Academy of Management Journal, 48 (2005), 661-676. doi: 10.5465/AMJ.2005.17843944.  Google Scholar

[15]

A. Grübler, Technology and Global Change, The Press Syndicate of the University of Cambridge, Cambridge, UK, 1998. Google Scholar

[16]

R. Henderson, A. B. Jaffe and M. Trajtenberg, Universities as a source of commercial technology: A detailed analysis of university patenting, 1965-1988, Review of Economics and Statistics, 80 (1998), 119-127. doi: 10.1162/003465398557221.  Google Scholar

[17]

G. Z. Hu Albert and A. B. Jaffe, Patent citations and international knowledge flow: The cases of Korea and Taiwan, International Journal of Industrial Organization, 21 (2005), 849-880. Google Scholar

[18]

A. B. Jaffe and M. Trajtenberg, International knowledge flows: Evidence from patent citations, Economics of Innovation and New Technology, 8 (1999), 105-136. doi: 10.3386/w6507.  Google Scholar

[19]

A. B. Jaffe, M. Trajtenberg, S. Michael and Fogarty, Knowledge spillovers and patent citations: Evidence from a survey of inventors, American Economic Review, 90 (2000), 215-218. doi: 10.1257/aer.90.2.215.  Google Scholar

[20]

A. B. Jaffe and M. Trajtenberg, Patents, Citations, and Innovations: A Window on the Knowledge Economy, The MIT Press Cambridge, Massachusetts, 2002. Google Scholar

[21]

N. Jonard and M. Yildizoglu, Interaction of local interactions: Localized learning and network externalities, in The Economics of Networks: Interaction and Behaviours, Springer Berlin, (1998), 189-204. doi: 10.1007/978-3-642-72260-8_8.  Google Scholar

[22]

N. Jonard and M. Yildizoglu, Technological diversity in an evolutionary model with localized learning and network externalities, Structural Change and Economic Dynamics, 9 (1998), 35-53. doi: 10.1016/S0954-349X(97)00027-1.  Google Scholar

[23]

W. Keller, The Geography and Channels of Diffusion at the World's Technology Frontier, NBER Working Paper 8150,, 2001., ().   Google Scholar

[24]

J. E. Keymer, M. A. Fuentes and P. A. Marquet, Diversity emerging: From competitive exclusion to neutral coexistence in ecosystems, Theoretical Ecology, 5 (2012), 457-463. doi: 10.1007/s12080-011-0138-9.  Google Scholar

[25]

D. A. Levinthal, The slow pace of rapid technological change: Gradualism and punctuated in technological change, Industrial and Corporate Change, 7 (1998), 217-247. doi: 10.1093/acprof:oso/9780199269426.003.0008.  Google Scholar

[26]

C. Marchetti, Society as a learning system: Discovery, invention and innovation cycles revisited, Technol. Forecast. Soc. Chang., 18 (1980), 267-282. doi: 10.1016/0040-1625(80)90090-6.  Google Scholar

[27]

T. Modis, Predictions: Societys Telltale Signature Reveals the Past and Forecasts the Future, Simon and Scuster, New York, 1992. Google Scholar

[28]

A. Nair and D. Ahlstrom, Delayed creative destruction and the coexistence of technologies, J. Eng. Technol. Manage, 20 (2003), 345-365. doi: 10.1016/j.jengtecman.2003.08.003.  Google Scholar

[29]

R. Nelson and S. Winter, In search of a useful theory of innovation, Research Policy, 6 (1977), 36-76. doi: 10.1016/0048-7333(77)90029-4.  Google Scholar

[30]

, Overview of the OECD Activities on Climate Change and the Main Policy. Tackling Climate Change and Growing the Economy, OECD Report,, 2010. Available from: , ().   Google Scholar

[31]

F. Phillips, On S-curves and tipping points, Technol. Forecast. Soc. Chang., 74 (2007), 715-730. doi: 10.1016/j.techfore.2006.11.006.  Google Scholar

[32]

J. A. Schumpeter, The theory of economic development, The European Heritage in Economics and the Social Sciences, 1 (2003), 61-116. doi: 10.1007/0-306-48082-4_3.  Google Scholar

[33]

S.-J. Lee, D.-J. Lee and H.-S. Oh, Technological forecasting at the Korean stock market: A dynamic competition analysis using Lotka-Volterra model, Technol. Forecast. Soc. Chang., 72 (2005), 1044-1057. Google Scholar

[34]

J. Shot and F. W. Geels, Niches in evolutionary theories of technical change. A critical survey of the literature, Industrial and Corporate Change, 17 (2007), 605-622. doi: 10.1007/s00191-007-0057-5.  Google Scholar

[35]

G. Silverberg, G. Dosi and L. Orsenigo, Innovation, diversity and diffusion: A self-organisation model, The Economic Journal, 98 (1988), 1032-1054. doi: 10.2307/2233718.  Google Scholar

[36]

A. Stirling, On the Economics and Analysis of Diversity, SPRU Electronic Working Paper Series, 28 (1998). Google Scholar

[37]

J. Tan and M. W. Peng, Organizational slack and firm performance during economic transitions: Two studies from an emerging economy, Strategic Management Journal, 24 (2003), 1249-1263. doi: 10.1002/smj.351.  Google Scholar

[38]

M. L. Tushman and P. Anderson, Technological discontinuities and organizational environments, Administrative Science Quartely, 31 (1986), 439-465. doi: 10.2307/2392832.  Google Scholar

[39]

C. Watanabe, R. Kondo, N. Ouchi and A. Wei, The dynamics of adaptation and evolutionary branching, Physical Review Letters, 78 (1997), 2024-2027. Google Scholar

[40]

C. Watanabe, R. Kondo and A. Nagamatsu, Policy options for the diffusion orbit of competitive innovations: An application of Lotka-Volterra equations to Japan's transition from analog to digital TV broadcasting, Management Science, 23 (2003), 437-445. doi: 10.1016/S0166-4972(02)00004-4.  Google Scholar

[41]

C. Watanabe, R. Kondo, N. Ouchi and A. Wei, A substitution orbit model of competitive innovations, Technol. Forecast. Soc. Chang., 71 (2004), 365-390. doi: 10.1016/S0040-1625(02)00351-7.  Google Scholar

[42]

H. P. Young, Innovation Diffusion in Heterogeneous Populations: Contagion, Social Influence and Social Learning, SFI Working Papers,, 2007., ().   Google Scholar

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