IDEAS home Printed from https://ideas.repec.org/p/csc/ircrwp/201706.html
   My bibliography  Save this paper

A mathematical toy model of R&D process. How this model may be useful in studying territorial development

Author

Abstract

This work describes a mathematical application of a technological model of the R&D process, presented in a previous work, with the objective to contribute to a better knowledge of relation between R&D investments and growth. The model considers R&D as an organized flux of knowledge and capitals generating new technologies and a general knowledge exploitable for further R&D activities. The mathematical model makes an oversimplification of the R&D activity considering R&D investments related to number of R&D projects carried out, and economic growth, stagnation or decline, related to the number of new technologies entering in use. The model considers the circulating knowledge in a territory in term of number of information packages generated by R&D projects and external contributions in term of scientific, technical or other knowledge. A combinatory process with all available packages gives the total number of potential innovative ideas, part of them generating R&D project proposals. The ratio between the number of R&D proposals and the total number of potential innovative ideas may be considered related to the innovative system efficiency of the territory. Proposals are selected forming the number of R&D projects effectively carried out following the adopted strategies for financing R&D projects. The number of new technologies entering in use depends on a selection rate of all R&D projects carried out, and the number of new successful technologies with high rates of return of investment depends on a selection rate of all new technologies entering in use. The study considers an application of the model consisting in the introduction of a variable number of initial R&D projects in a territory with various degrees of innovative efficiency resulting or not, after a certain time, in entering in use of new technologies and possible successful technologies. Calculations show that dependence curves, in term of number of carried out R&D projects as a function of the innovative efficiency of the territory, and following dependence of formation or not of new or successful technologies, delimit three specific areas in the diagram corresponding to development, stagnation and decline of the technological asset of the territory. The results of calculations of the model show how complex is the relation between R&D investments and economic growth, characterized by absence or weak growth at level of R&D investments under a critical value, and exponential growth above due to the autocatalytic effect of R&D. This discontinuity resulting by the model calculations is in contrast with assumed continuity of dependence of growth by R&D investments often considered in econometric models.

Suggested Citation

  • Angelo Bonomi, 2017. "A mathematical toy model of R&D process. How this model may be useful in studying territorial development," IRCrES Working Paper 201706, CNR-IRCrES Research Institute on Sustainable Economic Growth - Moncalieri (TO) ITALY - former Institute for Economic Research on Firms and Growth - Torino (TO) ITALY.
    • Handle: RePEc:csc:ircrwp:201706
    as

    Download full text from publisher

    File URL: http://www.ircres.cnr.it/images/wp/wp_06_2017_Bonomi.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lam, Alice, 2011. "What motivates academic scientists to engage in research commercialization: ‘Gold’, ‘ribbon’ or ‘puzzle’?," Research Policy, Elsevier, vol. 40(10), pages 1354-1368.
    2. Bronwyn Hall & Francesca Lotti & Jacques Mairesse, 2009. "Innovation and productivity in SMEs: empirical evidence for Italy," Small Business Economics, Springer, vol. 33(1), pages 13-33, June.
    3. Angelo Bonomi, 2017. "A technological model of the R&D process and its implications with scientific research and socio-economic activities," IRCrES Working Paper 201702, CNR-IRCrES Research Institute on Sustainable Economic Growth - Moncalieri (TO) ITALY - former Institute for Economic Research on Firms and Growth - Torino (TO) ITALY.
    4. Bettina Becker, 2013. "The Determinants of R&D Investment: A Survey of the Empirical Research," Discussion Paper Series 2013_09, Department of Economics, Loughborough University, revised Sep 2013.
    5. Scherer, F. M. & Harhoff, Dietmar, 2000. "Technology policy for a world of skew-distributed outcomes," Research Policy, Elsevier, vol. 29(4-5), pages 559-566, April.
    6. Georges Haour, 2004. "Resolving the Innovation Paradox," Palgrave Macmillan Books, Palgrave Macmillan, number 978-0-230-51055-5.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Angelo Bonomi, 2018. "Le tecnologie di Industria 4.0 e le PMI/Technologies of Industry 4.0 and SMEs," IRCrES Working Paper 201804, CNR-IRCrES Research Institute on Sustainable Economic Growth - Moncalieri (TO) ITALY - former Institute for Economic Research on Firms and Growth - Torino (TO) ITALY.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Angelo Bonomi, 2017. "A technological model of the R&D process and its implications with scientific research and socio-economic activities," IRCrES Working Paper 201702, CNR-IRCrES Research Institute on Sustainable Economic Growth - Moncalieri (TO) ITALY - former Institute for Economic Research on Firms and Growth - Torino (TO) ITALY.
    2. Hall, B.H., 2011. "Innovation and productivity," MERIT Working Papers 2011-028, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    3. Andræs Barge-Gil, 2013. "Open Strategies and Innovation Performance," Industry and Innovation, Taylor & Francis Journals, vol. 20(7), pages 585-610, October.
    4. Baumann, Julian & Kritikos, Alexander S., 2016. "The link between R&D, innovation and productivity: Are micro firms different?," Research Policy, Elsevier, vol. 45(6), pages 1263-1274.
    5. Diego d’Andria & Dimitrios Pontikakis & Agnieszka Skonieczna, 2018. "Towards a European R&D incentive? An assessment of R&D provisions under a common corporate tax base," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 27(5-6), pages 531-550, August.
    6. Cohle, Zachary & Ortega, Alberto, 2023. "The effect of the opioid crisis on patenting," Journal of Economic Behavior & Organization, Elsevier, vol. 214(C), pages 493-521.
    7. Hille, Erik & Althammer, Wilhelm & Diederich, Henning, 2020. "Environmental regulation and innovation in renewable energy technologies: Does the policy instrument matter?," Technological Forecasting and Social Change, Elsevier, vol. 153(C).
    8. Laura Barbieri & Daniela Bragoli & Flavia Cortelezzi & Giovanni Marseguerra, 2015. "Public Support to Innovation Strategies," DISCE - Quaderni del Dipartimento di Scienze Economiche e Sociali dises1509, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).
    9. Silverberg, Gerald & Verspagen, Bart, 2002. "A Percolation Model of Innovation in Complex Technology," Research Memorandum 032, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).
    10. Borrás , Susana & Edquist , Charles, 2014. "Innovation Policy for Knowledge Production and R&D: the Investment Portfolio Approach," Papers in Innovation Studies 2014/21, Lund University, CIRCLE - Centre for Innovation Research.
    11. Tom Broekel & Matthias Brachert & Matthias Duschl & Thomas Brenner, 2015. "Joint R and D subsidies, related variety, and regional innovation," Working Papers on Innovation and Space 2015-01, Philipps University Marburg, Department of Geography.
    12. Roberto Iorio & Sandrine Labory & Francesco Rentocchini, 2014. "Academics’ Motivations and Depth and Breadth of Knowledge Transfer Activities," Working Papers 1401, c.MET-05 - Centro Interuniversitario di Economia Applicata alle Politiche per L'industria, lo Sviluppo locale e l'Internazionalizzazione.
    13. Anna Maria Biscotti & Eugenio D’Amico, 2019. "Does Equity Market Differently Perceive IC Management and Disclosure Behaviours?," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 10(2), pages 756-775, June.
    14. Richard Harris & John Moffat, 2011. "R&D, Innovation and Exporting," SERC Discussion Papers 0073, Centre for Economic Performance, LSE.
    15. Aiello, Francesco & Albanese, Giuseppe & Piselli, Paolo, 2019. "Good value for public money? The case of R&D policy," Journal of Policy Modeling, Elsevier, vol. 41(6), pages 1057-1076.
    16. Ioannis Giotopoulos & Alexander S. Kritikos & Aggelos Tsakanikas, 2023. "A lasting crisis affects R&D decisions of smaller firms: the Greek experience," The Journal of Technology Transfer, Springer, vol. 48(4), pages 1161-1175, August.
    17. Julia Olmos‐Peñuela & Paul Benneworth & Elena Castro‐Martínez, 2015. "Exploring the factors related with scientists’ willingness to incorporating external knowledge," CHEPS Working Papers 201504, University of Twente, Center for Higher Education Policy Studies (CHEPS).
    18. Hottenrott, Hanna & Lawson, Cornelia, 2014. "Flying the nest: How the home department shapes researchers’ career paths," Department of Economics and Statistics Cognetti de Martiis LEI & BRICK - Laboratory of Economics of Innovation "Franco Momigliano", Bureau of Research in Innovation, Complexity and Knowledge, Collegio 201409, University of Turin.
    19. Beck, Mathias & Junge, Martin & Kaiser, Ulrich, 2017. "Public Funding and Corporate Innovation," IZA Discussion Papers 11196, Institute of Labor Economics (IZA).
    20. Çağatay Bircan & Ralph De Haas, 2020. "The Limits of Lending? Banks and Technology Adoption across Russia," The Review of Financial Studies, Society for Financial Studies, vol. 33(2), pages 536-609.

    More about this item

    Keywords

    Technology innovation; Research & development; R&D model; R&D management; Socio-economic growth; Territorial development;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:csc:ircrwp:201706. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Anna Perin or Giancarlo Birello (email available below). General contact details of provider: https://edirc.repec.org/data/cerisit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.