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The Product Life Cycle of Durable Goods

  • Kaldasch, Joachim

A dynamic model of the product lifecycle of (nearly) homogeneous durables in polypoly markets is established. It describes the concurrent evolution of the unit sales and price of durable goods. The theory is based on the idea that the sales dynamics is determined by a meeting process of demanded with supplied product units. Taking advantage from the Bass model for first purchase and a logistic model for repurchase the entire product lifecycle of a durable can be established. For the case of a fast growing supply the model suggests that the mean price of the good decreases according to a logistic law. Both, the established unit sales and price evolution are in agreement with the empirical data studied in this paper. The presented approach discusses further the interference of the diffusion process with the supply dynamics. The model predicts the occurrence of lost sales in the initial stages of the lifecycle due to supply constraints. They are the origin for a retarded market penetration. The theory suggests that the imitation rate B indicating social contagion in the Bass model has its maximum magnitude for the case of a large amount of available units at introduction and a fast output increase. The empirical data of the investigated samples are in qualitative agreement with this prediction.

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Paper provided by ZBW - German National Library of Economics in its series EconStor Preprints with number 50530.

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Date of creation: 2011
Date of revision:
Handle: RePEc:zbw:esprep:50530
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  1. Joachim Kaldasch, 2015. "Dynamic Model of the Price Dispersion of Homogeneous Goods," Papers 1509.01216,
  2. Banerjee, Anand & Yakovenko, Victor M. & Di Matteo, T., 2006. "A study of the personal income distribution in Australia," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 54-59.
  3. Kaldasch, Joachim, 2011. "Evolutionary model of an anonymous consumer durable market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2692-2715.
  4. Shlomo Kalish, 1985. "A New Product Adoption Model with Price, Advertising, and Uncertainty," Management Science, INFORMS, vol. 31(12), pages 1569-1585, December.
  5. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518,, revised Dec 2009.
  6. De Fabritiis, G. & Pammolli, F. & Riccaboni, M., 2003. "On size and growth of business firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 38-44.
  7. Teck-Hua Ho & Sergei Savin & Christian Terwiesch, 2002. "Managing Demand and Sales Dynamics in New Product Diffusion Under Supply Constraint," Management Science, INFORMS, vol. 48(2), pages 187-206, February.
  8. Sandro Sapio, 2006. "An Empirically Based Model of the Supply Schedule in Day-Ahead Electricity Markets," LEM Papers Series 2006/12, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  9. Zhu Wang, 2008. "Income Distribution, Market Size and the Evolution of Industry," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 542-565, July.
  10. Growiec, Jakub & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2008. "On the size distribution of business firms," Economics Letters, Elsevier, vol. 98(2), pages 207-212, February.
  11. Anand Banerjee & Victor M. Yakovenko & T. Di Matteo, 2006. "A study of the personal income distribution in Australia," Papers physics/0601176,
  12. Joachim Kaldasch, 2011. "Dynamic Model of Markets of Homogenous Non-Durable," Papers 1109.5791,, revised Jul 2015.
  13. Steffens, Paul R, 2001. "An Aggregate Sales Model for Consumer Durables Incorporating a Time-Varying Mean Replacement Age," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(1), pages 63-77, January.
  14. Sergey V. Buldyrev & Jakub Growiec & Fabio Pammolli & Massimo Riccaboni & H. Eugene Stanley, 2007. "The Growth of Business Firms: Facts and Theory," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 574-584, 04-05.
  15. Kaldasch, Joachim, 2014. "Evolutionary model of stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 449-462.
  16. Frank M. Bass & Trichy V. Krishnan & Dipak C. Jain, 1994. "Why the Bass Model Fits without Decision Variables," Marketing Science, INFORMS, vol. 13(3), pages 203-223.
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