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The Product Life Cycle of Durable Goods

  • Joachim Kaldasch

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 in its series Papers with number 1109.0828.

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Date of creation: Sep 2011
Date of revision: Sep 2015
Publication status: Published in British Journal of Economics, Management & Trade 10(2): 1-17, 2015, Article no.BJEMT.20395
Handle: RePEc:arx:papers:1109.0828
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  1. Kaldasch, Joachim, 2014. "Evolutionary model of stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 449-462.
  2. Kaldasch, Joachim, 2015. "Dynamic Model of the Price Dispersion of Homogeneous Goods," MPRA Paper 64723, University Library of Munich, Germany.
  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.
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  9. 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.
  10. 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.
  11. Joachim Kaldasch, 2011. "Dynamic Model of Markets of Homogenous Non-Durable," Papers 1109.5791,, revised Jul 2015.
  12. 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.
  13. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518,, revised Dec 2009.
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  16. 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.
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