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The product life cycle of durable goods

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  • Kaldasch, Joachim

Abstract

The model presented here derives the product life cycle of durable goods. It is based on the idea that the purchase process consists of first purchase and repurchase. First purchase is determined by the market penetration process (diffusion process), while repurchase is the sum of replacement and multiple purchase. The key property of durables goods is to have a mean lifetime in the order of several years. Therefore replacement purchase creates periodic variations of the unit sales (Juglar cycles) having its origin in the initial diffusion process. The theory suggests that there exists two diffusion processes. The first can be described by Bass diffusion and is related to the information spreading process within the social network of potential consumers. The other diffusion process comes into play, when the price of the durable is such, that only those consumers with a sufficient personal income can afford the good. We have to distinguish between a monopoly market and a polypoly/oligopoly market. In the first case periodic variations of the total sales occur caused by the initial Bass diffusion, even when the price is constant. In the latter case the mutual competition between the brands leads with time to a decrease of the mean price. This change is associated with an effective increase of the market volume, which can be interpreted as a diffusion process. Based on an evolutionary approach, it can be shown that the mean price decreases exponentially and the corresponding diffusion process is governed by Gompertz equation (Gompertz diffusion). Most remarkable is that Gibrat's rule of proportionate growth is a direct consequence of the competition between the brands. The model allows a derivation of the lognormal size distribution of product sales and the logistic replacement of durables in competition. A comparison with empirical data suggests that the theory describes the main trend of the product life cycle superimposed by short term events like the introduction of new models.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 33174.

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Date of creation: Sep 2011
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Handle: RePEc:pra:mprapa:33174

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Keywords: Product Life Cycle; Consumer Durables; Product Diffusion; Bass Diffusion; Competition; Gompertz Diffusion; Replicator Equation; Logistic Growth; Evolutionary Economics; Monopoly; Takeoff; Gibrat's Rule; Juglar Cycles;

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References

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  1. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
  2. 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.
  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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  5. 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.
  6. Anand Banerjee & Victor M. Yakovenko & T. Di Matteo, 2006. "A study of the personal income distribution in Australia," Papers physics/0601176, arXiv.org.
  7. 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.
  8. 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.
  9. 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.
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Cited by:
  1. Kaldasch, Joachim, 2011. "Evolutionary Model of Non-Durable Markets," EconStor Preprints 50531, ZBW - German National Library of Economics.
  2. Kaldasch, Joachim, 2011. "The experience curve and the market size of competitive consumer durable markets," MPRA Paper 33370, University Library of Munich, Germany.

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