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Predicting product life cycle patterns

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Abstract

In this paper, we propose a new model of adoption and repurchase due to upgrades driven by the utility of technology products that keep improving. The model is able to predict product life cycle patterns that could not be explained previously. Such patterns were used to challenge diffusion theory validity. Mathematically, the model is described as a nonlinear discrete system that depends on a small set of parameters. We investigate the dynamic properties of the nonlinear system using numerical stability analysis. We find domains in the parameters space in which the equilibrium point and the periodical orbits are stable. The domains correspond to population heterogeneity, tendency to upgrade, and the influence of industry response on market dynamics. We also implement our model to fit actual data of two real-world product life cycles with many irregularities and benchmark the results of our model vs. well-known models.

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Notes

  1. The examples are available from the authors upon request.

  2. Note that, unlike Chandrasekaran and Tellis (2011), we model the entire product life cycle and are not limited to forecasting only the edges of the “irregular” periods.

  3. Adoption is measured as a portion of the maximal potential market (at maximum utility).

  4. We calculated sales for up to 100 periods while the adoption peak time was at 20.

  5. The threshold is not precisely the peak, which match utility increase of \( 0.5\times \left( {1-{{{\widetilde{u}}}_0}} \right) \), but a short time, observed numerically, after the peak.

  6. We calculated the sales for 100 periods.

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Acknowledgments

The authors thank the editor and anonymous reviewers for the very helpful and constructive comments that lead to a significantly improved manuscript. In addition, the authors thank Oded Gottlieb for his very helpful advice regarding the numerical analysis of cycles and chaos in nonlinear dynamic systems.

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  1. Graduate School of Business Administration, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Yair Orbach & Gila E. Fruchter

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  1. Yair Orbach
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  2. Gila E. Fruchter
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Correspondence to Gila E. Fruchter.

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Orbach, Y., Fruchter, G.E. Predicting product life cycle patterns. Mark Lett 25, 37–52 (2014). https://doi.org/10.1007/s11002-013-9239-0

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