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Evolutionary Model of a Anonymous Consumer Durable Market

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  • Joachim Kaldasch

Abstract

An analytic model is presented that considers the evolution of a market of durable goods. The model suggests that after introduction goods spread always according to a Bass diffusion. However, this phase will be followed by a diffusion process for durable consumer goods governed by a variation-selection-reproduction mechanism and the growth dynamics can be described by a replicator equation. Describing the aggregate sales as the sum of first, multiple and replacement purchase the product life cycle can be derived. Replacement purchase causes periodic variations of the sales determined by the finite lifetime of the good (Juglar cycles). The model suggests that both, Bass- and Gompertz diffusion may contribute to the product life cycle of a consumer durable. The theory contains the standard equilibrium view of a market as a special case. It depends on the time scale, whether an equilibrium or evolutionary description is more appropriate. The evolutionary framework is used to derive also the size, growth rate and price distribution of manufacturing business units. It predicts that the size distribution of the business units (products) is lognormal, while the growth rates exhibit a Laplace distribution. Large price deviations from the mean price are also governed by a Laplace distribution (fat tails). These results are in agreement with empirical findings. The explicit comparison of the time evolution of consumer durables with empirical investigations confirms the close relationship between price decline and Gompertz diffusion, while the product life cycle can be described qualitatively for a long time period.

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Paper provided by arXiv.org in its series Papers with number 1306.3395.

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Date of creation: Jun 2013
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Publication status: Published in Physica A 390(2011)2692 2715
Handle: RePEc:arx:papers:1306.3395

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Cited by:
  1. Kaldasch, Joachim, 2011. "The Product Life Cycle of Durable Goods," EconStor Preprints 50530, ZBW - German National Library of Economics.
  2. Joachim Kaldasch, 2012. "Evolutionäre Diffusion und der Produktlebenszyklus von Gebrauchsgütern," EconStor Preprints 59748, ZBW - German National Library of Economics.
  3. Joachim Kaldasch, 2012. "Evolutionary Model of the Growth and Size of Firms," Papers 1208.1123, arXiv.org.
  4. Kaldasch, Joachim, 2011. "Evolutionary Model of Non-Durable Markets," EconStor Preprints 50531, ZBW - German National Library of Economics.
  5. Kaldasch, Joachim, 2011. "The experience curve and the market size of competitive consumer durable markets," MPRA Paper 33370, University Library of Munich, Germany.
  6. Kaldasch, Joachim, 2012. "Evolutionary model of the personal income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5628-5642.
  7. Kaldasch, Joachim, 2014. "Evolutionary Model of Moore’s Law," MPRA Paper 54397, University Library of Munich, Germany.

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