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Evolutionary Model of Non-Durable Markets

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  • Joachim Kaldasch

Abstract

Presented is an evolutionary model of consumer non-durable markets, which is an extension of a previously published paper on consumer durables. The model suggests that the repurchase process is governed by preferential growth. Applying statistical methods it can be shown that in a competitive market the mean price declines according to an exponential law towards a natural price, while the corresponding price distribution is approximately given by a Laplace distribution for independent price decisions of the manufacturers. The sales of individual brands are determined by a replicator dynamics. As a consequence the size distribution of business units is a lognormal distribution, while the growth rates are also given by a Laplace distribution. Moreover products with a higher fitness replace those with a lower fitness according to a logistic law. Most remarkable is the prediction that the price distribution becomes unstable at market clearing, which is in striking difference to the Walrasian picture in standard microeconomics. The reason for this statement is that competition between products exists only if there is an excess supply, causing a decreasing mean price. When, for example by significant events, demand increases or is equal to supply, competition breaks down and the price exhibits a jump. When this supply shortage is accompanied with an arbitrage for traders, it may even evolve into a speculative bubble. Neglecting the impact of speculation here, the evolutionary model can be linked to a stochastic jump-diffusion model.

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Paper provided by arXiv.org in its series Papers with number 1109.5791.

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Date of creation: Sep 2011
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Handle: RePEc:arx:papers:1109.5791

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  1. Kaldasch, Joachim, 2011. "Evolutionary model of an anonymous consumer durable market," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 390(14), pages 2692-2715.
  2. Joachim Kaldasch, 2011. "The Product Life Cycle of Durable Goods," Papers 1109.0828, arXiv.org.
  3. Kaldasch, Joachim, 2011. "The experience curve and the market size of competitive consumer durable markets," MPRA Paper 33370, University Library of Munich, Germany.
  4. Giulio Bottazzi & Sandro Sapio & Angelo Secchi, 2004. "Some Statistical Investigations on the Nature and Dynamics of Electricity Prices," LEM Papers Series, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy 2004/13, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
  6. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 12(04), pages 627-627, November.
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Cited by:
  1. Kaldasch, Joachim, 2012. "Evolutionary Model of the Personal Income Distribution," MPRA Paper 37865, University Library of Munich, Germany.
  2. Kaldasch, Joachim, 2012. "Evolutionary model of the growth and size of firms," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 391(14), pages 3751-3769.

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