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Evolutionary Model of a Anonymous Consumer Durable Market

Sat, 01 Jun 2013 04:19:07 GMT

A 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 Bass diffusion. However, this phase will be followed for durable consumer goods by a diffusion process governed by a variation-selection-reproduction mechanism and the growth dynamics can be described by a replicator equation.The theory suggests that products play the role of species in biological evolutionary models. It implies that the evolution of man made products can be arranged into an evolutionary tree. The model also suggests that each product can be characterized by its product fitness. The fitness space contains elements of both sites of the market, supply and demand. The unit sales of products with a higher product fitness compared to the mean fitness increase. Durables with a constant fitness advantage replace other goods according to a logistic law. The model predicts in particular that the mean price exhibits an exponential decrease over a long time period for durable goods. The evolutionary diffusion process is directly related to this price decline and is governed by Gompertz equation. Therefore it is denoted as Gompertz diffusion. 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). 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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