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.Describing the aggregate sales as the sum of first, multiple and replacement purchase the product lifecycle 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 2 2 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.
A second-order perturbation theory based on statistical thermodynamics is employed to calculate the phase diagram of suspensions of charge-stabilized, monodisperse, spherical, colloidal particles that are assumed to interact by a standard DLVO potential. Taking into account van der Waals forces, the phase diagram consists of an ordered colloidal crystal, a disordered fluid phase, and a liquid phase that is formed by particles flocculated into the secondary minimum.
The authors previously introduced an activation model for the onset of shear thickening in electrically stabilized colloidal suspensions. It predicts that shear thickening occurs, when particles arranged along the compression axis in a sheared suspension do overcome the electrostatic repulsion at a critical shear stress, and are captured in the primary minimum of the DLVO interaction potential. A comparison with an experimental investigation on nonaqueous silica suspensions, carried out by Maranzano and Wagner, is performed. For particle systems that fall into the applicability range of the theory, a good coincidence between the experimental data and the model predictions can be found.
Presented is an analytic microeconomic model of the temporal price dispersion of homogeneous goods in polypoly markets. This new approach is based on the idea that the price dispersion has its origin in the dynamics of the purchase process. The price dispersion is determined by the chance that demanded and supplied product units meet in a given price interval. It can be characterized by a fat-tailed Laplace distribution for short and by a lognormal distribution for long time horizons. Taking random temporal variations of demanded and supplied units into account both the mean price and also the standard deviation of the price dispersion are governed by a lognormal distribution. A comparison with empirical investigations confirms the model statements.
A dynamic model of the product lifecycle of (nearly) homogeneous durables in polypoly markets is established. It describes the concurrent evolution of the unit sales and price of durable goods. The theory is based on the idea that the sales dynamics is determined by a meeting process of demanded with supplied product units. Taking advantage from the Bass model for first purchase and a logistic model for repurchase the entire product lifecycle of a durable can be established. For the case of a fast growing supply the model suggests that the mean price of the good decreases according to a logistic law. Both, the established unit sales and price evolution are in agreement with the empirical data studied in this paper. The presented approach discusses further the interference of the diffusion process with the supply dynamics. The model predicts the occurrence of lost sales in the initial stages of the lifecycle due to supply constraints. They are the origin for a retarded market penetration. The theory suggests that the imitation rate B indicating social contagion in the Bass model has its maximum magnitude for the case of a large amount of available units at introduction and a fast output increase. The empirical data of the investigated samples are in qualitative agreement with this prediction.
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