The model presented here derives the product life cycle of durable goods. It is based on the idea that the purchase process consists of first purchase and repurchase. First purchase is determined by the market penetration process (diffusion process), while repurchase is the sum of replacement and multiple purchase. The key property of durables goods is to have a mean lifetime in the order of several years. Therefore replacement purchase creates periodic variations of the unit sales (Juglar cycles) having its origin in the initial diffusion process. The theory suggests that there exists two diffusion processes. The first can be described by Bass diffusion and is related to the information spreading process within the social network of potential consumers. The other diffusion process comes into play, when the price of the durable is such, that only those consumers with a sufficient personal income can afford the good . We have to distinguish between a monopoly market and a polypoly/oligopoly market. In the first case periodic variations of the total sales occur caused by the initial Bass diffusion, even when the price is constant. In the latter case the mutual competition between the brands leads with time to a decrease of the mean price. Based on an evolutionary approach , it can be shown that the mean price decreases exponentially and the corresponding diffusion process is governed by Gompertz equation (Gompertz diffusion). Most remarkable is that Gibrat's rule of proportionate growth is a direct consequence of the competition between the brands . The model allows a derivation of the lognormal size distribution of product sales and the logistic replacement of durables in competition. A comparison with empirical data suggests that the theory describes the main trend of the product life cycle superimposed by short term events like the introduction of new models .
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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The model presented here derives the product life cycle of
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
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It
The theory
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purchase process consists of
sales dynamics is determined by a meeting process of demanded with supplied product units. Taking advantage from the Bass model for
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repurchase. First purchase is determined by the market penetration process (diffusion process), while repurchase is the sum of replacement and multiple purchase. The key property of durables goods is to have a mean lifetime in the order of several years. Therefore replacement purchase creates periodic variations of the unit sales (Juglar cycles) having its origin in the initial diffusion process. The theory suggests that there exists two diffusion processes. The first can be described by Bass diffusion and is related to the information spreading process within the social network of potential consumers. The other diffusion process comes into play, when the
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
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durable is such, that only those consumers with a sufficient personal income can afford the good . We have to distinguish between a monopoly market and a polypoly/oligopoly market. In the first case periodic variations of the total sales occur caused by the initial Bass diffusion, even when the price is constant. In the latter case the mutual competition between the brands leads with time to a decrease of the mean price. Based on an evolutionary approach , it can be shown that the mean price decreases exponentially and the corresponding diffusion process is governed by Gompertz equation (Gompertz diffusion). Most remarkable is that Gibrat's rule of proportionate growth is a direct consequence of the competition between the brands
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
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allows a derivation of the lognormal size distribution of product sales and the logistic replacement of durables in competition. A comparison with empirical data
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
R
theory describes the main trend of the product life cycle superimposed by short term events like the introduction of new models
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