The Product Life Cycle of Durable Goods

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

Evolutionary Model of Non-Durable Markets

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.non-durables; evolutionary economics; economic growth; price distribution; Laplace distribution; replicator equation; firm growth; growth rate distribution; competition; jump-diffusion model

The product life cycle of durable goods

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. This change is associated with an effective increase of the market volume, which can be interpreted as a diffusion process. 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.Product Life Cycle, Consumer Durables, Product Diffusion, Bass Diffusion; Competition; Gompertz Diffusion; Replicator Equation; Logistic Growth; Evolutionary Economics; Monopoly; Takeoff; Gibrat's Rule; Juglar Cycles;

The experience curve and the market size of competitive consumer durable markets

An evolutionary model of the product life cycle is applied to derive the experience curve and the market size of (expensive) durable goods. The experience (learning) curve suggests that the real costs per unit decrease with an increasing cumulative output (Henderson's law). Based on the idea that in a competitive market firms are forced to pass cost advantages on to the price, the evolutionary model suggests that the mean price and also the mean costs are governed by an exponential decline with time. Simultaneously the mean price evolution satisfies Henderson's law. The market size is defined here by the number of active firms. The market size is shown to follow the total market revenue if the latter exhibits fast variations, else the size is nearly constant. A comparison with an empirical investigation confirms the model predictions.experience curve; learning curve; market evolution; evolutionary economics; economic growth; product diffusion; Gompertz diffusion; product life cycle; durable goods

The Product Life Cycle of Durable Goods

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. This change is associated with an effective increase of the market volume, which can be interpreted as a diffusion process. 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. --Consumer Durables,Product Life Cycle,Product Diffusion,Bass Diffusion,Gompertz Diffusion,Replicator Dynamics,Logistic Growth,Evolutionary Economics,Monopoly,Gibrat's Rule,Juglar Cycles

Evolutionary Model of the Personal Income Distribution

The aim of this work is to establish the personal income distribution from the elementary constituents of a free market; products of a representative good and agents forming the economic network. The economy is treated as a self-organized system. Based on the idea that the dynamics of an economy is governed by slow modes, the model suggests that for short time intervals a fixed ratio of total labour income (capital income) to net income exists (Cobb-Douglas relation). Explicitly derived is Gibrat's law from an evolutionary market dynamics of short term fluctuations. The total private income distribution is shown to consist of four main parts. From capital income of private firms the income distribution contains a lognormal distribution for small and a Pareto tail for large incomes. Labour income contributes an exponential distribution. Also included is the income from a social insurance system, approximated by a Gaussian peak. The evolutionary model is able to reproduce the stylized facts of the income distribution, shown by a comparison with empirical data of a high resolution income distribution. The theory suggests that in a free market competition between products is ultimately the origin of the uneven income distribution

The Price Distribution of Consumer Goods in Retail Markets

Derived is an analytic dynamic model of the price distribution of consumer goods in retail markets. The stationary price distribution is established from the conservation equation of offered units and two simplifying assumptions. Under the condition that independent traders make small random price variations around a nearly constant supply price, the stationary price distribution of a good must have the form of a fat-tailed Laplace distribution. The standard deviation of the distribution is determined by the price volatility of the goods. Also, the price distribution of an ensemble of goods is established and applied to empirical data with good quantitative agreement

Evolutionary Model of Non-Durable Markets

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