The Product Life Cycle of Durable Goods

TL;DR

This paper develops a dynamic model for the product lifecycle of durable goods, integrating sales and price evolution, and validates it with empirical data, highlighting the impact of supply constraints and diffusion processes.

Contribution

It introduces a comprehensive model combining sales, pricing, and diffusion dynamics for durable goods, extending the Bass model with supply considerations.

Findings

Price decreases follow a logistic law during rapid supply growth.

Supply constraints cause initial lost sales and slow market penetration.

Imitation rate peaks with high initial supply and fast output increase.

Abstract

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.