Stochastic modelling of household behaviour before, during and after a consumer price promotion

A stochastic model is developed to study household behaviour with regard to purchase quantity, brand choice and purchase timing before, during and after a price change and a price promotion such as price‐offs and price‐cuts. The basic assumption of the model is that price promotion and levels of consumer inventory influence a household's purchase‐timing and brand‐switching decisions. The model incorporates market segments and brand switching on aggregated demand for the brands by the use of multivariate Markov processes. A transient stochastic model is employed to analyse the dynamic process of household behaviour before, during, and after a price promotion. The interpurchase time that is derived from the model does not require any assumptions and is not independently, identically distributed. An empirical analysis using the Information Resources Incorporated cracker data indicated that (1) price promotion does affect household purchase of the brand and (2) households with larger family size tend to purchase promoted items. We conjecture that households with larger family size take advantage of the lower price of the promoted brands while smaller households tend to remain loyal to one brand.