Demand systems and frequency of purchase models

Understanding the frequencies of purchase and the average purchased quantities is important for marketing strategies such as the loss-leader pricing strategy. We develop a framework for analysing a demand system incorporating both these dimensions and show how the results can be used to formulate profitable marketing strategies for large food retailers. In our microeconomic model, total purchases are determined by two demand systems; one for frequencies and one for average quantities purchased conditional on positive purchase frequencies. An econometric model was developed to estimate the two systems by a Bayesian estimation method, which allows for an unrestricted covariance structure within each system. We estimated the systems using French scanner data for purchases of fresh salmon, fresh white fish and other fresh fish. The own-price elasticities for total quantities purchased were very similar in magnitude, whereas the own-price elasticities for purchase frequencies and average quantities purchased varied more. This variation can be used to determine good loss-leader products for a large retailer. In our case, it involves lowering the price of salmon and increasing the price of white fish.