Using Relative Utility Pricing to Explain Multibuy Prices in Supermarkets and on the Internet

Abstract

The Relative Utility Pricing (RUP) model is used to explain the prices for commodities being sold in supermarkets and on the internet. Grocery prices offered by the supermarkets, Tesco, Sainsbury and Waitrose in December 2009 and August 2013, are considered, as well as the prices of electronic items offered by Amazon on the internet at the same dates. The observed price for a pack can be given an explanation in terms of its size relative to the smallest pack considered by the customer (the baseline pack), the price and variable cost associated with the baseline pack and the demand density. The optimal price may be predicted using a profit maximising calculation if these data are available. Even if the vendor’s knowledge of the demand density is poor or non-existent, it is still possible for a vendor knowing his unit variable cost to calculate a useful approximation to the profit-maximising price by using a uniform or Rectangular demand density to represent customer demand. Alternatively, if there are no independent data on the demand density but the prices of the packs are available, it is possible to determine the approximate shape of the demand density leading to those prices. This demand density will then indicate whether the demand is soft or hard, with the Rectangular distribution indicating a neutral market. We consider the vendor to be a large retailer, such as a supermarket, who can obtain the product that he wishes to sell from a variety of suppliers at constant per-unit variable cost and hence marginal cost. Any sales at a price above marginal cost will contribute to profit. The RUP model provides an approximate match to the prices observed for supermarket milk and eggs by adjusting the demand density. A softening of the market for farm retail commodities is revealed between December 2009 and August 2013, fully consistent with the coincident long period of low growth and falling real wages in the UK economy. It is shown how the vendor may use product differentiation to buck this trend. The RUP model explains also the current prices of USB memory sticks, how those prices have evolved and how they are likely to evolve over time.