Explaining the “Buy One Get One Free” Promotion: The Golden Ratio as a Marketing Tool

Buy-one-get-one-free (BOGOF) promotions are a common feature of retail food markets, but why are they so widespread? The theory of Relative Utility Pricing (RUP) developed in this paper provides an explanation not only for supermarket promotional offers but also for more general pricing of packs of different sizes in supermarkets and on the internet. A clear and simple explanation is given for the two most widely used quantity promotions: BOGOF and 3-for-the-price-of-2. The RUP model may be linked to the theory of iso-elastic utility functions, and this allows the relationships amongst risk-aversion, pack-size ratio and demand elasticity to be explored. “Cautious consumers”, as defined in the paper, are found to be the only sensible target for quantity promotions. It is argued that the needs of cautious consumers of retail commodities will be best addressed if the vendor sets the ratio of successive pack sizes as the square of the Golden Ratio, namely 2.62, and the price-ratio at the Golden Ratio, 1.62. Thus the Golden Ratio may be regarded as a marketing guide for vendors considering both their best interests and those of their customers. This proposition is supported by an analysis showing that higher profits are more likely to come from Golden Ratio sizing than from either BOGOF or 3-for-2 when variable costs lie in most of the upper half of the range that is required for any of these multibuy offers to generate profit. The paper’s theoretical predictions for both pack sizes and prices are supported by examples from the retail sector: grocery, paperback books and electronics.