TITLE:
Explaining the “Buy One Get One Free” Promotion: The Golden Ratio as a Marketing Tool
AUTHORS:
Philip Thomas, Alec Chrystal
KEYWORDS:
Relative Utility Pricing; Golden Ratio Pricing; Buy One Get One Free; Multibuy Promotions; Utility Theory
JOURNAL NAME:
American Journal of Industrial and Business Management,
Vol.3 No.8,
December
12,
2013
ABSTRACT:
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.