Econometric analyses of demand for butter in a number of countries have produced results which appeared to conflict with expectations. Specifically the sign of the co‐efficient for margarine price was negative rather than the positive sign expected with a presumed substitute product.Gollnick (1954), who was the first econometrician to meet this problem, advanced the hypothesis of a constant fat budget to explain the paradox. Among other works which reported similar paradoxical results were Hesse (1967), Wierenga (1968 and 1974), Oskam and Wierenga (1974), Upton and Wittenberg (1974) and Vertessen (1979). The markets studied were Germany, Netherlands and Belgium.In this paper we discuss the Gollnick hypothesis (it appears to have been ignored in English language economic journals), explore its mathematical implications, present some recent results which appear to support it and discuss whether the hypothesis might be valid for other product