Inferior Goods, Giffen Goods, and Shochu

According to a well-known result by W. Hildenbrand [6], if all consumers possess the same demand function and the density of the expenditure distribution is decreasing, than the average income effect term is non-negative even if inferior goods are present, so that the aggregate demand must be monotone. We show that if the expenditure density is uni-modal and a certain relation between the income density and individual demand is satisfied, than the average income effect term is negative and Giffen goods are not ruled out. We show that the lowest-grade rice-based Japanese spirit (shochu) satisfies this condition. The data suggest that this commodity might be a Giffen good.