A note on the classification of consumer demand functions with respect to retailer pass-through rates

Tyagi (1999) derived conditions on the curvature of consumer demand functions which make it optimal for a profit-maximizing retailer to pass-through greater (less) than 100% of a manufacturer trade deal amount. Since the pass-through is customarily evaluated at the optimal wholesale price, then additional sufficient conditions are needed to ensure the existence of an optimal wholesale price. The purpose of this note is to derive the additional required conditions on the curvature of the consumer demand functions for the existence of a greater (less) than 100% retailer pass-through rate at the optimal wholesale price.