Pricing for profit in dynamic competitive markets using logit demand models: closed form optima and some corollaries

Abstract

This manuscript develops and simplifies a pricing decision model for maximum profit as a function of unit variable cost, 3 estimated price-demand response points, a simplified representation of known competitor intensity and dynamic pricing behaviour and typically known down-channel demanded mark-ups that uses a logit price-demand response model. Including a logit price-demand response model supports pricing decisions that simultaneously optimise both net profit, and Gross Marginal Return On Investment or GMROI. Differential calculus methods are used to produce a simplified function to optimise profitability. Worked examples demonstrate the ease of use and practical usefulness of such supported pricing decisions in typical decision making contexts using conventional decision making aids. Pilot surveys of pricing decision makers indicated two qualitatively different decision making processes, only one of which is near optimal. This method adapts to a range of logit price-demand response model complexity from a simple primary category demand response capturing a pricing decision-maker’s response expectations to more complex alternative-specific-coefficient multinomial logit models fitted to scanner panel revealed preference or stated preference survey data. The model also adapts across channel depth from direct manufacturer sales to many channel members. Market simulations using typical brand equity, price elasticity, competitor intensity and dynamic pricing response heuristics delivers informative insights that somewhat contradict more established market pricing axioms and interpretation