Why demand models must be monotonic in price: A deep dive into model choice for markdown optimization

In markdown optimization and retail pricing, one of the fundamental modeling constraints is that predicted demand must be a monotonically decreasing function of price.

This principle—though often taken for granted—has profound implications for model selection, interpretability, and the economic validity of downstream optimization. In this post, I’ll unpack why monotonicity matters, what models satisfy this requirement, and why this constraint often rules out the use of black-box machine learning methods in prescriptive pricing systems.

In plain terms, the predicted demand curve should either stay flat or decline as price rises. This ensures that the model respects the law of demand and allows for consistent estimation of price elasticity, which is central to optimization and decision-making.

This requirement—simple in theory—has strong implications for the types of predictive models we can use in markdown optimization or dynamic pricing systems.