Industry: Retail Product: ModelRisk Application: Understanding and Predicting Consumer Behavior
A category manager about to push list price up 8% wants one number: how much volume walks out the door? The pricing deck answers with a point estimate — plug the historical elasticity, get -9.5%, sign off. But that single figure hides the real exposure. When a multinational retail chain rebuilt the calculation in ModelRisk, treating the price elasticity as uncertain (it varies category to category) and adding a shared consumer-sentiment swing that moves every category at once, the answer became a distribution, not a digit. The mean still lands at -9.3%, almost exactly the point estimate — but the probability that volume falls by more than 10% is 46.7%, essentially a coin flip, and there is an 18.3% chance it falls more than 15%. The deck's tidy "-9.5%" gives no hint of that downside.
This is a market-level behavioral question — how the aggregate category responds to a driver — not a question about any individual shopper. The driver here is price; the same machinery handles an income shift or a sentiment shock.
Aggregate demand follows the constant-elasticity (log-log) law D = D0 x (P/P0)^(-E). Feed it one "best" elasticity and you get one demand number. But elasticity is not one number — across the categories in this chain it is dispersed (modeled Normal, mean 1.30, sd 0.45, clipped positive so a price rise never raises volume), and a market-wide sentiment factor multiplies every category's response in any given quarter. Because that sentiment shock is shared, the category-level response does not average away to its mean by the law of large numbers — a jittery quarter is jittery for the whole shelf at once. The point estimate throws away both sources of spread and reports only the center, which is precisely the information a pricing committee does not need: they already know the average; they need the odds of a bad outcome.
D = D0 x (P/P0)^(-E)
Sweeping the price move from 0% to 20% turns the single decision into a response surface, with the mean response and the P10-P90 band at every price point.
The band, not the line, is the decision content: at the chosen +8%, the worst-decile outcome is roughly twice the mean loss.
Ranking drivers by their effect on the mean is misleading — the average is nearly insensitive to spread parameters. The committee cares about the downside, so the tornado ranks each driver by its effect on the P10 (worst-decile) volume loss, baseline -17.2%.
The surprise is that sentiment volatility rivals the price move itself in setting the downside — a result invisible to any mean-based analysis, because sentiment volatility leaves the mean untouched and only fattens the tail.
At the fixed +8% price rise, the probability of losing more than x% of volume depends sharply on whether the market is calm or jittery.
The two curves cross near the 10% threshold: sentiment volatility barely changes the typical outcome but transforms the tail. In a calm market a 20%-plus collapse is a 1-in-250 event; in a jittery market it is better than 1-in-9. Knowing which regime you are entering is worth more than refining the elasticity estimate.
The average response to a price rise is the question the pricing deck already answers. The question worth modeling is the probability of a damaging volume loss — and Monte Carlo turns that into a defensible percentage the category committee can sign against.