Practice — Pricing Optimization & Marketplace Economics (6 questions)

You are the data scientist at a grocery delivery app with 40,000 SKUs and about 2 million weekly orders across 60 cities. The pricing team wants SKU-level price elasticities to drive weekly price updates. Historical logs show prices that were set by category managers (they cut prices on slow items and raise them around holidays), plus occasional supplier-driven cost changes. A first regression of log units on log price gave a pooled slope of -0.4.

Explain what is wrong with that number, and design the estimation program: where the price variation comes from, the unit of randomization, the model, how you handle the many SKUs with little data, how you handle substitutes, and what you report to the pricing team.

A retailer holds 250 units of a seasonal jacket for the last 3 weeks of the season. Each week it can sell at price level 40, 32 or 24 dollars. Estimated weekly demand at each price level is:

Unsold units after week 3 are worth nothing. (a) Formulate a linear program that maximizes revenue. (b) State what the dual of the inventory constraint means and estimate it. (c) The LP gives fractional weeks. How do you deal with that? (d) Name three constraints or complications a real markdown system adds.