algo-price-elasticity

# Price Elasticity of Demand ## Overview Price elasticity measures the percentage change in quantity demanded for a 1% change in price. Ed = %ΔQ / %ΔP. |Ed| > 1 = elastic (price-sensitive), |Ed| < 1 = inelastic (price-insensitive). Critical for pricing decisions and revenue optimization. ## When to Use **Trigger conditions:** - Estimating how a price change will affect unit sales and revenue - Determining if demand is elastic or inelastic for a product - Optimizing price for maximum revenue or profit **When NOT to use:** - When you need consumer willingness-to-pay distribution (use Van Westendorp or conjoint) - When pricing multiple products together (use bundle pricing) ## Algorithm ``` IRON LAW: Elasticity Is NOT Constant Along a Linear Demand Curve It varies at every price point. At high prices, demand is elastic (small price increase → big volume drop). At low prices, demand is inelastic. Always calculate at the SPECIFIC price point of interest. Revenue-maximizing price is where Ed = -1 (unit elastic). ``` ### Phase 1: Input Validation Collect: price-quantity pairs over time (or across markets). Control for: seasonality, promotions, competitor actions, other confounders. **Gate:** Minimum 10 price-quantity observations, confounders identified. ### Phase 2: Core Algorithm **Point elasticity:** Ed = (dQ/dP) × (P/Q) at a specific price point **Arc elasticity:** Ed = ((Q₂-Q₁)/((Q₂+Q₁)/2)) / ((P₂-P₁)/((P₂+P₁)/2)) between two points **Regression method:** log(Q) = α + ...