Price Elasticity Calculator

Price Elasticity Calculator — Price Elasticity Analysis + Optimal Pricing

A skill that enhances the pricing analysis capabilities of pricing-simulator and competitive-analyst.

Target Agents

• pricing-simulator — Quantitatively analyzes the impact of price change scenarios
• competitive-analyst — Analyzes cross-price elasticity of competitor price changes

Price Elasticity Core Formulas

Price Elasticity of Demand (PED)

PED = (% Change in Quantity Demanded) / (% Change in Price)
    = (dQ/Q) / (dP/P)

Midpoint Formula (more accurate):
PED = [(Q2-Q1)/((Q1+Q2)/2)] / [(P2-P1)/((P1+P2)/2)]

Interpretation:
  |PED| > 1: Elastic — demand is sensitive to price changes
  |PED| = 1: Unit elastic — no change in revenue
  |PED| < 1: Inelastic — demand is insensitive to price changes

Example:
  10% price increase, 15% demand decrease
  PED = -15% / 10% = -1.5 (elastic)

Cross-Price Elasticity (XED)

XED = (% Change in Own Demand) / (% Change in Competitor Price)

Interpretation:
  XED > 0: Substitute relationship (competitor price up → own demand up)
  XED < 0: Complement relationship
  XED ≈ 0: Unrelated

Example:
  Competitor price increase 20%, own demand increase 10%
  XED = 10% / 20% = 0.5 (weak substitute)

Industry Elasticity Benchmarks

Optimal Price Derivation

Revenue-Maximizing Price

Revenue R = P x Q(P)
Demand function: Q(P) = a - b*P  (linear assumption)

Optimal price P* = a / (2b)

Example:
  Q = 10,000 - 50P (monthly demand)
  P* = 10,000 / (2x50) = 100
  Q* = 10,000 - 50x100 = 5,000
  R* = 100 x 5,000 = 500,000

Profit-Maximizing Price

Profit pi = (P - C) x Q(P)
  C = unit variable cost

Optimal price P* = (a + b*C) / (2b)

Example:
  Q = 10,000 - 50P, unit variable cost C = 30
  P* = (10,000 + 50x30) / (2x50) = 115
  Q* = 10,000 - 50x115 = 4,250
  pi* = (115-30) x 4,250 = 361,250

Price Change Simulation

Scenario Analysis Template

Current State:
  Price: P0 = $100
  Demand: Q0 = 5,000 units/month
  Revenue: R0 = $500,000/month
  Elasticity: PED = -1.5

Scenario 1: 10% Increase
  New Price: $110
  Demand Change: -15% → 4,250 units
  New Revenue: $467,500 (-6.5%)
  Net Profit Change: [Calculate with margin]

Scenario 2: 10% Decrease
  New Price: $90
  Demand Change: +15% → 5,750 units
  New Revenue: $517,500 (+3.5%)
  Net Profit Change: [Calculate with margin]

Scenario 3: 20% Increase + Feature Addition
  New Price: $120
  Expected Elasticity: -1.0 (dampened by increased value)
  Demand Change: -20% x (-1.0/-1.5) = -13.3%
  ...

P&L Impact Analysis

| Item | Current | Scenario 1 | Scenario 2 | Scenario 3 |
|------|---------|-----------|-----------|-----------|
| Price | $100 | $110 | $90 | $120 |
| Demand | 5,000 | 4,250 | 5,750 | 4,333 |
| Revenue | $500K | $467.5K | $517.5K | $520K |
| Variable Cost | $150K | $127.5K | $172.5K | $130K |
| Contribution Margin | $350K | $340K | $345K | $390K |
| Fixed Cost | $200K | $200K | $200K | $220K |
| Net Profit | $150K | $140K | $145K | $170K |

Price Increase Execution Strategy

1. Gradual Increase
   - 2-3 small increases per year (5-10%)
   - Minimize customer resistance
   - Set grace period for existing customer discounts

2. Value-Based Increase
   - Increase simultaneously with new feature launch
   - Message: "We are delivering more value"
   - Maintain existing plans + add premium plan

3. Segmented Increase
   - Apply to new customers first
   - 6-12 month grace period for existing customers
   - Separate management for price-sensitive segments

4. Discount Reduction
   - Maintain list price, reduce discount depth
   - Positioned as "discount normalization" rather than price increase

Price War Response

Decision tree when competitor cuts price:

1. High cross-elasticity (XED > 0.5)?
   +-- Yes → High churn risk
   |   +-- Do we have cost advantage? → Price matching
   |   +-- If not → Strengthen value differentiation
   +-- No → Can ignore, maintain price

2. Is competitor's cut sustainable?
   +-- Temporary (promotion) → Ignore or limited-time promotion
   +-- Structural (cost advantage) → Compete on non-price factors