Constant Demand Elasticity- A and B Formula Explained

What the Hell Is Demand Elasticity?

Demand elasticity measures how much the quantity people buy changes when the price changes. That's it. If you raise your price and sales tank, you've got elastic demand. If sales barely budge, you've got inelastic demand.

Most products don't have consistent elasticity across all price points. But some do. That's where constant demand elasticity comes in.

The A and B Formula: The Actual Math

Constant elasticity demand follows this formula:

Q = A × P^B

Where:

• Q = Quantity demanded
• P = Price
• A = Scale factor (shifts the entire curve up or down)
• B = Elasticity parameter (determines how responsive demand is to price)

The B value is your elasticity. It's constant regardless of where you are on the demand curve.

What the B Value Actually Tells You

• B = -1: Unitary elasticity. Revenue stays the same when price changes.
• B < -1: Elastic demand. Price cuts increase total revenue.
• B > -1: Inelastic demand. Price cuts decrease total revenue.
• B = 0: Perfectly inelastic. Quantity doesn't change with price (theoretical only).
• B → -∞: Perfectly elastic. Any price increase kills all demand.

Why Use This Formula?

Because it makes calculations stupid simple. With regular demand curves, elasticity changes at every point. With constant elasticity, B is always B.

This matters when you're:

• Setting prices across product lines
• Forecasting demand changes
• Running margin analysis
• Building financial models

How To Actually Use This

Step 1: Estimate Your B Value

You need historical data. Look at past price changes and the resulting quantity changes. Calculate elasticity for each period:

Elasticity = (% Change in Quantity) / (% Change in Price)

Average your elasticity estimates across multiple periods. That's your B.

Step 2: Find Your A Value

Rearrange the formula:

A = Q / P^B

Plug in any known Q and P combination from your data. Solve for A.

Step 3: Plug and Play

Now you can predict quantity at any price:

Q_new = A × P_new^B

Real Example

Let's say your data shows:

• At $10, you sell 1,000 units
• At $12, you sell 800 units

Calculate elasticity:

• % change in quantity = (800-1000)/1000 = -20%
• % change in price = (12-10)/10 = +20%
• B = -20% / +20% = -1.0

Now find A using the $10, 1000 unit data:

A = 1000 / 10^-1 = 1000 / 0.1 = 10,000

Your demand function: Q = 10,000 × P^-1

Want to predict sales at $15?

Q = 10,000 × 15^-1 = 10,000 / 15 = 667 units

Constant Elasticity vs. Linear Demand

Where This Breaks Down

Constant elasticity models have real limitations:

• They assume elasticity doesn't change. In reality, competitors react, consumer tastes shift, and income levels change.
• At P = 0, Q → ∞. The model predicts infinite demand at zero price. That's not realistic.
• At P → ∞, Q → 0. This part actually works.
• Doesn't account for income effects. Only price changes.

Use this for small price changes within a stable market period. Don't extrapolate to extreme price points or timeframes.

Getting Started Checklist

• Pull 3-5 periods of historical price and quantity data
• Calculate elasticity for each period
• Average the elasticities → that's your B
• Solve for A using any data point
• Test your model against known data points
• If predictions are way off, your demand probably isn't constant elasticity

The Bottom Line

The A and B formula works when you have reason to believe elasticity stays constant. It's a tool, not a crystal ball. Get your B right from solid data, and you can make decent predictions. Get it wrong, and you'll be blaming the model instead of your assumptions.

Start with your actual sales data. Calculate. Test. Adjust.