Estimate demand curves from data, translate demand into revenue and profit under economic assumptions, and optimize price under alternative objectives. Compare model-driven prices against naïve heuristics.
Of the 4 Ps of marketing, price is the only one that directly generates revenue. Product, place, and promotion all cost money—price is what brings it in. Yet most companies set prices using gut instinct, competitor benchmarking, or cost-plus rules of thumb. The question is: can we do better?
The answer is yes—if we can estimate a demand curve. A demand curve tells us how many customers will buy at any given price. Once we know that relationship, we can combine it with our costs and business goals to find the price that maximizes profit, revenue, or market penetration. This is the core of price optimization.
In an introductory economics class, demand curves look simple—clean downward-sloping lines on a whiteboard. In reality, we almost never observe them directly. Here's why:
So we're stuck with an imperfect but critical task: using the data we do have to approximate the demand curve as best we can.
In practice, marketing analysts build demand curves from historical transaction data— records of past prices and whether customers purchased (or how many units were sold). The workflow is:
This tool walks you through every step. You'll load (or upload) real pricing data, choose a demand model, inspect the estimated parameters, and see exactly how the optimal price is derived. The goal isn't just to find a number—it's to understand where that number comes from and how sensitive it is to your assumptions.
💡 Learning Objectives: After working through this tool, you should be able to:
Shows how quantity demanded changes with price. Steeper curves = less price-sensitive customers.
$$R = P \times Q(P)$$
Revenue depends on both price AND quantity—raising price may reduce volume.
$$\pi = R - TC = P \times Q(P) - (FC + MC \times Q)$$
Profit accounts for fixed costs and marginal costs per unit.
$$\varepsilon = \frac{\%\Delta Q}{\%\Delta P}$$
Measures price sensitivity. |ε| > 1 means elastic (price-sensitive); |ε| < 1 means inelastic.
$$P(\text{buy}) = \frac{1}{1 + e^{-(\beta_0 + \beta_1 \times Price)}}$$
Best for 0/1 purchase outcomes. Naturally bounded [0,1].
$$Q = A \times P^{-\varepsilon}$$
Log-log model. Same % change in Q for any % change in P.
$$P(\text{buy}) = \alpha + \beta \times Price$$
Can predict outside [0,1]. Included for educational comparison only.
Load realistic pricing case studies with pre-configured data and economics. Each scenario demonstrates a different pricing challenge.
Upload a CSV with at least a price column and an outcome column (binary 0/1 purchase, or counts).
Drag & Drop CSV file (.csv, .tsv, .txt)
Accepts: (1) Binary format: price + outcome (0/1), or (2) Aggregate format: price + visitors + purchasers
No file uploaded.
Enter price points and corresponding purchase rates directly.
| Price ($) | Purchase Rate (%) | Sample Size | |
|---|---|---|---|
Adjust model settings above, then click to estimate demand and generate visualizations.
$$P(\text{buy}) = \frac{1}{1 + e^{-(\hat{\beta}_0 + \hat{\beta}_1 \times P)}}$$
| Parameter | Estimate | SE | z-value | p-value |
|---|---|---|---|---|
| β₀ (Intercept) | -- | -- | -- | -- |
| β₁ (Price) | -- | -- | -- | -- |
Configure cost structure and market assumptions to translate demand into profit.
Total addressable customers in your market
Variable cost to produce/deliver one unit
Overhead costs regardless of volume
Maximum units you can produce/serve
| Price | P(Buy) | Units | Revenue | Variable Cost | Total Cost | Profit | Margin |
|---|
How does the data-driven optimal price compare against common "rule-of-thumb" strategies? Configure each heuristic below to see the profit you'd leave on the table.
| Strategy | Price | P(Buy) | Units | Revenue | Profit | vs. Optimal Profit |
|---|---|---|---|---|---|---|
| 🎯 Data-Driven Optimal | $-- | --% | -- | $-- | $-- | — |
Explore how changes in market conditions and cost structure affect optimal pricing. All downstream calculations update in real time.