Optimize SaaS pricing and profit
Overview
This question evaluates pricing optimization, linear demand modeling, capacity-constrained profit maximization, and the impact of subscription churn on lifetime value within an Analytics & Experimentation data-science context.
OneMain Financial
Oct 13, 2025, 9:49 PM
Data Scientist
Technical Screen
Analytics & Experimentation
0
0
SaaS Pricing: Linear Demand, Capacity Constraint, and Subscription Churn
Context: You are pricing a single-seat SaaS product (one seat per customer per month). Demand for new seats in a given month follows a linear demand curve. Costs include a per-seat variable cost and a fixed monthly overhead.
Given:
- Demand (new seats/month): q(p) = 10,000 − 50·p
- Variable cost per seat: c = $5
- Fixed monthly cost: F = $100,000
Tasks:
- Unconstrained pricing: Derive the profit-maximizing price p* and quantity q*, and compute the resulting maximum monthly profit. Show your calculus.
- Capacity constraint: If capacity is limited to 6,000 seats/month, what price maximizes profit under this constraint?
- Subscription twist: In a subscription setting, a 10% price increase raises monthly churn from 2% to 4%. Explain how the model changes and how you would estimate an LTV-optimized price instead of a static monthly profit optimum.
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