Set membership fee under investment constraints

Q: Set membership fee under investment constraints

This question evaluates quantitative skills in pricing optimization, constrained investment allocation, and interpretation of willingness-to-pay curves, testing competency in combining economic reasoning with statistical and mathematical modeling.

Q: How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

Q: What difficulty level is this interview question?

This is a medium difficulty Statistics & Math question, commonly asked during HR Screen rounds at Capital One.

Q: What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Capital One during technical interviews.

Question

Streaming membership pricing vs. content investment

Context

You are designing a monthly membership for a streaming service. Producing original shows increases members' willingness to pay (WTP). The WTP as a function of the number of shows is given by a known "WTP curve" from the prior question. You price at the maximum WTP implied by the number of shows, but price cannot exceed a $20/month cap.

Each show costs $5M to produce.
You can choose how many shows to produce, subject to the investment amount.
Price set = min(WTP implied by the chosen number of shows, $20 cap).

Task

a) With a total investment of $150M, how many shows do you produce and what monthly price do you set?

b) If total investment increases to $250M (same per-show cost), recompute the number of shows and the price.

State all assumptions and show your calculations.

Set membership fee under investment constraints

Quick Overview

Set membership fee under investment constraints

Streaming membership pricing vs. content investment

Context

Task

Write your answer