Calculate profit and break-even across pricing models

You are evaluating a cloud-storage startup that currently uses only unit-based pricing. Use the data below and assume there are no other revenues or costs:

• Subscribers: 20
• Fixed monthly cost (FC): $400
• Variable cost per user (VC_user): $5
• Price to customers: $1 per GB
• Average usage: 15 GB per user per month

Assume identical usage across users.

(a) Calculate monthly revenue, total variable cost, total cost, and profit. Show the formulas and intermediate steps.

(b) Use the numbers to explain why the firm is operating at a profit or a loss. Which lever—price, usage, user count, FC, or VC_user—has the greatest effect on the sign and size of profit here, and why?

(c) If the number of subscribers doubles while the usage distribution stays the same, does the firm break even? If it does not, calculate the exact subscriber count required to break even under this model.

(d) The company is considering a two-tier model to replace per-GB revenue: a Free tier with $0 revenue and $1 cost per free user per month, and a Paid tier with $54 revenue and $5 cost per paid user per month. Fixed cost stays at $400. For $T = 20$ total users, what minimum percentage of paid users is needed to break even? Derive the general formula for the minimum paid share as a function of $T$.

(e) If only 25% of users convert to the Paid tier, how many total users are needed to break even under the two-tier model? Give the inequality you solve and the smallest integer solution.

Overview: This question tests unit economics, break-even analysis, and how pricing models affect profitability by asking for calculations of revenue, variable and fixed costs, and profit under both per-GB and two-tier pricing scenarios.