A gym faces a cheaper competitor
The companies and data in this case are made up.
A gym has 1,000 monthly members. A competitor charges $25. The manager is choosing between cutting the gym’s $40 price for everyone and offering a retention package to members likely to leave.
Suggested time: 20 minutes for a written response, then 5 minutes for the challenge. This is a practice exercise, not a full Regionals paper or a statement of the final exam format.
A · Current monthly economics
| Measure | Value |
|---|---|
| Members | 1,000 |
| Monthly price | $40 |
| Variable cost per member | $10 |
| Monthly fixed costs | $24,000 |
| Members expected to leave next month without intervention | 100 |
B · Manager estimates for next month
| Option | Expected members | Price | Extra monthly cost |
|---|---|---|---|
| No intervention | 900 | $40 | $0 |
| Cut everyone’s price | 1,150 | $30 | $0 |
| Targeted retention package | 970 | $40 | $1,500 |
Evidence limit: Membership numbers are forecasts, not randomized test results. Fixed costs and cost per member are assumed unchanged. No acquisition cost or longer-run competitor response is supplied.
Your task
- Calculate current monthly contribution and operating surplus.
- Calculate next-month operating surplus for each option. How many members would the $30 price need to match the no-intervention option?
- Recommend a strategy and a test. Explain one way your recommendation could fail.
Your answer stays on this page. It is not submitted or saved; copy it before leaving.
Follow-up challenge
The price cut produces the highest revenue. Why not choose it?
Read a worked response
Current contribution is 1,000 × ($40 − $10) = $30,000. After $24,000 fixed costs, operating surplus is $6,000.
No intervention yields 900 × $30 − $24,000 = $3,000. A price cut yields 1,150 × $20 − $24,000 = −$1,000. The targeted package yields 970 × $30 − $24,000 − $1,500 = $3,600. To match the $3,000 no-intervention surplus at $30, the gym needs ($24,000 + $3,000) / $20 = 1,350 members, 200 above the estimate.
I would test the targeted package. It has the best forecast surplus, but its advantage over doing nothing is only $600 per month. It needs more than 50 retained members to cover its $1,500 incremental cost; the estimate is 70. Assign comparable at-risk members to a package and a control group, then measure paid retention and support costs. If the package retains no more than 50 additional members at these costs, it fails to improve surplus. Longer-run pricing and member capacity also need checking.
Other recommendations can earn full credit when they follow from the exhibits and acknowledge the limits.
Score your response · 100-point practice rubric
This self-assessment assigns 20 points to each category. These weights apply only to this practice exercise; official competition weights remain unpublished.
| Category | Evidence needed for 20/20 |
|---|---|
| Interpretation | Identify profitability and retention as the decision, rather than revenue alone. |
| Evidence | Use variable costs, fixed costs and package costs consistently. |
| Reasoning | Show all three profits, the 1,350-member threshold and the 50-member retention threshold. |
| Judgment | Choose a proportionate test and identify a realistic failure condition. |
| Defense & adaptability | Explain why $34,500 revenue under the price cut can coexist with a $1,000 loss. |
| Score per category | Practice standard |
|---|---|
| 0 | Missing, irrelevant or fundamentally incorrect. |
| 5 | Some relevant observations, with major errors or unsupported assertions. |
| 10 | Partly correct; important evidence or a reasoning step is missing. |
| 15 | Sound analysis with a minor omission or an underdeveloped limitation. |
| 20 | Accurate, supported and complete for the task; assumptions and limits are explicit. |
The worked response illustrates full-credit evidence in the first four categories. For Defense & adaptability, score your own response to the follow-up challenge; reading the model answer does not demonstrate that skill.
What to practice
A company’s position against its competitors.
- Competitive advantage
- Pricing
- Unit economics
- Operations
- Growth and market entry
- Resource allocation
- Strategic diagnosis
How to use this case
- Read the case and restate the decision in one sentence. List the quantities, units and constraints before calculating.
- Work each question without the model response. Write the calculation and the inference separately.
- Compare your work with the model. Mark one arithmetic error, missing assumption or unsupported claim to correct.
- Ask a partner to challenge your recommendation. Give a specific condition that would change it.
Skills checklist
| Skill | Application in this case |
|---|---|
| Interpretation | Identify profitability and retention as the decision, rather than revenue alone. |
| Evidence | Use variable costs, fixed costs and package costs consistently. |
| Reasoning | Show all three profits, the 1,350-member threshold and the 50-member retention threshold. |
| Judgment | Choose a proportionate test and identify a realistic failure condition. |
| Defense & adaptability | Explain why $34,500 revenue under the price cut can coexist with a $1,000 loss. |
Common mistakes
- Quoting a number without explaining what it changes.
- Treating a forecast as an observed fact, or a correlation as a causal effect.
- Optimizing revenue while ignoring cost, risk or opportunity cost.
- Listing uncertainties without making a provisional decision.
A second practice session
Change one numerical assumption in the exhibit. Recalculate the decision threshold, explain whether your recommendation changes, and say which original assumptions still matter. Have a partner check units and arithmetic.
The content areas above describe preparation topics. They do not assign exam percentages or finalize time limits, permitted resources or grading weights. See the handbook draft for adopted rules.