The Canteen Memo
A facilities memo reads: 'Canteen revenue fell 12% in the quarter in which we replaced the à la carte menu with a fixed-price buffet. Office attendance fell 8% in the same quarter, after the hybrid-work policy took effect on the first day of that quarter. The buffet is clearly the cause of the revenue loss, and we should restore the old menu before the next quarter.' The finance head adds two facts the memo omits: the buffet was priced 15% below the average à la carte spend per head, and the canteen's rent - a fixed monthly charge - was renegotiated upward by 6% in the same quarter. She wants an assessment before the memo goes to the board.
1. Identify the conclusion, the key assumption, and one alternative explanation the memo ignores.
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Conclusion: the buffet caused the 12% revenue fall, therefore restoring the old menu will recover the revenue.
Key assumption: nothing else that affects canteen revenue changed in the quarter - or, more precisely, that the fall cannot be explained by attendance and pricing, which are named in the very same memo. That assumption is doing all the work, and it is unstated.
Alternative explanation the memo ignores: the 15% price cut. If every customer paid 15% less per head, revenue would fall even if the same number of meals were bought - a pricing decision, not a failure of the buffet format. A second alternative: the 8% attendance drop mechanically reduces revenue. The memo mentions attendance and then declines to use it, treating a rival cause as background. Restoring the menu would leave both alternatives untouched.
2. The author replies: 'Attendance fell only 8% while revenue fell 12%, so the buffet must explain the extra 4 points.' Evaluate this reasoning with numbers.
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The 'extra 4 points' is a subtraction of two percentages with different bases, and it is invalid.
Revenue = attendance × spend per head. So 0.92 × s = 0.88, giving s = 0.9565 - spend per head fell about 4.35%, not 4 percentage points of revenue.
That number is fatal to the memo rather than helpful. A 15% price cut should have dragged spend per head down by 15%; it fell only 4.35%, which means items per head rose: 0.85 × 1.125 ≈ 0.956. On these figures the buffet increased consumption per visitor by roughly 12.5% and the revenue fall is the arithmetic of a deep price cut, not evidence that customers rejected the format. The memo has converted a pricing effect into a menu verdict. Whatever the board decides, the inference as written does not survive.
3. What single piece of evidence would best test the buffet explanation, and how should the rent increase affect the decision?
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Best evidence: canteen spend per head and items per head, week by week, for the same quarter a year earlier - or, failing that, a split by day of week comparing attendance-adjusted spend per head before and after the change. Revenue alone confounds traffic and price; spend per head separates them, and a year-on-year comparison controls for seasonality that a single quarter cannot.
The rent increase is irrelevant to the memo's revenue claim but crucial to the decision the board is actually being asked to make. Restoring the menu cannot lower rent, and a 6% rise in a fixed charge is a cost event that no menu change addresses. If the board is judging profitability rather than revenue, it needs contribution per head against the new rent, not a revenue comparison - a format that raises items per head may be worth keeping even at lower revenue. The decision rule should be profit, and the memo argues from the wrong quantity.