The Council's Recycling Proposal
A town council proposes a new recycling scheme. The leaflet says: "Separating waste will cut landfill by 40% within a year. Residents who sort correctly will pay $20 less in rates. Those who do not will pay $20 more. The scheme costs $500,000 to set up and $80,000 a year to run. It will pay for itself."
A resident reads the leaflet and objects: "You can't promise 40% and also say it pays for itself - those are different claims." A councillor replies that both are true because "recycling saves money and reduces waste at the same time."
The town has 5,000 households. The council's own figures show each household currently sends 400 kg to landfill per year.
1. Explain the resident's objection. Are the two claims really in conflict, or is the councillor right?
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The resident is confusing two different kinds of claim, and the councillor's reply is also too loose.
- "Cut landfill by 40%" is a claim about waste volume.
- "Pays for itself" is a claim about money.
These are not automatically in conflict: a scheme can reduce waste and recover its costs. So the resident's flat objection ("you can't say both") is wrong - the two claims are compatible in principle.
But the councillor is also too glib. "Recycling saves money" does not prove this scheme pays for itself; the leaflet gives no figures linking the 40% to the $500,000 + $80,000 costs. So the councillor has asserted compatibility without showing it. The honest answer: the claims can both be true, but the leaflet has not demonstrated that they are.
2. Using the household figures, assess whether the "pays for itself" claim is plausible. State any assumption you must make.
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Costs: setup $500,000 (one-off) + running $80,000/year.
Income mechanism: the scheme moves $20 between households - those who sort pay $20 less, those who don't pay $20 more. This is a redistribution, not new revenue. If everyone sorts correctly, the council collects $0 extra and loses $20 × 5,000 = $100,000 in rates. So the $20 lever does not fund the scheme by itself.
Waste figures: 5,000 households × 400 kg = 2,000,000 kg (2,000 tonnes) to landfill per year. A 40% cut = 800 tonnes diverted.
Assumption needed: the council must save money per tonne diverted (e.g. landfill levies avoided). To recover $80,000 running costs from 800 tonnes, the saving must be at least $100 per tonne. To also repay $500,000 setup within, say, 5 years, it needs a further $100,000/year, i.e. about $225 per tonne total.
Verdict: "Pays for itself" is possible only if the per-tonne landfill saving is high enough - the leaflet never states it, so the claim is unproven. The resident is right to demand the missing figure.