Ruataniwha's $14.5 Million Capital Budget
The Ruataniwha District Council has a capital budget of $14.5 million for the next financial year. Three proposals are on the table. (1) Replace the 1962 water-treatment plant at a cost of $9.2 million; the plant has failed 11 times in three years, each failure triggering a boil-water notice for about 300 households. (2) Build a 6.2 km shared cycleway at $6.8 million; council consultants estimate 1,100 extra trips a week and $1.1 million a year in additional visitor spending. (3) A combined package costing $16.4 million, which exceeds the budget. Engineers note the water upgrade has two stages: the first $7.0 million restores reliability to 99% (from 91%), while the final $2.2 million lifts it from 99% to 99.7%. The cycleway's benefits are concentrated in the first 2 km through the town centre, where 80% of the estimated trips would occur. Councillors argue that 'doing both' is impossible without a rates rise of 4.8%.
1. Explain the opportunity cost to the district of choosing the cycleway. In your answer, identify the next-best alternative and distinguish opportunity cost from the accounting cost of the cycleway.
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Opportunity cost is the value of the next-best alternative forgone. Choosing the cycleway does not forgo the whole $14.5m, because $7.7m remains. The realistic next-best use of a similar sum is the first stage of the water upgrade ($7.0m), so the opportunity cost is the reliability improvement that this money would have bought - reducing boil-water notices for about 300 households.
The accounting cost of the cycleway is $6.8m: the actual money spent. The opportunity cost is measured in forgone outcomes - household health risk, avoided sick days, and lost trust in the council - not just dollars. It also includes any interest if the project is debt-financed and the future rates revenue committed.
If councillors instead raised rates by 4.8%, that too has an opportunity cost for ratepayers, who give up private consumption. The key exam point is that opportunity cost is about the best forgone alternative, valued in the same units as the benefit being considered, not about listing every alternative.
2. Use marginal analysis to advise councillors on how they could allocate the $14.5 million. State a recommendation and explain the reasoning.
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Marginal analysis compares the additional benefit of the next dollar spent with its additional cost.
- Water stage 1: $7.0m buys 8 percentage points of reliability, about $0.875m per point.
- Water stage 2: $2.2m buys 0.7 points, about $3.1m per point - a much lower marginal benefit per dollar.
- Cycleway town-centre section: 80% of 1,100 trips (880 trips) for roughly $2.2m if costs are proportionate.
- Cycleway outer section: $4.6m for only 220 trips.
Recommendation: fund water stage 1 ($7.0m) plus the town-centre cycleway ($2.2m), using $9.2m and leaving $5.3m for the highest-value remaining option or as contingency against the $1.5m overrun risk.
The rule is to fund projects in descending order of marginal benefit per dollar until the budget is exhausted. Note that the water project addresses a statutory health obligation, which may justify weighting its marginal benefit. Partial completion of both projects beats completing only one, provided each staged design still functions on its own.
3. Explain how the council's decision could be represented on a production possibility curve for the district, and why the curve might shift outward over time.
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A PPC shows maximum combinations of two outputs - here, 'water-service reliability' and 'cycleway kilometres' - given fixed resources and technology. Points on the curve are productively efficient; a point inside the curve, such as spending the full budget on a low-value project, is inefficient. The budget constraint means the council chooses a point along the curve, and the slope represents the marginal opportunity cost of one output in terms of the other. Concavity reflects increasing opportunity cost as resources are less suited to the alternative use: engineers cannot build cycleways.
Outward shifts occur if the projects raise the district's productive capacity - for example, visitor spending and rates revenue from the cycleway, or reduced health costs and lost workdays from the water upgrade. Better technology or new infrastructure would also shift the curve out. Conversely, deferred maintenance can shift it inward.
A rates rise of 4.8% does not shift the PPC outward; it moves the council along a higher budget line at the expense of ratepayers' private consumption. That is a distributional question, not a change in productive capacity - a distinction worth marks.