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Worked-example setupScope and assumptions
- Rowan Advisory and every output quantity are fictional teaching facts from the linked dataset.
- One analyst-day, technology, completion threshold, and output definitions remain fixed, and fractional output is permitted in the linear model.
- The frontier classifies modeled combinations; it does not predict Rowan's actual production or establish that a displayed mix is desirable.
- Period
- One fictional analyst-day
- Units
- Completed reconciliations and completed forecast packages per comparable analyst-day
- Rounding
- Exact ratios
Hold the model basis fixed
Rowan can complete at most 12 reconciliations or 6 forecast packages in one comparable analyst-day. Every output must meet the same supplied quality threshold. The straight line between those intercepts is a deliberately simple production model, not an observed time sheet or a promise about tomorrow.
For any point, compute frontier utilization:
reconciliations / 12 + forecasts / 6
| Point | Reconciliations | Forecasts | Frontier utilization | Classification |
|---|---|---|---|---|
| Efficient mixed | 8 | 2 | 1.000 | Feasible and productively efficient |
| Interior | 4 | 2 | 0.667 | Feasible but productively inefficient |
| Unattainable | 10 | 2 | 1.167 | Outside the current modeled capability |
The efficient point exhausts modeled capacity. The interior point leaves capacity unused under the model. The unattainable point would require changed resources, technology, definitions, or assumptions before it could be treated as feasible.
Read the slope with units
Moving from the all-forecast intercept to the all-reconciliation intercept
gives up 6 forecasts to gain 12 reconciliations. One reconciliation therefore
costs 6 / 12 = 0.5 forecast. The reciprocal cost is 2 reconciliations per
forecast, and the two reciprocal rates multiply to 1.
Keep classification separate from judgment
Productive efficiency says that a point is on the modeled boundary. It does not say the mix serves clients well, maximizes profit, treats workers fairly, reduces risk, or satisfies any other decision criterion. Those conclusions need values, prices, evidence, constraints, and authority not supplied here.
Common wrong paths
- Call the interior point impossible: it is feasible; it simply does not use all modeled productive capacity.
- Call the outside point impossible forever: it is unattainable under the current model, not under every future technology or resource set.
- Call every frontier point best: the frontier establishes productive efficiency, not allocative desirability.
Verified calculation · economics foundations analysis
The curriculum loader recomputed this example before it entered the site build. Expand any structured input to inspect the stated facts.
- production possibilities
- 1 field
Inspect data
{
"rowan_frontier": {
"max_output_a": 12,
"max_output_b": 6,
"output_a_name": "reconciliations",
"output_b_name": "forecasts",
"points": {
"efficient_mixed": {
"output_a": 8,
"output_b": 2
},
"interior": {
"output_a": 4,
"output_b": 2
},
"unattainable": {
"output_a": 10,
"output_b": 2
}
}
}
}Recomputed result
| Measure | Value |
|---|---|
| efficient mixed feasible | 1 |
| efficient mixed frontier utilization | 1 |
| efficient mixed productively efficient | 1 |
| interior frontier utilization | 0.6667 |
| interior interior | 1 |
| opportunity cost output a in output b | 0.5 |
| opportunity cost output b in output a | 2 |
| reciprocal cost product | 1 |
| unattainable frontier utilization | 1.1667 |
| unattainable unattainable | 1 |