Activity versus value
The quality index is deliberately simplified to expose how rankings can change when outputs are valued differently.
Comparison
Teaching point: A higher consultation rate per pound is a productivity finding. Calling it efficiency requires appropriate outcomes, quality, case mix and a feasible comparator.
Position a provider
Maximum feasible output—
Output-oriented TE—
Potential output gain—
Illustrative production frontier
Teaching point: A frontier score is relative to the specified production technology. It does not prove that the service mix is allocatively efficient or equitable.
Allocate a fixed budget
The remainder goes to treatment. Both services are assumed to operate technically efficiently; the question is whether the mix maximises the stated outcome.
Allocation result
Total health—
Health-maximising share—
Health opportunity gap—
Teaching point: This optimum follows one stated objective: maximise the synthetic health total. A real decision may also consider equity, severity, access, resilience and implementation.
Teaching notes and limitations
- Productivity is an observed output-to-input relationship. Efficiency requires a feasible or desirable reference.
- Technical efficiency asks whether output could increase without additional input, or input could fall without reducing output.
- Productive efficiency also considers whether the input mix produces the output at the lowest feasible cost.
- Allocative efficiency asks whether resources are distributed among activities in a way that best advances the stated objective.
- All values and production relationships in this lab are synthetic. They are designed to teach concepts, not rank real hospitals or prescribe resource allocation.