Shadow price
A shadow price is the change in the optimal objective value from a one-unit relaxation of a constraint, within the range for which the current marginal relationship remains valid. For a scarce input in contribution maximisation, it measures the extra contribution obtainable from one more unit. It is not unlimited and may change when another constraint becomes binding. Distinguish it from an input’s normal purchase cost and from the total value of a large capacity expansion.
Worked example
One additional machine hour raises optimal contribution from $2,000 to $2,006, giving shadow price $6 per hour within the stated range.
Common mistake
Do not multiply the shadow price by an unrestricted large resource purchase or treat it as the total resource price without considering costs already in the model.
Where it appears in your exams
| Qualification | Exam | Relationship | Period |
|---|---|---|---|
| ACCA | PM | Direct | September 2026–June 2027 |