Practice question · Multiple choice
The Lagrange multiplier is sometimes dismissed as a bookkeeping device with no meaning. What does it actually measure?
Hints
- Ask what happens to the optimal value if the constraint is loosened slightly.
- The envelope theorem is the formal statement.
Show the answer
D. The shadow price: how much the optimum improves per unit
Why
is the value of relaxing the constraint by one unit. This makes it directly usable: it prices an extra hour of machine time or an extra euro of budget without re-solving the problem.
Practise Lagrange Multipliers
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More questions on Lagrange Multipliers
- The Lagrange multiplier λ has an economic meaning at the optimum. What is it?
- At the consumer's optimum, MUx / px = MUy / py. What does this say?
- Which statements about λ are correct?
- At the constrained optimum, the level curves of the objective function are tangent to the constraint curve.
- A factory has λ = 8 for its capacity constraint. Management can add 10 units of capacity. Estimate the output…
- Match each economic problem to its Lagrange setup.