Practice question · Multiple choice
The Lagrange multiplier λ has an economic meaning at the optimum. What is it?
Hints
- Ask what one more euro of budget would buy in extra utility.
- The multiplier appears when you differentiate the value function with respect to the constraint. What is that derivative?
Show the answer
A. The shadow price: the gain from relaxing the constraint by one
Why
λ is the derivative of the optimal value with respect to the constraint level, so it prices the constraint itself, which turns 'is the extra machine worth buying?' into a number you already computed. Treating it as algebraic bookkeeping discards the most useful output of the method.
Practise Lagrange Multipliers
The app has 6 more questions on this lesson, and keeps your place in the course. Business I is free to start.
More questions on Lagrange Multipliers
- The Lagrange multiplier λ is sometimes dismissed as a bookkeeping device with no meaning. What does 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.