How does a firm choose the least-cost K–L mix for target output?
At an interior optimum, marginal product per baht is equalized, so MRTS equals relative input prices.
Follow the cause and effect
Write the constraint f(K,L)=qbar.
Set MRTS=MPL/MPK=w/r for an interior solution.
Solve with the target and compare costs and boundaries.
The model you are using
Conditions for this model
Both inputs variable, fixed input prices, positive target output and convex input requirements.
The exam trap
Output maximization and cost minimization share tangency conditions but answer different questions.
Connect the reasoning to the graph
What changes
- A higher wage steepens the isocost and shifts an interior mix toward less L and more K when substitution is possible.
What stays fixed
Both inputs variable, fixed input prices, positive target output and convex input requirements.
Keep these conditions throughout the comparison; change only what the case above specifies.
What to inspect
Solve with the target and compare costs and boundaries.
Compare before and after, and locate the conclusion on the graph.
5 MINUTES · TRANSFER THE IDEA
Can you explain it without the lesson?
Find the cost-minimizing mix for q=√KL after w doubles and explain the isocost rotation.