Practice question · Multiple choice
A manager finds the output where marginal profit is zero and stops there. What has been skipped, and what could go wrong?
Hints
- Draw a curve with a flat spot at the bottom of a valley. What is the derivative there?
- Ask what distinguishes a peak from a trough, given both are flat.
Show the answer
A. The second-order condition, since zero marks three possibilities
Why
Flatness is shared by peaks and troughs, so the sign of the second derivative is what tells them apart, and a manager who skips it can confidently produce at the profit minimum. The FOC finds candidates and the SOC selects among them, which is why the ritual has two steps.
Practise Optimization in Economics
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