Business I / Optimization in Economics
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
  1. Draw a curve with a flat spot at the bottom of a valley. What is the derivative there?
  2. 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.

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