Practice question · Multiple choice
The mixed partials and are equal for the functions used in economics. What does that equality say about the two inputs?
Hints
- Read each mixed partial aloud as a sentence about the two inputs.
- Clairaut’s theorem needs continuity of the second partials, it is not automatic.
Show the answer
D. That the complementarity is one number, not two
Why
Symmetry means the interaction between two inputs is a single quantity. It is also a modelling constraint, not a mathematical inevitability: it requires the continuity conditions to hold.
Practise Partial Derivatives
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