Practice question · Multiple choice
A firm's output depends on capital and labour, and the partial derivative with respect to labour is called the marginal product of labour. What does 'holding capital constant' correspond to in the business?
Hints
- Ask how quickly a firm can change its number of workers, and how quickly it can change its factory.
- Which of the two horizons freezes one input by definition?
Show the answer
C. The short run, where capital is fixed and labour varies
Why
The short run is defined by at least one fixed input, which is the same condition the partial derivative imposes, so the mathematics and the economics agree by construction. Option 3 is a different claim: partials hold other inputs fixed whether or not the inputs interact, and cross-partials measure that interaction.
Practise Partial Derivatives
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More questions on Partial Derivatives
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