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Study of the behavior of firms in organizing their production and allocating productive resources.

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Is it true that $\frac{dL}{dq}=1/\frac{\partial q}{\partial L}$?

It is valid but only in the short run with the assumption that the capital is fixed. By assuming that output depends on labor and capital you can write $$q=q(L,K)$$ Now taking the total derivative …
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