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Suppose I have a utility function $u(c,l)$, where c is consumption and l is leisure. What does $u_{cl}$ mean in economic terms for example, or in general what is the economic meaning of cross derivatives?

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There isn’t a general answer (beside the pure mathematical answer) because the meaning will be different in different fields. E.g. in theory of production interpretation would be different (if you for example examine the cross derivative of production function).

Generally cross-derivative $f_{xy}’’$ tells you how the slope $x$ changes with respect to changes in $y$.

When it comes to the utility $u(c,l)$ the cross derivative $u_{cl}’’$ tells you how much the marginal utility of $c$ changes when you change amount of $l$.

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