Talk:Inada conditions

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Property 4: concavity[edit]

The correct property is: $\partial ^{2}f(x)/\partial x_{i}^{2}<0$ . This is equivalent to saying

the first derivative of the function is decreasing in $x_{i}$
the second derivative of the function is negative

It seems that people think that it is equivalent to saying "the second derivative of the function is decreasing in $x_{i}$ ". However, this is a statement about the third derivative of $f$ , and thus it is unrelated to property 4. Thefroyo (talk) 19:04, 2 October 2013 (UTC)[reply]

Example?[edit]

Is it possible to give an example? A concrete function equation and/or plot? E.g. cobb-douglas-style. thanks --WissensDürster (talk) 07:35, 5 August 2015 (UTC)[reply]

Added Cobb-Douglas plot. 195.83.197.185 (talk) 10:20, 4 November 2022 (UTC)[reply]

Inada isn't just production functions[edit]

Don't utility functions also necessarily satisfy Inada conditions? AllGloryToTheHypnotoad (talk) 14:27, 18 August 2017 (UTC)[reply]

Yup, added. Utility functions satisfying Inada conditions also are necessary for an Euler equation for consumption to be well-defined (we have consumption at the denominator, so we need

c(t)\neq 0\;\forall \;t\in \mathbb {R} _{+}

and Inada conditions make sure this happens by having infinite marginal utility at 0), but since this is already very technical I'm not sure how much it would add to specify this. 195.83.197.185 (talk) 10:22, 4 November 2022 (UTC)[reply]