Which class of functions have the property of being always elastic?and instead always inelastic?
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I don’t think that there are any classes of functions where you can ex ante say that it is elastic or inelastic, since this will depend on the function parameters.
However, there is a class of functions for which you can say the elasticity is always constant, these are isoelastic functions.
For example, consider function:
$$Q(p)=ap^b$$
By definition elasticity for this function is:
$$\frac{Q’(p)p}{Q(p)}=b$$
Now this kind of function will be always elastic ($b$>1), inelastic ($b$<1) or unit elastic ($b$=1) depending on the actual value of the parameter $b$
answered Nov 23, 2019 at 21:48
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$\begingroup$ Yes , but this type of functions haven't the properties of a demand function . If there isn't a class , which can be a good unique example of such a function? $\endgroup$– TortarNov 23, 2019 at 23:33
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$\begingroup$ My problem is that in a problem is required to graph a elastic function , but I don't know how to do it $\endgroup$– TortarNov 23, 2019 at 23:34
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$\begingroup$ @Tortar the function I showed was just an example. You can definitely have isoelastic demand function. Heck my example could be demand function for Giffen good and with just adding a minus sign it could be standard demand function. Also if you wanted graph you should asked for that in question, regardless just google isoelastic demand and you will get a graph with demand function with constant elasticity $\endgroup$– 1muflon1 ♦Nov 23, 2019 at 23:49