I want to show that when 0<p<1 then the inequality holds for all values of d and b that are >0. And for p>1 then the inequality does not hold for any values of d and b >0.
I know the answer as I have "solved" it numerically in excel, however I do not know how to do it with algebra. I have this inequality:
(1+(b*d)^(1/p))^(p-1) > (b*d+b)/((b*d)^(1/p)+b)
Please see attachment for picture of the inequality.
b, d and p are all greater than 0. It is clear that when p=1 than the inequality holds for all values of b and d.
It is for my thesis in economics. I am trying to show how the difference in consumption paths between two types of consumers depend on the parametric values.
Any help would be greatly appreciated!