I have the utility equation $U(a,b) = a^{2}b^{3}$
How can I tell if the indifference curves are convex? I was under the impression that if:
$U_{a} > 0$ and $U_{b} < 0$
then the curve would be convex. In this case, those conditions don't hold, but when I try graphing the equation, the curve appears convex. What am I missing?
Also are these conditions true:
if $U_{a} > 0$ , there is not diminishing marginal utility. if < 0 , there is diminishing marginal utility, and if = 0 , constant.
Are these conditions the same for good $b$ ?
I've been given lots of conflicting info and am now just confused.