A monopolist faces a demand curve $q = p^{-b}, q>0$. The cost function is $c(q) = q^2$. What restrictions must be placed on $b$ for profit maximising solution to exist? Given the restrictions what is the profit maximising output?
I tried the question , first by converting the demand function in to inverse demand function expressing $p$ in terms of $q$.
You want to maximize $\Pi = q p - C(q) = p^{-b+1} -p^{-2b}$. There will be a maximum if $b>1$ or $b \leq -1$. The range $b \leq -1$ may experience some economical objections.