For what demand function is a monopoly most harmful?
An arbitrarily large ratio should occur with demand curve 

$P=\begin{cases}
\frac{1}{Q} &amp; \text{if } Q&gt;1 \\
2-Q &amp; \text{if } Q\leq 1 \\
\end{cases}$.

The monopolist prices at $P=1$, but the consumers' surplus if $P=0$ is infinite, because the area under the demand curve contains $\int_1^\infty \frac{1}{Q}dQ=\infty$.