Consumer surplus with isoelastic demand Let $q(p) = \frac{1}{p}$ denote the demand function and $p^*$ some equilibrium price. Consumer surplus is defined as 
\begin{align}
CS = \int_{p^*}^\infty\frac{1}{p} dp= \ln(\infty) - \ln(p^*) = \infty 
\end{align}
which is quite unsatisfactory. What's the convention here?

Edit: Since I wanna compare welfare under price and quantity competition I found a workaround. Let $n$ the number of firms in the market, $\bar \pi^j$, equilibrium profits of the firm, $\bar p^j$ equilibrium prices and $j \in \{b,c\}$ is the index for the compeition type. 
Now we may calculate the welfare difference as
\begin{align}
\Delta W := W^c - W^b &amp;= n(\bar \pi^c - \bar \pi^b) + \int_{\bar p^c}^\infty\frac{1}{p}dp - \int_{\bar p^b}^\infty\frac{1}{p}dp\\
&amp; = n(\bar \pi^c - \bar \pi^b) + \ln(\bar p^b) - \ln(\bar p^c) 
\end{align}

Suppose we get the following relationship
\begin{align}
\Delta W = \frac{(n-1)(\sigma-1)^2}{\sigma n^2(\sigma(n-1)+1)} + \ln\left(\frac{\sigma(n-1)+1}{n \sigma}\right)
\end{align}
with $n \geq 2$ and $\sigma \in [0,\infty)$ is a parameter.
Clearly $\Delta W = 0$ for $\sigma = 1$ and for all $n$. 
I wanna further show that $\Delta W &gt; 0$ for $\sigma &lt; 1$ and $\Delta W &lt; 0$ for $\sigma &gt; 1$. Any ideas how to proceed?
This simply tells us that the mathematical object $f(x) = 1/x$ is not friendly to all the economic concepts we want to associate/obtain from its use as a demand function.
So, it is not the right tool to represent a demand function, we should use something else.

Mathematically, this relates to the harmonic series which is divergent (think of the integral as a discrete sum).