  We introduce a microscopic model for the dynamics of the order book to study
how the lack of liquidity influences price fluctuations. We use the average
density of the stored orders (granularity $g$) as a proxy for liquidity. This
leads to a Price Impact Surface which depends on both volume $\omega$ and $g$.
The dependence on the volume (averaged over the granularity) of the Price
Impact Surface is found to be a concave power law function
$<\phi(\omega,g)>_g\sim\omega^\delta$ with $\delta\approx 0.59$. Instead the
dependence on the granularity is $\phi(\omega,g|\omega)\sim g^\alpha$ with
$\alpha\approx-1$, showing a divergence of price fluctuations in the limit
$g\to 0$. Moreover, even in intermediate situations of finite liquidity, this
effect can be very large and it is a natural candidate for understanding the
origin of large price fluctuations.
