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 $<phi(omega,g)>_gsimomega^delta$ with $deltaapprox 0.59$. Instead the dependence on the granularity is $phi(omega,g|omega)sim g^alpha$ with $alphaapprox-1$, showing a divergence of price fluctuations in the limit $gto 0$. 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.
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