  We consider the two-dimensional version of Calder\`on's problem. When the D-N
map is assumed to be known up to an error level $\varepsilon_0$, we investigate
how the resolution in the determination of the unknown conductivity
deteriorates the farther one goes from the boundary. We provide explicit
formulas for the resolution, which apply to conductivities which are
perturbations, concentrated near an interior point $q$, of the homogeneous
conductivity.
