  We consider a screened Coulomb interaction between electrons in graphene and
determine their dynamic response functions, such as a longitudinal and a
transverse electric conductivity and a polarization function and compare them
to the corresponding quantities in the short-range interaction model. The
calculations are performed to all orders for short-range interaction by taking
into account the self-energy renormalization of the electron velocity and using
a ladder approximation to account for the vertex corrections, ensuring that the
Ward identity (charge conservation law) is satisfied. Our findings predict a
resonant response of interacting electron-hole pairs at a particular frequency
below the threshold $qv=\omega$ and further predict an instability for
sufficiently strong interactions.
