  The paper contains the discussion of the magnetocaloric and electrocaloric
effect in a model dimer (pair cluster). The system of interest is modelled with
a Hubbard Hamiltonian including the external electric and magnetic field. The
thermodynamics of such pair is described exactly, on the grounds of the grand
canonical ensemble, focusing on the half-filling of energy states. The
quantities of interest, such as magnetic entropy, magnetic specific heat as
well as isothermal entropy change resulting from the variation of either
electric or magnetic field and appropriate Gr\"uneisen ratios are calculated
and discussed in a wide range of external fields. The importance of singlet to
triplet transition for the observed behaviour is emphasized. The ranges of
direct and inverse caloric effects are found and the manifestations of the
magnetoelectric phenomena are described. In particular, the tunability of the
magnetocaloric effect with electric field as well as tunability of the
electrocaloric effect with magnetic field are demonstrated.
