A zero-dimensional analysis based on available scaling laws for the global energy confinement time of tokamak plasmas is presented, in order to consistently compute the fusion power as a function of the plasma density and of the plasma size. It is shown that the fusion power is a very sensitive function of the dependence of the confinement time on the plasma density. Considering recent expressions for the density limit in tokamaks, for which reactor operation could reach significantly higher densities than those predicted by the regularly applied Greenwald density limit, the implications on the possibility of reducing the size of a reactor plasma by increasing the plasma density are explored, also when heat exhaust requirements are taken into account. Completely different projections are obtained depending on which scaling law for the energy confinement time is adopted among those which have been derived from the ITPA global confinement database. Finally a set of considerations is presented on the possible origin of the different density exponents in the global confinement scaling laws.