Horizontal equity, equal progression: an utilitarian approach

We consider an heterogeneous population in which we make a partition into two groups that are homogeneous with respect to the characteristics, other than the income, with fiscal incidence. The differences between both groups are taken into account by means of a profile of utility functions and the fiscal system is constituted by two tax schedules, one for each group. In this context, taking as equal those tax payers with the same level of utility, we define a scale of equivalence and we give several definitions of the horizontal equity principle. We characterize the fiscal systems which satisfy it in terms of utility loss, it allows us the incorporation of the equal sacrifice principle to the analysis. Furthermore, we obtain the conditions under which the equal face the same degree of progression. Finally, we particularize our results to the case of isoelastic utility functions.