A utility maximizing consumer with a completely known system of ordinary demand functions q = h(p,C) is considered. Let (p^o, q^o) and (p^1,q^1) to two arbitrary equilibrium situations; the problem is to evaluate in which of the situations the utility is higher without knowing the utility function. Revealed preference theory tells that the ordinary demand functions (which are in principle observable) contain enough information to solve the problem. Remaining difficulties are therefore mainly computational. We present how the how the compensated income C^1 = C(p^1,q^o) and the compensated demand q^1 = h(p^1,C^1) are calculated with arbitrary accuracy using only the ordinary demand system. Our two efficient algorithms also have interesting interpretations in terms of index numbers and consumer surplus measures.