The Lindahl equilibrium is mostly motivated by a rather artificial price mechanism. Even though the analogy to a competitive market has been emphasised by Lindahl himself his approach does not directly explain the normative ideas, which are behind this concept. In the present paper we therefore show how the Lindahl equilibrium can be deduced from some simple equity axioms that in particular are related to the equal sacrifice principle and a nonenvy postulate as norms for distributional equity. Fairness among agents with different preferences is taken into account by considering their marginal willingnesses to pay as virtual prices. In this way it might also become more understandable why the Lindahl solution can be perceived as an outcome of fair cooperation.