The motivation for the Lindahl equilibrium is mostly a rather artificial price mechanism. Even though the analogy to a competitive market was emphasised by Lindahl himself, his approach does not directly explain the normative ideas behind his concept. In the present paper we therefore show how the Lindahl equilibrium can be deduced from some simple equity axioms. These normative assumptions are the benefit principle on the one hand and the equal sacrifice principle (or, equivalently, a non-envy condition) as a postulate for distributional equity on the other. Fairness among agents with different preferences and incomes is taken into account by considering their marginal willingness to pay as shadow prices. In this way, the reason why the Lindahl solution can be perceived as an outcome of fair cooperation might become more understandable.