For the classical marriage model (introduced in Gale and Shapley, 1962) efficiency and envy-freeness are not always compatible, i.e., fair matchings do not always exist. However, for many allocation of indivisible goods models (see Velez, 2008, and references therein), fairness can be restored if a sufficiently large amount of money is available for distribution/compensation as well. Interpreting the agents as the objects to be allocated, one might try to restore fairness for marriage markets in a similar fashion. We prove that there are marriage markets where no amount of money can guarantee the existence of a fair allocation.