… is from page 255 of the English translation of Hayek’s 1962 essay “The Economy, Science, and Politics,” which is chapter 18 in Hayek’s 1967 collection, Studies in Philosophy, Politics, and  Economics :
The power of any particular [labor] union to push up the wages of its members, that is, to make them higher than they would be without the activity of the union, rests entirely on its ability to prevent the entry into the trade of workers willing to work for a lower wage. This will have the effect that the latter either must work elsewhere at still lower wages or that they will remain unemployed.
Hayek here is writing about labor-unionization of workers in privately owned industries. In 1962 it was likely difficult for Hayek or anyone else to foresee the rise – both relative to the power of private-sector unions and absolutely – of public-sector labor unions. While Hayek’s analysis is spot-on correct about the manner in which private-sector labor unions benefit their members (which is necessarily at the expense of non-members and of the larger economy), I believe that this analysis doesn’t quite work for public-sector labor unions. The chief reason is that governments, unlike private firms, face no hard-and-fast bottom line. Private firms (at least those without any special privileges from government to protect them from the entry of new rivals) have no surpluses that can be bargained over. In contrast, governments that grant economically unjustified wage increases to their workers have taxpayers to farm more intensely.