Using a money‐in‐the‐utility‐function model, this paper considers long‐run stagnation where insatiable demand for money persistently creates aggregate demand deficiency and consequent unemployment in the presence of nominal wage stickiness attributed to union wage setting. In this long‐run stagnation, generous unemployment benefits reduce unemployment. Moreover, paradoxically, unemployment declines if labor unions give weight to nominal wage gains rather than employment increases.