The main concern of this paper is to show the importance of demand uncertainty in the determination of the "natural rate of unemployment". In the goods market there is demand heterogeneity -coming from preferences, and demand uncertainty -related solely to heterogeneity. Demand uncertainty is introduced in a monopoly union model where unions set wages at the first stage of the game, without knowing with certainty the demand for the good produced by the firm. Because the union assigns a positive probability at the event "underemployment equilibrium", it expects that the expected unemployment rate be positive. Since all the uncertainty is firm specific (i.e., there is not aggregate uncertainty), aggregate employment is equal to the union expected employment and then there is unemployment at equilibrium. In some islands the idiosyncratic demand shock is high and firms produce constrained by its full-employment capacity, but at the same time in the other islands the idiosyncratic demand shock is low and firms optimally produce less than its full-employment output