Involuntary unemployment with divisible labor supply with a three-periods overlapping generations model under monopolistic competition

We show the existence of involuntary unemployment without assuming wage rigidity. We derive involuntary unemployment by considering utility maximization of consumers and profit maximization of firms in an overlapping generations model under monopolistic competition with increasing or constant returns to scale technology and homothetic preferences of consumers. Indivisibility of labor supply may be a ground for the existence of involuntary unemployment. However, we show that there exists involuntary unemployment even when labor supply is divisible. The existence involuntary unemployment in our model is due to that we use an overlapping generations model of consumptions and labor supply. In a two-periods overlapping generations model it is possible that a reduction of the nominal wage rate reduces unemployment. However, if we consider a three-periods overlapping generations model including a childhood period, a reduction of the nominal wage rate does not necessarily reduce unemployment