Positive or negative real balance effects, involuntary unemployment, three-generations overlapping generations model

We examine positive or negative real balance effect (or so-called Pigou effect) by falls in the nominal wage rate and the prices of the goods in situations where there is involuntary unemployment using a three-generations overlapping generations model with childhood period and pay-as-you go pension system for the older generation consumers. We will show that if the net savings of the younger generation consumers are larger than their debts due to consumption in their childhood period, there exists positive real balance effect and the employment increases by a fall in the nominal wage rate; on the other hand, if the net savings of the younger generation consumers are smaller than their debts, there exists negative real balance effect and the employment decreases by a fall in the nominal wage rate.