Microeconomic foundation for Phillips curve with three-periods overlapping generations model and negative real balance effect

We show a negative relation between the inflation rate and the unemployment rate , that is, the Phillips curve using a three-periods overlapping generations (OLG) model with childhood period and pay-as-you-go pension for older generation under monopolistic competition. We consider the effects of a change in nominal wage rate with negative real balance effect and the effects of an exogeneous change in labor productivity. In a three periods OLG model there may exist a negative real balance effect. A fall (or rise) in nominal wage rate induces a fall (or rise) in the price, then by negative real balance effect the unemployment rate rises (or falls), and we get a negative relation between the inflation rate and the unemployment rate. This conclusion is based on the premise of utility maximization of consumers and profit maximization of firms. Therefore, we presented a microeconomic foundation of the Phillips curve. About the effects of a change in labor productivity we obtain similar results. We also examine the effects of fiscal policy financed by seigniorage.