The Fiscal Theory of the Price Level (FTPL) is an important theory that recognizes the interaction between monetary and fiscal policy. In its simplest form, the FTPL assumes that the government commits to a fixed and exogenous present value of primary surpluses implying the adjustment of the price level to equate the real government debt to the present value of primary surpluses. The FTPL relies on the presence of primary surpluses to work. We show that this condition is not necessary in a non-Ricardian economy. The FTPL still hold even when exogenous primary surpluses are null. We consider an overlapping generations of infinitely-lived dynasties model with simple fiscal and monetary policies, where the effective lower bound on nominal interest rates is taken into account. A bubble-like component of government debt appears inducing the determination of the price level by the fiscal policy, when the effective lower bound on nominal interest rates is binding and even when the government primary surpluses equal zero.