Bt_ = y st+s
Pt 0O (1 + r )s+1
(6)
where Bt stands for the government nominal liabilities in period t, including the stock of
public debt (for simplicity one year securities) and monetary base; st is the primary
budget government surplus in period t, including seigniorage revenues, in real terms; r
is the real interest rate, assumed constant, and considering also the usual transversality
condition
lim Bt+s
= 0.
(7)
t + s
s > ∞ (1 + r )s+1
However, it is relevant to bear in mind that fiscal and monetary policy, directly or
indirectly, both end up being responsible for the fulfilment of the government budget
constraint. Equation (6) will be successfully met if the government adopts a non-
Ricardian fiscal policy, using Woodford’s terminology. Therefore, after the government
having arbitrarly chosen a sequence of fiscal balances, by choosing the level of public
expenditures, the price level will adjust endogenously to ensure compliance with the
budget constraint. In other words, if equation (6) is to be met for any value of price
level, than fiscal policy must adjust passively (Leeper [1991]), in line with a Ricardian
regime (Woodford [1995]).
2.3. The price level fiscal theory approach
For the presentation of the FTPL framework, lets assume a model of numerous and
infinitely lived households that maximize an utility function with money as an
argument. This type of money-in-the-utility-function (MIUF) model is inspired in
Sidrauski (1967) and Brock (1975) and the utility function of the consumers, supposed
to be additive, may be written as
U(ct, mt ) = (1 - σ) 1A1 ct 1 σ + (1 - η) 1A2mt 1 η , σ>0; η>0; (8)