The consolidated government budget constraint (including the Central Bank) is as
follows,
P,(g, - tx, ) = M.. -M + -BÎ1- - B, (13)
1 + i,
with the budget deficit financed, either by the issuance of money, either by the issuance
of public debt. B,+1 are government bonds issued in period t, at price 1/(1+i,), to be
reimbursed in period ,+1 for one monetary unit, and g, and ,x, are respectively the
government expenditure and taxes in real terms, in period ,. The budget constraints of
the households and of the government imply the following equilibrium condition for the
goods and services market in the economy, after adding (9) and (13),
y = ct + gt. (14)
In real terms the government budget constraint can also be presented as
g,- txt
Mt+1 P,+1 Mt , Bt+1 Pm 1 Bt
P P P P P 1 + i P
1 1+1 1 t 1 t 1 1+1 1 t ɪ + lt 1 t
(15)
and, using once more the definitions bt = Bt/Pt and mt = Mt/Pt, it is possible to write the
government budget constraint as
P P1
(16)
gt - txt = mt+1 —--mt + bt+1 ~ — - bt.
P, Pt 1+ i,
By definition, the real interest rate is given by the Fisher relation,
1 + i, = (1 + r, )(1 + π te+1) (17)
and supposing that the price level is correctly predicted for t+1, that is, assuming
perfect forecast for the expected inflation rate, π tβ+1 (with Pt+1 = Pt+1 ),
π t+1 π t+1
P,+1 - Pt
Pt
(18)