3
at a constant rate g. The propensity to save of the rentiers is
larger than that of the tax payers by percentage points. .It is
assumed that the price level is stable. We have then the following
difference equation for the public debt D:
Y t = Y« (1 + g) fc : National income excl.of interest on publ.debt
F : Public debt
B : Savings gap which has to be compensated by deficit spending,as
percent of national income
i interest
a : differential saving propensity of rentiers as compared with
tax payers
Price level is assumed to be stable.
A. F t - F t+1 - F t = 6 Y t + «i F t
(1)
Losung der homogenen Gleichung:
e t+l _ e t = ai gfc-
F t " F 0 e
(2)
e = 1 + ai.
F t+1 - (1 + ai)F t = Y 0 B(l+g) t .
Using shift operator E we obtain a particular solution:
F YpBd+gjt.
E - (1 + ai)
F t = {1/ (1+g- (l+ia) ) } YpJMl+gjt
F t = 6/(g-ia).(i+g) t Y 0 .
The complete solution is thus
F t = F 0 (l+ia) t + {6/(g-ia)).(1+g) t Y 0
and the debt in relation to the national income is
F t /Y t = Fq/Yq {(l+ia)/(1+g)) fc + B/(g-ia).