EC 1500: Fiscal sustainability exercise
From class notes, you know the following:
Deficit = B(t)  B(t1) =
∆
REAL government debt
Where: B(t) = Public debt (bonds) outstanding at time t
Deficit = B(t)  B(t1) = rB(t1) + G(t)  T(t)
Where: r = real interest rate
G(t) = government spending at time t
T(t) = government revenues(from taxes)at time t
rB(t1) = REAL interest payments
G(t)  T(t) = REAL primary deficit
And we made these transformations:
B(t)  B(t1) = rB(t1) + G(t)  T(t)
B(t) = (1+r)B(t1) + G(t)  T(t)
B(t)/Y(t) = (1+r)B(t1)/Y(t) + [G(t)  T(t)]/Y(t)
Where Y(t)= output, or income, or GDP in year t
now multiply first term on the RHS by Y(t1)/Y(t1)
B(t)/Y(t) = (1+r)[Y(t1)/Y(t)][B(t1)/Y(t1)] + [G(t)  T(t)]/Y(t)
note that [Y(t)Y(t1)]/Y(t1) = growth = g
Y(t)/Y(t1)  1 = g, 1+g =Y(t)/Y(t1)
1/[1+g] = Y(t1)/Y(t), thus …
(1)
B(t)/Y(t) = [(1+r)/(1+g)][B(t1)/Y(t1)] + [G(t)  T(t)]/Y(t)
Using the approximation (1+r)/1+g) = 1+ r  g
B(t)/Y(t) = [1 + r  g][B(t1)/Y(t1)] + [G(t)  T(t)]/Y(t)
B(t)/Y(t)  B(t1)/Y(t1) = [r  g][B(t1)/Y(t1)] + [G(t)  T(t)]/Y(t)
(2)
∆
[B(t)/Y(t)] = [rg][B(t1)/Y(t1)] + [G(t)  T(t)]/Y(t)
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 Fall '10
 CARKOVIC
 Deficit, Public Finance, 1%, Keynesian economics, 1 percent, 2.5%

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