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Fiscal sustainability exercise

# Fiscal sustainability exercise - EC 1500 Fiscal...

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EC 1500: Fiscal sustainability exercise From class notes, you know the following: Deficit = B(t) - B(t-1) = REAL government debt Where: B(t) = Public debt (bonds) outstanding at time t Deficit = B(t) - B(t-1) = rB(t-1) + 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(t-1) = REAL interest payments G(t) - T(t) = REAL primary deficit And we made these transformations: B(t) - B(t-1) = rB(t-1) + G(t) - T(t) B(t) = (1+r)B(t-1) + G(t) - T(t) B(t)/Y(t) = (1+r)B(t-1)/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(t-1)/Y(t-1) B(t)/Y(t) = (1+r)[Y(t-1)/Y(t)][B(t-1)/Y(t-1)] + [G(t) - T(t)]/Y(t) note that [Y(t)-Y(t-1)]/Y(t-1) = growth = g Y(t)/Y(t-1) - 1 = g, 1+g =Y(t)/Y(t-1) 1/[1+g] = Y(t-1)/Y(t), thus … (1) B(t)/Y(t) = [(1+r)/(1+g)][B(t-1)/Y(t-1)] + [G(t) - T(t)]/Y(t) Using the approximation (1+r)/1+g) = 1+ r - g B(t)/Y(t) = [1 + r - g][B(t-1)/Y(t-1)] + [G(t) - T(t)]/Y(t) B(t)/Y(t) - B(t-1)/Y(t-1) = [r - g][B(t-1)/Y(t-1)] + [G(t) - T(t)]/Y(t) (2) [B(t)/Y(t)] = [r-g][B(t-1)/Y(t-1)] + [G(t) - T(t)]/Y(t)

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