ECON1002 · Introductory Macroeconomics
Fiscal Policy & Government Debt
Fiscal policy uses spending and tax changes to shift planned expenditure and close output gaps. Because part of a tax cut is saved, the spending multiplier exceeds the tax multiplier, and a matched ΔG = ΔT still raises output (the balanced-budget multiplier). The chapter also measures inequality with the Gini coefficient off the Lorenz curve, and assesses debt sustainability through the government budget constraint, where trouble arises when the real interest rate exceeds the growth rate.
It is examined as multiplier calculations (spending vs tax vs balanced-budget) and concept MCQ on automatic stabilisers, crowding out and the Gini coefficient.
What this chapter covers
- 011. Spending vs tax changes to close output gaps (a tax cut raises the PAE slope)
- 022. Spending multiplier K_G = 1/(1 − c(1−t)); tax multiplier K_T = −c/(1 − c(1−t))
- 033. Spending > tax in absolute effect (part of a tax cut is saved)
- 044. Balanced-budget multiplier: ΔG = ΔT still raises Y; K_BB = K_G + K_T
- 055. Gini coefficient (0-1) = A/(A+B) under the Lorenz curve; higher = more unequal
- 066. Automatic stabilisers: taxes fall and transfers rise in a recession (and vice versa)
- 077. Crowding out: government borrowing raises interest rates, lowering private investment
- 088. Debt sustainability: rising public debt when real interest rate > growth rate
Balanced-budget change in output
- 1 markFind the change in autonomous expenditure. A spending change adds fully (ΔG), but a tax change only removes the spent fraction c·ΔT: Δautonomous = ΔG − c·ΔT = 80 − 0.8 × 80 = 80 − 64 = 16.
- 1 markApply the multiplier: ΔY = Δautonomous × multiplier = 16 × 3.33 = 53.3.
Key terms
- Spending multiplier (K_G)
- The change in equilibrium output per unit change in government spending: K_G = 1/(1 − c(1−t)). Because government spending adds fully to demand, it has a larger absolute effect than an equal-sized tax change.
- Tax multiplier (K_T)
- The change in output per unit change in (lump-sum) taxes: K_T = −c/(1 − c(1−t)). It is negative (higher taxes lower output) and smaller in magnitude than the spending multiplier, because only the consumed fraction c of a tax change affects demand.
- Balanced-budget multiplier
- The output effect of equal increases in spending and taxes (ΔG = ΔT). It equals K_G + K_T and is positive — output still rises — because the spending injection is full while the tax leakage is only the saved part (1 − c).
- Gini coefficient
- A measure of income inequality between 0 (perfect equality) and 1 (perfect inequality), equal to A/(A+B), the area between the Lorenz curve and the 45° equality line as a share of the whole triangle. A higher Gini means a more unequal distribution.
- Automatic stabilisers
- Features of the budget that cushion the cycle without new legislation: in a downturn, tax receipts fall and transfer payments (like unemployment benefits) rise, supporting demand; in a boom the reverse happens. They moderate fluctuations automatically.
- Debt sustainability
- From the government budget constraint, the public-debt-to-GDP ratio tends to rise when the primary deficit is large, the real interest rate is high, or output growth is low. Sustainability worsens sharply when the real interest rate exceeds the growth rate.
Fiscal Policy & Government Debt FAQ
How is fiscal policy examined in ECON1002?
Mainly as multiplier calculations: compute the spending multiplier and the tax multiplier, compare their magnitudes, and work out a balanced-budget change in output (the recurring IST/sample-final type). It is rounded out with concept MCQ on automatic stabilisers, crowding out, the Gini coefficient, and when public debt becomes unsustainable.
Why is the spending multiplier bigger than the tax multiplier?
Because government spending enters demand fully — every dollar of G is a dollar of spending — whereas a tax cut only raises demand by the fraction households choose to consume (c), with the rest (1 − c) saved. So in absolute size the spending multiplier 1/(1 − c(1−t)) exceeds the tax multiplier c/(1 − c(1−t)). This is why dollar-for-dollar, spending is a more powerful stimulus than a tax cut.
How can a balanced budget still boost output?
Because the spending and tax changes do not have equal effects. Raising G by an amount adds that full amount to autonomous demand, but raising T by the same amount only removes the consumed fraction c of it. The net injection is (1 − c) of the change, which the multiplier then magnifies — so a matched ΔG = ΔT leaves output higher, the balanced-budget multiplier result.
What makes government debt unsustainable?
From the budget constraint, debt as a share of GDP grows when interest on existing debt and any primary deficit outpace economic growth. The key condition is the real interest rate versus the growth rate: when the real interest rate exceeds the growth rate, the debt ratio tends to snowball even with a balanced primary budget, whereas growth above the real rate helps the economy 'grow out' of debt.
Exam move
Memorise the three multipliers and how they relate: spending K_G = 1/(1 − c(1−t)), tax K_T = −c/(1 − c(1−t)), and balanced-budget K_BB = K_G + K_T. The fastest route to the balanced-budget answer is Δautonomous = ΔG − c·ΔT, then × multiplier — drill that so you never make the mistake of cancelling ΔG against ΔT. Keep one-line notes for the conceptual MCQ: the Gini is the area ratio A/(A+B) (higher = more unequal); automatic stabilisers smooth the cycle without new laws; crowding out works through a higher interest rate; and debt is unsustainable when the real interest rate beats the growth rate. Pair each calculation with the intuition (part of a tax cut is saved) since the explanation can carry marks in Section B.
