06/06/2026, 16:17 Debt Dynamics – Revision Guide
ECON2291 · LEVEL 2 ECONOMIC THEORY
Deficits, Debt & Dynamics
A complete revision guide — formal theory, derivations, exam question
answers, and original practice questions
Notation Definitions Derivation Equilibrium Four Cases Sustainability
Consequences Solutions Money Financing Exam Questions Practice Questions
SECTION 1
Notation & Foundational Variables
Every variable in the debt dynamics framework carries a precise meaning.
Confusing nominal and real quantities, or levels and ratios, is a common source of
exam errors. The following notation is standard across your lectures and Gärtner
(2016).
B Nominal stock of government debt (level)
b = B/Y Debt-to-GDP ratio (the key variable of interest)
Y Nominal GDP
G Government expenditure (excluding interest payments)
T Tax revenues
g = G/Y Government spending as a share of GDP
t = T/Y Tax revenues as a share of GDP
i Nominal interest rate on government debt
r Real interest rate on government debt (r ≈ i − π)
y Growth rate of real GDP
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,06/06/2026, 16:17 Debt Dynamics – Revision Guide
π Inflation rate
Δb Change in the debt-to-GDP ratio from one period to the next
b* Equilibrium (steady-state) debt-to-GDP ratio
ΔB New borrowing in a given period (change in nominal debt stock)
m = M/PY Real money balances as a share of GDP (relevant for seigniorage)
u Growth rate of the money supply (relevant for money financing)
IMPORTANT CONVENTION
Lowercase ratios (g, t, b) always refer to shares of GDP. When the question gives you
numbers in levels (G = £500bn, Y = £2tn), convert to ratios before using any formula.
Assume zero inflation throughout (so i = r) unless the question explicitly introduces
inflation or money financing.
SECTION 2
Core Definitions
DEFINITION — BUDGET DEFICIT
Budget deficit = iBt−1 + (G − T)
The budget deficit has two components. The primary deficit is (G − T): government
spending in excess of tax revenues, before any interest is accounted for. The interest
component iBt−1 is the cost of servicing the pre-existing stock of debt.
DEFINITION — PRIMARY BALANCE
Primary balance = (T − G)
A primary surplus exists when T > G. A primary deficit exists when G > T. This is the
relevant policy instrument because a government can control (G − T) directly but
cannot unilaterally control total interest payments on existing debt.
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, 06/06/2026, 16:17 Debt Dynamics – Revision Guide
DEFINITION — GOVERNMENT BUDGET CONSTRAINT (NO MONEY FINANCING)
T + ΔB = G + iB
This is the flow constraint. Tax revenues plus new borrowing must finance spending
and interest payments on existing debt. The equation rearranges to ΔB = (G − T) + iB,
confirming that the change in the debt stock equals the primary deficit plus interest
servicing costs. This is the starting point for the full derivation.
DEFINITION — DEBT SUSTAINABILITY
Debt is sustainable when the debt-to-GDP ratio (b = B/Y) converges to a finite, stable
value rather than growing without bound. The distinction between the level of debt
and the ratio of debt to GDP is critical: a government can run a permanent deficit
without the ratio exploding, provided the economy grows fast enough relative to the
interest rate.
SECTION 3
Derivation of the Debt Dynamics Equation
This derivation moves from the government's budget constraint to the key equation
governing how the debt-to-GDP ratio evolves over time. You should be able to
reproduce every step under exam conditions.
PROOF — STEP-BY-STEP DERIVATION
1 Start with the budget constraint (no money financing):
T + ΔB = G + iB
Rearranging: ΔB = (G − T ) + iB. This says new borrowing equals the primary
deficit plus interest on existing debt.
2 Divide through by nominal GDP (Y):
file:///C:/Users/tyala/Downloads/debt_dynamics_revision_guide (2).html#exam-qs 3/25
ECON2291 · LEVEL 2 ECONOMIC THEORY
Deficits, Debt & Dynamics
A complete revision guide — formal theory, derivations, exam question
answers, and original practice questions
Notation Definitions Derivation Equilibrium Four Cases Sustainability
Consequences Solutions Money Financing Exam Questions Practice Questions
SECTION 1
Notation & Foundational Variables
Every variable in the debt dynamics framework carries a precise meaning.
Confusing nominal and real quantities, or levels and ratios, is a common source of
exam errors. The following notation is standard across your lectures and Gärtner
(2016).
B Nominal stock of government debt (level)
b = B/Y Debt-to-GDP ratio (the key variable of interest)
Y Nominal GDP
G Government expenditure (excluding interest payments)
T Tax revenues
g = G/Y Government spending as a share of GDP
t = T/Y Tax revenues as a share of GDP
i Nominal interest rate on government debt
r Real interest rate on government debt (r ≈ i − π)
y Growth rate of real GDP
file:///C:/Users/tyala/Downloads/debt_dynamics_revision_guide (2).html#exam-qs 1/25
,06/06/2026, 16:17 Debt Dynamics – Revision Guide
π Inflation rate
Δb Change in the debt-to-GDP ratio from one period to the next
b* Equilibrium (steady-state) debt-to-GDP ratio
ΔB New borrowing in a given period (change in nominal debt stock)
m = M/PY Real money balances as a share of GDP (relevant for seigniorage)
u Growth rate of the money supply (relevant for money financing)
IMPORTANT CONVENTION
Lowercase ratios (g, t, b) always refer to shares of GDP. When the question gives you
numbers in levels (G = £500bn, Y = £2tn), convert to ratios before using any formula.
Assume zero inflation throughout (so i = r) unless the question explicitly introduces
inflation or money financing.
SECTION 2
Core Definitions
DEFINITION — BUDGET DEFICIT
Budget deficit = iBt−1 + (G − T)
The budget deficit has two components. The primary deficit is (G − T): government
spending in excess of tax revenues, before any interest is accounted for. The interest
component iBt−1 is the cost of servicing the pre-existing stock of debt.
DEFINITION — PRIMARY BALANCE
Primary balance = (T − G)
A primary surplus exists when T > G. A primary deficit exists when G > T. This is the
relevant policy instrument because a government can control (G − T) directly but
cannot unilaterally control total interest payments on existing debt.
file:///C:/Users/tyala/Downloads/debt_dynamics_revision_guide (2).html#exam-qs 2/25
, 06/06/2026, 16:17 Debt Dynamics – Revision Guide
DEFINITION — GOVERNMENT BUDGET CONSTRAINT (NO MONEY FINANCING)
T + ΔB = G + iB
This is the flow constraint. Tax revenues plus new borrowing must finance spending
and interest payments on existing debt. The equation rearranges to ΔB = (G − T) + iB,
confirming that the change in the debt stock equals the primary deficit plus interest
servicing costs. This is the starting point for the full derivation.
DEFINITION — DEBT SUSTAINABILITY
Debt is sustainable when the debt-to-GDP ratio (b = B/Y) converges to a finite, stable
value rather than growing without bound. The distinction between the level of debt
and the ratio of debt to GDP is critical: a government can run a permanent deficit
without the ratio exploding, provided the economy grows fast enough relative to the
interest rate.
SECTION 3
Derivation of the Debt Dynamics Equation
This derivation moves from the government's budget constraint to the key equation
governing how the debt-to-GDP ratio evolves over time. You should be able to
reproduce every step under exam conditions.
PROOF — STEP-BY-STEP DERIVATION
1 Start with the budget constraint (no money financing):
T + ΔB = G + iB
Rearranging: ΔB = (G − T ) + iB. This says new borrowing equals the primary
deficit plus interest on existing debt.
2 Divide through by nominal GDP (Y):
file:///C:/Users/tyala/Downloads/debt_dynamics_revision_guide (2).html#exam-qs 3/25
