Interactive modelAdvanced Macro & Growthadvanced

Government Budget Constraint & Seigniorage

Deficits, debt dynamics, and the inflation tax when governments print to pay.

Equilibrium: π* = 20.0, R* = 32.0

Current equations

Seigniorage revenue: R = 0 + 2·π − 0.02·π²Deficit to finance: R = 32

Governments that cannot tax or borrow can print. The curve shows the revenue inflation raises by eroding the money people hold. It is a hill: at low inflation there is room to raise more, but past the peak people flee the currency and more inflation raises LESS.

Shift the curves

Deficit financed by printing0

The bigger the bill handed to the printing press, the higher the inflation needed to pay it.

The Government Budget Constraint & Seigniorage model, in writing

Definition

The government's intertemporal accounting: deficits are financed by borrowing or money creation, and money creation earns seigniorage, the inflation tax.

Deficit = ΔB + ΔM; seigniorage ≈ (money growth) × (real balances held)

The intuition

Debt today is taxes tomorrow, unless the printer runs. Printing collects revenue from everyone holding cash as inflation erodes it, which works until people flee the currency: the hyperinflation endgame of fiscal dominance.

Exam tip

Distinguish debt sustainability (r vs g dynamics) from seigniorage financing, mixing them costs marks.

Related models in Advanced Macro & Growth

IS-LM →Mundell-Fleming (Open-Economy IS-LM) →Fisher Equation →Solow-Swan Growth Model →