# The Bank of Israel - Vol. 1

By Haim Barkai; Nissan Liviatan | Go to book overview

Appendix G: Solvency and
Sustainability

A simple example may illustrate the ideas stated in the text relating to these concepts. The time-pattern stock of government bonds at any moment of time is given by

Db = (r − n)b + (pd − μm)    (G1)

where b is the stock of (indexed) government bonds, m is real balances (identical to base money), μm is seigniorage (μ being the rate of expansion of money base m), and pd is the primary deficit (all expressed as ratios of GDP), r is the real interest rate, and n is the rate of growth. D denotes the time derivative operator. Note that seigniorage can be expressed as μm = Dm + (n + π)m, where π denotes inflation, so that adding Dm to both sides of the Db equation yields

Da = (r − n)a + (pd − im)    (G2)

where im is the inflation tax (i = r + π being the nominal interest rate) and a = m + b is the public’s financial wealth. To simplify matters, let us denote pd−μm = pdb and (pd−im) = pda, and assume that (r−n) = ρ = constant. Using this notation, we express (G1) and (G2) as

Db = ρb + pdb and Da = ρa + pda.

To derive a sufficient condition for the solvency of b, we assume that pdb decreases linearly with b according to pdb = k − βb, where k and p are constants (the latter is positive). We may then write (G1) as

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