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Denoting <math>g_0\,</math> as the level of expenditure, debt <math>b(t)\,</math> evolves according to:
<math>\frac{db}{dt} = \underbrace{(1-\gamma)}_{\mbox{deficit}}\times\underbrace{[rb(t) + g_0]}_{\mbox{Total government spending}}\,</math>
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