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