Public debt/Addendum: Difference between revisions
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:::ΔD = (D + F + Dr)/{Y(1 + | Let D and Y be the levels of public debt and GDP at the begin of a year; and,<br> let F be the primary, or discretionary budget deficit (the total deficit excluding interest payments) and,<br> let r be the annual rate of interest payable on the public debt. | ||
:::ΔD/Y = (D + F + Dr)/{Y(1 + g)} - D/Y | |||
let 1/{Y(1 + g)} = A | let 1/{Y(1 + g)} = A | ||
Revision as of 01:26, 21 March 2009
Let D and Y be the levels of public debt and GDP at the begin of a year; and,
let F be the primary, or discretionary budget deficit (the total deficit excluding interest payments) and,
let r be the annual rate of interest payable on the public debt.
- ΔD/Y = (D + F + Dr)/{Y(1 + g)} - D/Y
let 1/{Y(1 + g)} = A
then:
- = A(D + F + Dr) - D/Y
- = A( D + F + Dr - D/AY)
- = A( D + F + Dr - D - Dg)
substituting for A:
- = {F + D(r - g)}/{Y(1 + g)}
or, approximately:-
- = {F + D(r - g)
- = F/Y +(r - g)D/Y
putting F/Y = f and D/Y = d:
- = f + d(r - g)