Public debt/Addendum: Difference between revisions
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imported>Nick Gardner No edit summary |
imported>Nick Gardner No edit summary |
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::: | :::Δ(D/Y) = (D + F + Dr)/{Y(1 + g)} - D/Y | ||
let 1/{Y(1 | let 1/{Y(1;+ g)} = A | ||
  | |||
then: | then: | ||
:::= A(D + F + Dr) - D/Y | :::Δ(D/Y) = A(D + F + Dr) - D/Y | ||
:::= A( D + F + Dr - D/AY) | ::::= A( D + F + Dr - D/AY) | ||
:::= A( D + F + Dr - D - Dg) | ::::= A( D + F + Dr - D - Dg) | ||
substituting for A: | substituting for A: | ||
:::= {F + D(r - g)}/{Y(1 + g)} | :::Δ(D/Y) = {F + D(r - g)}/{Y(1 + g)} | ||
or, approximately:- | or, approximately:- | ||
:::= {F + D(r - g) | :::Δ(D/Y) = {F + D(r - g) | ||
:::= F/Y +(r - g)D/Y | ::::= F/Y +(r - g)D/Y | ||
putting F/Y = f and D/Y = d: | putting F/Y = f and D/Y = d: | ||
:::= f + d(r - g) | :::Δ(D/Y) = f + d(r - g) | ||
</small> | </small> | ||
Revision as of 02:11, 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.
- Δ(D/Y) = (D + F + Dr)/{Y(1 + g)} - D/Y
let 1/{Y(1;+ g)} = A
 
then:
- Δ(D/Y) = A(D + F + Dr) - D/Y
- = A( D + F + Dr - D/AY)
- = A( D + F + Dr - D - Dg)
- Δ(D/Y) = A(D + F + Dr) - D/Y
substituting for A:
- Δ(D/Y) = {F + D(r - g)}/{Y(1 + g)}
or, approximately:-
- Δ(D/Y) = {F + D(r - g)
- = F/Y +(r - g)D/Y
- Δ(D/Y) = {F + D(r - g)
putting F/Y = f and D/Y = d:
- Δ(D/Y) = f + d(r - g)