Public debt/Addendum

ΔD = (D + F + Dr)/{Y(1 + r)} - 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)}/Y