8. In the box on New Zealand, we derived an equation showing how the IIP changes over time: IIPt+1 = (1 + r)IIPt + NXt. Show that if g = (GDPt+1 - GDPt)>GDPt is the growth rate of nominal output (GDP), and lowercase variables denote ratios to nominal GDP (as in the chapter), we can express this same equation in the form:

iipt+1 =

(1 + r)iipt + nxt 1 + g

.

Use this expression to find the ratio of net exports to GDP that holds the IIP to GDP ratio iip constant over time.