Let d be the percentage change in government debt,g the rate of growth in real GDP,RGDP the real GDP,NGDP the nominal GDP,P the price level,and p the inflation rate.Let G[X] denote the growth rate in variable X,which is the same thing as the percentage change in X;thus,G[X] = (X2 - X1)/X1 ×100% for small changes in X.Here are two properties of the growth rate operator G: (i)G[X×Y] = G[X] + G[Y],and (ii)G[X/Y] = G[X] - G[Y].
a.Show that the growth rate in NGDP is equal to g + p, where g is the real GDP growth rate and p is the inflation rate.
b.Show that d is equal to (Deficit/Debt) × 100%.
c.Show that the percentage change in the Debt/NGDP ratio is equal to d - (g + p).
d.Show that the condition for the Debt to NGDP ratio not to increase is d = g + p.

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The Answer of Let d be the percentage change in government debt,g the rate of growth in real GDP,RGDP the real GDP,NGDP the nominal GDP,P the price level,and p the inflation rate.Let G[X] denote the growth rate in variable X,which is the same thing as the percentage change in X;thus,G[X] = (X2 - X1)/X1 ×100% for small changes in X.Here are two properties of the growth rate operator G: (i)G[X×Y] = G[X] + G[Y],and (ii)G[X/Y] = G[X] - G[Y].
a.Show that the growth rate in NGDP is equal to g + p, where g is the real GDP growth rate and p is the inflation rate.
b.Show that d is equal to (Deficit/Debt) × 100%.
c.Show that the percentage change in the Debt/NGDP ratio is equal to d - (g + p).
d.Show that the condition for the Debt to NGDP ratio not to increase is d = g + p.

Let D Be the Percentage Change in Government Debt,g the Rate