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 $\pi$ 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 + $\pi$ .
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 + $\pi$ ).
d.Show that the condition for the Debt to NGDP ratio not to increase is d = g + $\pi$ .

Question

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

\pi

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 +

\pi

.
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 +

\pi

).
d.Show that the condition for the Debt to NGDP ratio not to increase is d = g +

\pi

.

Quizplus · Accepted Answer

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 $\pi$ 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 + $\pi$. 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 + $\pi$). d.Show that the condition for the Debt to NGDP ratio not to increase is d = g + $\pi$.

Let D Be the Percentage Change in Government Debt, G π\piπ

Let D Be the Percentage Change in Government Debt, G $\pi$