Anmol On FIscal Policy Part 2

Anmol On Fiscal Policy:2

In my previous article I discussed how beyond a point running deficits reduces a country’s debt as a proportion of GDP. Now, we’ll do the math to calculate the position of that point, as well as finding how much your debt increases as a proportion of your GDP in any situation.
Basically, there are 4 different variables: Deficit (I), inflation multiplier(mpc*Gs/Gs+Gd) (M), GDP, and debt(d). Net Gain from deficit= debt/GDP (2)-debt/GDP (1). We assume GDP=1 for simplicity, because the actual value is irrelevant. In other words,
Gain= (d+d*I*M+I/1+I)-(d)
Multiplying and dividing by 1+I we get:
Gain=(d+dIM+I)-(d+dI)/1+I
Gain=d+dIM+I-d-dI/1+I
Gain=dIM+I-dI/1+I
Gain=dI(M-1)+I/1+I
Gain=I[d(M-1)+1)/1+I
Gain=I[1-d(1-M)]/1+I

therefore, if you have the figures of debt, deficit, and inflation multiplier, you can use that simple formula to calculate reduction in debt burden.

If gain=0, the point of madness, I[1-d(1-M)]/1+I
if I is not = 0, 1-d(1-M)=0
1=d(1-M)
d=1/(1-M)

As you can see, the formula accurately plots the next year’s national debt, as a proportion of the previous year’s national debt.