Question

Suppose the government raises its revenue by a net tax of 20 percent on income, t = 0.2, the marginal propensity to consume out of disposable income is 0.75, the marginal propensity to import is 0.15, and the government has an outstanding public debt of 1,100. In addition, the autonomous expenditure in households, business and foreign sectors (C + I + X - IM) is 400 and government expenditure is 400.
Note: Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places.

a) What is the public debt ratio?

b) Now, suppose the government increases its expenditures by 110 to provide additional funding for national defense. What is the size of the outstanding public debt after the increase in government expenditure, assuming the economy has reached its new equilibrium national income in one year?

c) What is the debt ratio after the increase in government expenditure and equilibrium income?

Answer 1

Formula

Y = Consumption + Investment + Govt. Expenditure + (Export - Import)

Y = C + I + G + X- IM

In this (C + I + X - IM) = 400 and G = 400

Y = 400 + 0.75(Y - 0.2Y) + 400 - 0.15Y

Y = 800 + 0.75Y - 0.15Y - 0.15Y

Y = 800 + 0.45Y

Y - 0.45Y = 800

0.55Y = 800   

Y = 800/0.55

Y = 1454.54

A) public debt ratio

= (1100/1454.54) × 100 = 75.62%

B)  government increases its expenditures by 110 to provide.

Then G = 400 +110 = 510

Y = 400 + 510 + 0.45Y

Y - 0.45Y = 910

0.55Y = 910

Y = 910/0.55

Y = 1654.54

Now

initial tax receipt = 1454.54 × 0.2 = 290.90

new tax receipt = 1654.54 × 0.2 = 330.90

So increase in tax = 330.90 - 290.90 = 40

So new increse in debt = 110 - 40 = 70

Then new public debt = 1100 + 70 = 1170

C) the debt ratio after the increase in government expenditure and equilibrium income

New public debt ratio = (1170/1654.54) × 100 = 70.71%