In: Economics
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
0.06, and the government has an outstanding public debt of 800. In
addition, the autonomous expenditure in households, business and
foreign sectors (C + I + X - IM) is 340 and government expenditure
is 340.
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?
Public debt ratio = 0%
b) Now, suppose the government increases its
expenditures by 100 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?
New public debt = 0
c) What is the debt ratio after the increase in
government expenditure and equilibrium income?
New public debt ratio = 0%
Let's first calculate the equilibrium income in order to calculate the public debt ratio.
Y = C + I + G + X - IM
Y = (C + I + X - IM) + G + b(Y - tY) - 0.06Y
Y = 340 + 340 + 0.75( Y - 0.2Y) - 0.06Y
Y = 680 + 0.75 Y(1 - 0.2) - 0.06Y
Y = 680 + Y [0.75(0.8) - 0.06]
Y - Y[ 0.75×0.8 - 0.06] = 680
Y( 1 - 0.75×0.8 - 0.06) = 680
Y = 680/(1 - 0.6 - 0.06)
Y= 680/(1 - 0.66)
Y = 680/0.34
Y = 2,000
So the equilibrium level of income is 2,000.
And tax revenue will be equal to,
= 0.2 × 2,000
= 400
Now the public debt will be equal to,
= government revenue - government expenditure
= 400 - 340
= 60.
Previous outstanding debt of government was equal to 800 but now the government has a surplus of 60 which means the public debt reduces to,
= 800 - 60
= 740
So the public debt ratio will be equal to,
= public debt/aggregate income
= 740/2000
= 0.37 or 37%
So the public debt ratio is equal to 37%.
(b) Now the government expenditure increases by 100 now we will have to calculate the new equilibrium level of income.
Y = 680 + 100 + Y(0.75 × 0.8 - 0.06)
Y = 780 + Y(0.6 - 0.06)
Y - Y(0.6 - 0.06) = 780
Y ( 1 - 0.6 - 0.06) = 780
Y = 780/(1 - 0.66)
Y = 780/0.34
Y = 2294.11
So the equilibrium level of income now is 2294.11.
Now the tax revenue will be equal to,
= 2294.11 × 0.2
= 458.82
And the new government expenditure is equal to,
= 340 + 100
= 440.
And the government debt in this period will be equal to,
= 458.82 - 440
= 18.82
So the government is having a budget surplus of 18.82.
Now the public debt will be equal to previous outstanding debt minus the budget surplus of this period.
= 800 - 18.82
= 721.18
So the new public debt is equal to 721.18
(c) Now the new public debt ratio will be equal to,
= new public debt/new aggregate income level
= 721.18/2294.11
= 0.3143 or 31.43%.
So the new public debt ratio is equal to 31.43%.