Question 6 [12 points]

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 1,100. In addition, the autonomous expenditure in households, business and foreign sectors (C + I + X - IM) is 300 and government expenditure is 300.

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 =

0.62

%

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 =

1,141.2

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

New public debt ratio =

0.55

%

Marking:

(a)

Public debt ratio

Your answer was:0.62%

The correct answer was:84.33%

To find the public debt ratio we need to find the equilibrium GDP.

Y =A₀+ G₀1 - slope of AE=A₀+ G₀1 - c(1 - t) + m=$300 + $3001 - 0.75(1 - 0.2) + 0.06= 1,304.3478

Public debt ratio =Public debtY=1,1001,304.3478= 0.84333 = 84.3333%

You will lose 4 marks for this part.

(b)

New public debt

Your answer was:1,141.20

The correct answer was:1,156.52

To find the new size of the outstanding debt we need to figure out how the change in government expenditure impacts the government budget balance. As the increase in government expenditure is 100, we can figure out the increase in Y will be G multiplier = 100 2.173913 = 217.391.

The multiplier is calculated as:11 - c(1 - t) + m.

Now, to find the change in the public debt, use:

PD=-BB=-(tY - G)=-tY + G=-0.2(217.391) + 100=56.5217Therefore, the new debt is calculated by adding the previous outstanding public debt and the change in public debt:

New public debt = 1,100 + 56.5217 = 1,156.5217

You will lose 4 marks for this part.

(c)

New public debt ratio

Your answer was:0.55%

The correct answer was:76.00%

The new public debt ratio is our new public debt divided by our new Y.

In our case, it is1,156.52171,304.3478 + 217.391= 0.76 = 76%

You will lose 4 marks for this part.

Total marks for this question: 0

I do not understand how they came up with the answers