Question

 Consider an economy where in year t the government has a primary deficit of 2% of GDP. The government debt at the end of period t -1 is 80% of GDP on which the government has to pay a real interest rate of 3%. The economy's real GDP grows at

 an annual rate of 5%.

 (i) In the long run, what value will the debt-to-GDP ratio converge to?

 The government aims to reach a 60% debt ratio within 2 years and decides to cut the primary deficit to 0.6% of GDP. As an economist, you advise that this primary deficit is not low enough to achieve the goal.

 (ii) Show that the government's fiscal action will not help them achieve their goal. 

 (iii) Calculate the required primary deficit needed to achieve the debt criterion in two years.

Answer 1

Let us assume that GDP at t-1 = 100

Then government debt at t-1 = 80% of 100 = 80

The interest rate at t -1 = 3% of debt = 3% of 80 = 2.4

However the question does not tell about any fiscal deficit at t-1 year

Thus we consider that the revenue was sufficient for payment of interest on debt .

Debt to GDP ratio =( 80/100)*100 = 80%

Now the GDP grows at a rate of 5% per year .

Thus GDP at t = 100+5% = 105

Primary deficit at t = 2% of GDP = 2% of 105 = 2.1

Interest at t = 3% of 80 = 2.4

Now Primary deficit = Fiscal deficit - Interest payment

2.1 = Fiscal deficit - 2.4

Fiscal deficit = 4.5

To correct the fiscal deficit the government borrows money from the public thus increasing the debt amount from 80

to 84.5

ANSWER i :-

New Debt to GDP ratio = 84.5/105 = 80.48%

If the government aims to reach at debt to GDP ratio of 60 %

Where GDP at t+2 = 115.7625

It must have a debt of

60% = debt / GDP

New value of debt = .60*115.7625 = 69.4575

Interest payment calculations :-

At t+1 , interest payment = 3% of 84.5 = 2.5

Primary debt = 0.6 % of 110.25

=0.6

Fiscal deficit for t+1 = 2.5 + 0.6 =3.1

Debt amount at t+1 = 84.5+3.1 = 87.6

At t +2 = interest payment = 3%of 87.6 = 2.6

Primary deficit = 2% of 115.7625 = .69

Fiscal deficit at t +2 = 3.3

debt at t +2 = 87.6+3.3 = 90.9

Required debt = 69.5

Extra debt liability = 90.9- 69.5 = 21.4

Answer ii :-

The government should impose new taxes in order to increase its revenue to such an extent that it is able to pay both the primary deficit as well as the interest on the loans

Answer iii :-

There should be a primary surplus of 8.8 % to correct the about of debt :-

At t +1 ,

Primary surplus = 8.8% of 110.25 = 9.7

Interest payment = 2.4

Excess amount left for debt repayment = 9.7-2.4 = 7.4

Debt at t +1 = 77.1

At t+2,

Interest amount = 3% of 77.1 = 2.3

Now primary surplus = 8.8% of 115.7625 =10.1

Extra amount for debt repayment = 10.1 - 2.3 = 7.8

Debt at t +2 = 77.1 -7.8 = 69.3