Question

At the beginning of year one, there is no government debt outstanding. The government runs a $100 billion deficit in year one. Interest at a nominal rate of 10% must be paid starting in year two. Assume nominal GDP in year one is $2000 billion and the nominal growth rate of GDP is 4%. Assume the government balances its primary budget in the future and the interest rate and growth rate do not change. (a) What will be the government deficit in years two, three, four, and five? (b) What will be the value of government bonds outstanding at the end of the fifth year? (c) What will be the debt—GDP ratio at the end of year five?

Answer 1

a) Debt is used to finance deficit. Deficit refers to the situation when government expenditure is grater than government receipt. But surplus means the opposite things, in case of surplus receipt is grater then expenditure. Surplus is used to repay debt.

Government starts with a total debt of 3.5 billion or $3500 million

In first year government deficit = $400 million.

Government finances the deficit by borrowing. Hence the debt in first year =(3500+400)= $3900 million

In second year government deficit=$1 billion=1 million

Then debt in second year= (3900+1000)=$4900 million

In third government makes some surplus of $200 million, which is used to repay debt. If $200 million of debt is repaid then remaining debt =(4900-200)= $4700

Therefore at the end of three year total government debt is $4.7 billion.

b) The concept of Surplus and deficit is same as stated above. Balance budget refers to neither deficit nor budget. Thus in case of balance budget nothing is added to debt.

If government runs a budget deficit of $10 billion each year for five year, then the deficit is financed by borrowing. Then each year government debt equals to $10 billion. Hence total debt for five year is $50 billion. Then next ten years government makes some surplus of $1 billion each year. Now total surplus will be $10 billion. The amount of surplus will be used to repay the debt which is due for five year. After repayment, total debt remains of amount (50-10) $40 billion. Then next ten year government budget is balance so nothing is added to debt. Therefore total debt is $40 billion.