Suppose the real interest rate on government bonds is 5% while the growth rate of real GDP is 4%,and that the government's current debt-to-GDP ratio is 30%.If the government has a primary budget balance of zero in the current year,the debt-to-GDP ratio will

Question

Quizplus · Accepted Answer

The debt-to-GDP ratio can be expressed as:

Debt-to-GDP ratio = (Government debt) / (GDP)

Assuming a primary budget balance of zero, the government's total spending (including interest payments on debt) will be equal to its total revenue. If the government does not want the debt-to-GDP ratio to change, it must ensure that the nominal value of its debt grows at the same rate as nominal GDP. Given that the real interest rate on government bonds is 5%, and that the inflation rate is assumed to be zero, the nominal interest rate on government bonds will also be 5%. Therefore, to keep the nominal value of its debt constant, the government must ensure that its primary budget balance (i.e., total revenue minus non-interest expenditure) is equal to the product of its debt-to-GDP ratio and real GDP growth rate.

In equation form:

Primary budget balance = (Debt-to-GDP ratio) x (Real GDP growth rate)

Substituting the given values, we get:

Primary budget balance = 0.3 x 0.04 = 0.012 or 1.2%

Since the primary budget balance is zero, the government will have a surplus of 1.2% of GDP, which can be used to pay down the debt. As a result, the debt-to-GDP ratio will decrease by:

(Real interest rate) x (Debt-to-GDP ratio) - (Primary budget balance)

= 0.05 x 0.3 - 0.012 = 0.003 or 0.3 percentage points.

Therefore, the correct answer is B. The debt-to-GDP ratio will rise by 0.3 percentage points.

Suppose the Real Interest Rate on Government Bonds Is 5