Question

If a government runs a budget deficit of \(\$ 10\) billion dollars each year for ten years, then a surplus of \(\$ 1\) billion for five years, and then a balanced budget for another ten years, what is the government debt?

Short answer

The government's net debt after going through the three phases is \$95 billion.

Step-by-step solution

Calculate total deficit from the first phase

To calculate the total deficit during the first phase, we will multiply the annual deficit amount (\$10 billion) by the number of years in this phase (10 years): \[Total\_Deficit = Annual\_Deficit \times Number\_of\_Years\]

Calculate total surplus from the second phase

To calculate the total surplus during the second phase, we will multiply the annual surplus amount (\$1 billion) by the number of years in this phase (5 years): \[Total\_Surplus = Annual\_Surplus \times Number\_of\_Years\]

Calculate net debt by taking the difference between the deficit and surplus amounts

Subtract the total surplus from the total deficit to find the net government debt: \[Net\_Debt = Total\_Deficit - Total\_Surplus\]

Simplify and solve the equations

Using the equations from steps 1-3, let's calculate the values for the total deficit, total surplus, and net government debt: Total Deficit: \[Total\_Deficit = \$10 \ billion/year \times 10 \ years = \$100 \ billion\] Total Surplus: \[Total\_Surplus = \$1 \ billion/year \times 5 \ years = \$5 \ billion\] Net Debt: \[Net\_Debt = \$100 \ billion - \$5 \ billion = \$95 \ billion\] After going through the three phases, the government's net debt is \$95 billion.