Chapter 30: Problem 52

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

Expert verified

The total government debt at the end is $95$ billion dollars.

Step by step solution

Calculate the deficit in the first phase

To calculate the deficit in the first phase, we multiply the annual deficit of $10$ billion dollars by the number of years in this phase, which is $10$ years. We have: \[ Deficit_{Phase1} = 10 \times 10 = 100 \ \text{billion dollars} \]

Calculate the surplus in the second phase

To calculate the surplus in the second phase, we multiply the annual surplus of $1$ billion dollars by the number of years in this phase, which is $5$ years. We have: \[ Surplus_{Phase2} = 1 \times 5 = 5 \ \text{billion dollars} \]

Debt after the second phase

Given that the government starts by having a debt of $100$ billion dollars, after the surplus of the second phase, the debt is reduced by $5$ billion dollars. Therefore, we have: \[ Debt_{AfterPhase2} = Deficit_{Phase1} - Surplus_{Phase2} = 100 - 5 = 95 \ \text{billion dollars} \]

Debt after the third phase

Since the budget is balanced for the last ten years, there won't be any change in the government's debt. Therefore, the debt after the third phase remains the same as the debt after the second phase: \[ Debt_{AfterPhase3} = Debt_{AfterPhase2} = 95 \ \text{billion dollars} \]

Total government debt

Considering all the three phases, the total government debt at the end is $95$ billion dollars.

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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?