Final answer:
Government debt increases with a budget deficit and decreases with a surplus. Thus, after running deficits for a few years and then a surplus, the government debt at the end of year three is $4.7 billion. If the government runs a budget deficit for ten years, a surplus for five years, and a balanced budget for another ten years, the debt will be $95 billion.
Step-by-step explanation:
When considering a government's budget deficit or surplus, it's important to understand the impact on the total government debt. In the scenarios given, the government's annual activities result in changes to the debt.
For the year one deficit of $400 million, the total debt would increase to $3.9 billion. For year two, with a deficit of $1 billion, the debt goes up to $4.9 billion. Then, in year three, the government runs a surplus of $200 million, which would decrease the debt to $4.7 billion. Therefore, the total government debt at the end of year three would be $4.7 billion.
In the second scenario, running a deficit of $10 billion dollars each year for ten years would add $100 billion to the debt. The surplus of $1 billion each year for the next five years would subtract $5 billion from the total debt. Then, with a balanced budget for another ten years, the total government debt would remain the same because a balanced budget means no additional deficits or surpluses to affect the debt. Thus, the government debt after this period would be the original debt plus $100 billion, minus $5 billion, equaling $95 billion.