Question

In 2014 , the policy makers of the economy of Eastlandia projected the debt- GDP ratio and the ratio of the budget deficit to GDP for the economy for the next 10 years under different scenarios for growth in the government's deficit. Real GDP is currently \(\$ 1,000\) billion per year and is expected to grow by \(3 \%\) per year, the public debt is \(\$ 300\) billion at the beginning of the year, and the deficit is \(\$ 30\) billion in 2014 . a. Complete the accompanying table to show the debt-GDP ratio and the ratio of the budget deficit to GDP for the economy if the government's budget deficit remains constant at \(\$ 30\) billion over the next 10 years. (Remember that the government's debt will grow by the previous year's deficit.) b. Redo the table to show the debt-GDP ratio and the ratio of the budget deficit to GDP for the economy if the government's budget deficit grows by $3 \%$ per year over the next 10 years. c. Redo the table again to show the debt-GDP ratio and the ratio of the budget deficit to GDP for the economy if the government's budget deficit grows by $20 \%$ per year over the next 10 years. d. What happens to the debt-GDP ratio and the ratio of the budget deficit to GDP for the economy over time under the three different scenarios?

Short answer

Answer: In the constant budget deficit scenario, the debt-GDP ratio is smaller than the other two scenarios and decreases over time. In the 3% and 20% budget deficit growth scenarios, the debt-GDP ratio increases more than the constant budget deficit scenario. The higher the budget deficit growth rate, the faster the debt-GDP ratio will increase.

Step-by-step solution

Find the real GDP and debt-GDP ratio for each year (constant budget deficit scenario)

In this case, the budget deficit is constant at \$30 billion. Real GDP grows by 3% every year. We will find the real GDP and public debt for each year, then calculate the debt-GDP ratio for all 10 years. The public debt will grow by the previous year's deficit (\$30 billion). First year GDP: \(1000 \times 1.03^1 = \$ 1,030\) First year public debt: \(300 + 30 = \$ 330\) Debt-GDP ratio: \(\frac{330}{1030} = 0.3204\) Repeat this process for the next 9 years. b.

Find the real GDP and debt-GDP ratio for each year (3% budget deficit growth scenario)

In this case, the budget deficit grows by 3% every year. Follow the same steps as in the first scenario to find the real GDP and public debt for each year, but this time, the budget deficit will grow by 3%. First year GDP: \(1000 \times 1.03^1 = \$ 1,030\) First year budget deficit: \(30 \times 1.03^1 = \$ 30.9\) First year public debt: \(300 + 30.9 = \$ 330.9\) Debt-GDP ratio: \(\frac{330.9}{1030} = 0.3213\) Repeat for the next 9 years. c.

Find the real GDP and debt-GDP ratio for each year (20% budget deficit growth scenario)

In this case, the budget deficit grows by 20% every year. Follow the same steps as the previous scenarios to find the real GDP and public debt for each year, but this time, the budget deficit will grow by 20%. First year GDP: \(1000 \times 1.03^1 = \$ 1,030\) First year budget deficit: \(30 \times 1.20^1 = \$ 36\) First year public debt: \(300 + 36 = \$ 336\) Debt-GDP ratio: \(\frac{336}{1030} = 0.3262\) Repeat for the next 9 years. d.

Compare the results for all scenarios

In the constant budget deficit scenario, the debt-GDP ratio is smaller than the other two scenarios. Over time, real GDP grows, and the constant budget deficit represents a smaller share of GDP, causing the debt-GDP ratio to decrease. In the 3% and 20% budget deficit growth scenarios, as the budget deficit grows, so does the public debt. In these cases, the debt-GDP ratio increases more than the constant budget deficit scenario. The higher the budget deficit growth rate, the faster the debt-GDP ratio will increase.