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 $\mathrm{\$}1,000$ billion per year and is expected to grow by $3\mathrm{\%}$ per year, the public debt is $\mathrm{\$}300$ billion at the beginning of the year, and the deficit is $\mathrm{\$}30$ 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 $\mathrm{\$}30$ 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 $3\mathrm{\%}$ 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 $20\mathrm{\%}$ 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: $1000\times {1.03}^1=\mathrm{\$}1,030$ First year public debt: $300+30=\mathrm{\$}330$ 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: $1000\times {1.03}^1=\mathrm{\$}1,030$ First year budget deficit: $30\times {1.03}^1=\mathrm{\$}30.9$ First year public debt: $300+30.9=\mathrm{\$}330.9$ 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: $1000\times {1.03}^1=\mathrm{\$}1,030$ First year budget deficit: $30\times {1.20}^1=\mathrm{\$}36$ First year public debt: $300+36=\mathrm{\$}336$ 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.

Key concepts

Budget Deficit

A budget deficit occurs when a government's spending exceeds its revenue. This implies that the government needs to borrow money to cover the shortfall, which in turn increases public debt. In the context of the Eastlandian economy exercise, the government's budget deficit starts with a constant $\mathrm{\$}30$ billion. Over time, the deficit can grow, impacting the economy depending on the growth rate. If the deficit remains constant, despite a rising GDP, it can gradually become a smaller percentage of GDP. However, if the deficit grows by either $3\mathrm{\%}$ or $20\mathrm{\%}$ annually, it can represent an increasing share of GDP. When deficits grow, it can potentially lead to higher interest rates in the future if investors anticipate difficulty in managing or repaying the increased debt. Understanding the budget deficit's role is crucial as it acts as a springboard to understand public debt dynamics and economic growth's impact.

Economic Growth

Economic growth reflects an economy's ability to produce more goods and services over time and is measured by the increase in real GDP. In Eastlandia, real GDP is projected to grow annually at $3\mathrm{\%}$, which naturally affects both government policies and debt management. Growth in GDP is beneficial to the economy for several reasons:

• Increased income levels improve overall living standards.
• Higher GDP enlarges the tax base without raising rates, potentially reducing budget deficits.
• It can make existing public debt more manageable as a larger economy generates more revenue to service debt payments.

When GDP grows at a steady rate, like Eastlandia's $3\mathrm{\%}$, it can help offset increases in public debt, improving the debt-GDP ratio over time. Thus, sustainable economic growth is key to managing and reducing the effective burden of high public debt.

Public Debt

Public debt, also referred to as government debt, is the total amount of money that the government owes to creditors. In Eastlandia, the initial debt is $\mathrm{\$}300$ billion, and it increases by the amount of the budget deficit from year to year. For example, if the deficit is constant, the debt increases by that constant amount yearly. As the deficit grows by $3\mathrm{\%}$ or $20\mathrm{\%}$, the debt grows more rapidly each year. Public debt is often measured in relation to GDP, known as the debt-GDP ratio. This ratio is a vital indicator of economic health and fiscal sustainability.

• A lower debt-GDP ratio suggests that a country can service its debts without incurring significant interest costs.
• A higher ratio may indicate an economy struggling with its debt, potentially leading to higher interest rates and reduced investment in growth-enhancing sectors.

Managing public debt is crucial since it ensures the government can meet its financial obligations without undermining economic growth.