**Text Transcription for Educational Website** --- Assume that in an economy the real interest rate equals \( r = 0.05 \), the rate of growth of real GDP equals \( \gamma = 0.03 \), and the primary deficit-to-GDP ratio equals \( d = 0.03 \) and is expected to remain constant. a) Write the equation for the dynamics of the debt-to-GDP ratio and show the dynamics in a graph. In the case the debt stabilizes, calculate the equilibrium level of debt (as % of GDP). b) What should be the level of the real interest rate (\( r \)), to stabilize debt-to-GDP at 150% without change in the primary deficit? Present this situation in a graph. --- **Graph/Diagram Explanation:** There are two parts mentioned for graphical representation, though no actual graphs are included in the image: 1. **Debt-to-GDP Dynamics Graph**: This graph would illustrate how the debt-to-GDP ratio changes over time, taking into account the given interest rate, GDP growth, and primary deficit. The x-axis typically represents time, and the y-axis represents the debt-to-GDP ratio. The intersection point where the line stabilizes indicates the equilibrium level of debt. 2. **Stabilization Graph for Different Interest Rates**: This graph would show how changing the real interest rate affects the stabilization of the debt-to-GDP ratio at 150%. The graph would depict scenarios of different interest rates on the y-axis against the debt-to-GDP ratio on the x-axis, highlighting the point where the 150% stabilization goal is achieved. Such graphs help in visualizing the relationship between the economic variables and understanding the impact of different interest rates on debt stabilization.
**Text Transcription for Educational Website** --- Assume that in an economy the real interest rate equals \( r = 0.05 \), the rate of growth of real GDP equals \( \gamma = 0.03 \), and the primary deficit-to-GDP ratio equals \( d = 0.03 \) and is expected to remain constant. a) Write the equation for the dynamics of the debt-to-GDP ratio and show the dynamics in a graph. In the case the debt stabilizes, calculate the equilibrium level of debt (as % of GDP). b) What should be the level of the real interest rate (\( r \)), to stabilize debt-to-GDP at 150% without change in the primary deficit? Present this situation in a graph. --- **Graph/Diagram Explanation:** There are two parts mentioned for graphical representation, though no actual graphs are included in the image: 1. **Debt-to-GDP Dynamics Graph**: This graph would illustrate how the debt-to-GDP ratio changes over time, taking into account the given interest rate, GDP growth, and primary deficit. The x-axis typically represents time, and the y-axis represents the debt-to-GDP ratio. The intersection point where the line stabilizes indicates the equilibrium level of debt. 2. **Stabilization Graph for Different Interest Rates**: This graph would show how changing the real interest rate affects the stabilization of the debt-to-GDP ratio at 150%. The graph would depict scenarios of different interest rates on the y-axis against the debt-to-GDP ratio on the x-axis, highlighting the point where the 150% stabilization goal is achieved. Such graphs help in visualizing the relationship between the economic variables and understanding the impact of different interest rates on debt stabilization.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
1
Transcribed Image Text:**Text Transcription for Educational Website**
---
Assume that in an economy the real interest rate equals \( r = 0.05 \), the rate of growth of real GDP equals \( \gamma = 0.03 \), and the primary deficit-to-GDP ratio equals \( d = 0.03 \) and is expected to remain constant.
a) Write the equation for the dynamics of the debt-to-GDP ratio and show the dynamics in a graph. In the case the debt stabilizes, calculate the equilibrium level of debt (as % of GDP).
b) What should be the level of the real interest rate (\( r \)), to stabilize debt-to-GDP at 150% without change in the primary deficit? Present this situation in a graph.
---
**Graph/Diagram Explanation:**
There are two parts mentioned for graphical representation, though no actual graphs are included in the image:
1. **Debt-to-GDP Dynamics Graph**: This graph would illustrate how the debt-to-GDP ratio changes over time, taking into account the given interest rate, GDP growth, and primary deficit. The x-axis typically represents time, and the y-axis represents the debt-to-GDP ratio. The intersection point where the line stabilizes indicates the equilibrium level of debt.
2. **Stabilization Graph for Different Interest Rates**: This graph would show how changing the real interest rate affects the stabilization of the debt-to-GDP ratio at 150%. The graph would depict scenarios of different interest rates on the y-axis against the debt-to-GDP ratio on the x-axis, highlighting the point where the 150% stabilization goal is achieved.
Such graphs help in visualizing the relationship between the economic variables and understanding the impact of different interest rates on debt stabilization.
Expert Solution
Step 1
Given:
Rate of interest (r)=0.05
Rate of growth of real GDP = 0.03
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