Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
I have the correct answers. All i want is an in depth explanation for how to solve Part C and Part D. NOT A OR B. Please just explain how to solve part A and D thank you
![## Understanding the Economy of Cranberry Republic through the IS-LM-PC Model
### Key Equations
1. **Phillips Curve:**
\[
\pi_t = \pi_t^e + 0.0006(Y_t - Y_n)
\]
- \(\pi_t\): Inflation rate at year \(t\)
- \(\pi_t^e\): Expected inflation at the beginning of year \(t\)
- \(Y_t\): Actual level of output
- \(Y_n\): Potential output
2. **IS Equation:**
\[
Y_t = 1,450 - 5,000 \times r_t
\]
- \(r_t\): Real interest rate
3. **LM Equation:**
\[
r_t = r^*
\]
- \(r^*\): Equilibrium (natural) real interest rate
### Expectations Formation
- Expected inflation is formed as:
\[
\pi_t^e = \pi_{t-1}
\]
### Questions
#### a. Output and Inflation Analysis
- **Assumption:**
- Last year’s inflation rate (\(\pi_{t-1}\)) = 3%
- Potential output (\(Y_n\)) = 1,000
- Fed’s chosen interest rate (\(r_t\)) = 10%
- **Task:**
- Calculate the actual output \(Y\) and inflation rate \(\pi\) at year \(t\).
- Determine whether the economy is booming or in recession.
#### b. Monetary Policy at Year \(t+1\)
- **Objective:**
- Return the output to potential (\(Y_n\)).
- **Task:**
- Decide whether the Fed should use expansionary or contractionary monetary policy.
- Target the real interest rate.
#### c. Inflation at Potential Output
- **Task:**
- Determine inflation rate (\(\pi\)) when output is at potential \(Y_n\).
#### d. Achieving Potential Output with 1% Inflation
- **Objective:**
- Set the real interest rate to achieve potential output with an inflation rate of 1%.
- **Task:**
- Compute and show the steps.
### Explanation of Diagram
While the visual outlines the equations and questions, detailed calculations provide the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12a3b6ff-52e0-4bd5-a604-586aafad7720%2F2a2d5bf1-64da-4266-a525-7a9bd7a6766e%2F0fnjb4r_processed.png&w=3840&q=75)
Transcribed Image Text:## Understanding the Economy of Cranberry Republic through the IS-LM-PC Model
### Key Equations
1. **Phillips Curve:**
\[
\pi_t = \pi_t^e + 0.0006(Y_t - Y_n)
\]
- \(\pi_t\): Inflation rate at year \(t\)
- \(\pi_t^e\): Expected inflation at the beginning of year \(t\)
- \(Y_t\): Actual level of output
- \(Y_n\): Potential output
2. **IS Equation:**
\[
Y_t = 1,450 - 5,000 \times r_t
\]
- \(r_t\): Real interest rate
3. **LM Equation:**
\[
r_t = r^*
\]
- \(r^*\): Equilibrium (natural) real interest rate
### Expectations Formation
- Expected inflation is formed as:
\[
\pi_t^e = \pi_{t-1}
\]
### Questions
#### a. Output and Inflation Analysis
- **Assumption:**
- Last year’s inflation rate (\(\pi_{t-1}\)) = 3%
- Potential output (\(Y_n\)) = 1,000
- Fed’s chosen interest rate (\(r_t\)) = 10%
- **Task:**
- Calculate the actual output \(Y\) and inflation rate \(\pi\) at year \(t\).
- Determine whether the economy is booming or in recession.
#### b. Monetary Policy at Year \(t+1\)
- **Objective:**
- Return the output to potential (\(Y_n\)).
- **Task:**
- Decide whether the Fed should use expansionary or contractionary monetary policy.
- Target the real interest rate.
#### c. Inflation at Potential Output
- **Task:**
- Determine inflation rate (\(\pi\)) when output is at potential \(Y_n\).
#### d. Achieving Potential Output with 1% Inflation
- **Objective:**
- Set the real interest rate to achieve potential output with an inflation rate of 1%.
- **Task:**
- Compute and show the steps.
### Explanation of Diagram
While the visual outlines the equations and questions, detailed calculations provide the

Transcribed Image Text:### Transcription and Explanation
#### Educational Context: Adjusting the Real Interest Rate
At year t+3, the Federal Reserve (Fed) can now set the real interest rate back at `r` found in part (b) to achieve potential output at an inflation rate of 1%.
---
#### Answers and Explanations:
- **Answer 1:** 950
- This could refer to a monetary value or an economic indicator relevant to the scenario.
- **Answer 2:** 0
- This may indicate a value such as a growth rate or the level of change in a parameter.
- **Answer 3:** in a recession
- This describes the economic condition where there is a decline in GDP or economic activity over an extended period.
- **Answer 4:** expansionary
- Refers to policies or conditions that aim to increase economic growth and expand economic output.
- **Answer 5:** 9
- Could denote a percentage, rate, or other quantitative economic figure.
- **Answer 6:** 0
- Another possible static or unchanged economic value.
- **Answer 7:** 8.66
- Similar to Answer 5, this might refer to a specific economic rate or measurement.
- **Answer 8:** 1017
- Could represent an economic output, monetary figure, or other numerical result.
- **Answer 9:** 1
- Likely corresponds to a target inflation rate or a similar economic target.
Each answer marked "Correct!" suggests these are verified responses to previous economic calculations or predictions.
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