IS at is the ut and Yn is the potential output.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
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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
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
### 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.
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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