6. Suppose we hav following economy: • C=140+0.75Y ● Planned investment = 230 • G=280 T = 160 • TR (transfers) = 20 • NX=80 a. Find the planned aggregate expenditure function. b. What is the equilibrium output of this economy? c. If the economy's current output is 1,900, how much is the planned aggregate expenditure?
6. Suppose we hav following economy: • C=140+0.75Y ● Planned investment = 230 • G=280 T = 160 • TR (transfers) = 20 • NX=80 a. Find the planned aggregate expenditure function. b. What is the equilibrium output of this economy? c. If the economy's current output is 1,900, how much is the planned aggregate expenditure?
Chapter9: Demand-side Equilibrium: Unemployment Or Inflation?
Section9.A: The Simple Algebra Of Income Determination And The Multiplier
Problem 4TY
Related questions
Question
Please be sure to explain why and how to the questions
-Thank you
![---
### Aggregate Expenditure in an Economic Model
#### 6. Suppose we have the following economy:
- **Consumption Function (C)**: \( C = 140 + 0.75Y_d \)
- **Planned Investment**: 230
- **Government Spending (G)**: 280
- **Taxes (T)**: 160
- **Transfers (TR)**: 20
- **Net Exports (NX)**: 80
Questions:
**a. Find the planned aggregate expenditure function.**
To find the planned aggregate expenditure (AE), we sum up all the components of aggregate expenditure:
\[ AE = C + I_{planned} + G + NX \]
Given:
\[ C = 140 + 0.75Y_d \]
Where \( Y_d \) (disposable income) is:
\[ Y_d = Y - T + TR \]
Substituting \( Y_d \):
\[ Y_d = Y - 160 + 20 = Y - 140 \]
Therefore:
\[ C = 140 + 0.75(Y - 140) \]
\[ C = 140 + 0.75Y - 105 \]
\[ C = 35 + 0.75Y \]
Now, substitute into the AE equation:
\[ AE = C + I_{planned} + G + NX \]
\[ AE = (35 + 0.75Y) + 230 + 280 + 80 \]
\[ AE = 35 + 0.75Y + 590 \]
\[ AE = 625 + 0.75Y \]
**b. What is the equilibrium output of this economy?**
At equilibrium, output \(Y\) equals aggregate expenditure \(AE\):
\[ Y = AE \]
\[ Y = 625 + 0.75Y \]
Solving for \(Y\):
\[ Y - 0.75Y = 625 \]
\[ 0.25Y = 625 \]
\[ Y = \frac{625}{0.25} \]
\[ Y = 2500 \]
**c. If the economy’s current output is 1,900, how much is the planned aggregate expenditure?**
Using the AE function:
\[ AE = 625 + 0.75Y \]
For \( Y = 1900 \):
\[ AE = 625 + 0.75(1900) \]
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ab3af7c-68cd-4b68-9b3a-dae63e7506af%2F85ce5914-a60c-4ed5-b968-1b0825d46a83%2Fwosvti_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Aggregate Expenditure in an Economic Model
#### 6. Suppose we have the following economy:
- **Consumption Function (C)**: \( C = 140 + 0.75Y_d \)
- **Planned Investment**: 230
- **Government Spending (G)**: 280
- **Taxes (T)**: 160
- **Transfers (TR)**: 20
- **Net Exports (NX)**: 80
Questions:
**a. Find the planned aggregate expenditure function.**
To find the planned aggregate expenditure (AE), we sum up all the components of aggregate expenditure:
\[ AE = C + I_{planned} + G + NX \]
Given:
\[ C = 140 + 0.75Y_d \]
Where \( Y_d \) (disposable income) is:
\[ Y_d = Y - T + TR \]
Substituting \( Y_d \):
\[ Y_d = Y - 160 + 20 = Y - 140 \]
Therefore:
\[ C = 140 + 0.75(Y - 140) \]
\[ C = 140 + 0.75Y - 105 \]
\[ C = 35 + 0.75Y \]
Now, substitute into the AE equation:
\[ AE = C + I_{planned} + G + NX \]
\[ AE = (35 + 0.75Y) + 230 + 280 + 80 \]
\[ AE = 35 + 0.75Y + 590 \]
\[ AE = 625 + 0.75Y \]
**b. What is the equilibrium output of this economy?**
At equilibrium, output \(Y\) equals aggregate expenditure \(AE\):
\[ Y = AE \]
\[ Y = 625 + 0.75Y \]
Solving for \(Y\):
\[ Y - 0.75Y = 625 \]
\[ 0.25Y = 625 \]
\[ Y = \frac{625}{0.25} \]
\[ Y = 2500 \]
**c. If the economy’s current output is 1,900, how much is the planned aggregate expenditure?**
Using the AE function:
\[ AE = 625 + 0.75Y \]
For \( Y = 1900 \):
\[ AE = 625 + 0.75(1900) \]
\[
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Economics (MindTap Course List)
Economics
ISBN:
9781337617383
Author:
Roger A. Arnold
Publisher:
Cengage Learning
