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?

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Chapter9: Demand-side Equilibrium: Unemployment Or Inflation?
Section9.A: The Simple Algebra Of Income Determination And The Multiplier
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### 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 \( Y = 1900 \):
\[ AE = 625 + 0.75(1900) \]
\[
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 \( Y = 1900 \): \[ AE = 625 + 0.75(1900) \] \[
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