Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Given this model, what would be the new equi8librium level of income were Investment spending to decline by 50?
![### Understanding Aggregate Expenditure and Equilibrium Output
This image contains mathematical representations and definitions related to Aggregate Expenditure (AE) and equilibrium output (Q) in an economy. Here's a breakdown of the components:
#### Definitions:
- **Q = AE**: This states that the equilibrium output (Q) is equal to aggregate expenditure (AE).
- **AE ≡ C + I + G + Xn**: Aggregate Expenditure (AE) is the sum of Consumption (C), Investment (I), Government Spending (G), and Net Exports (Xn).
- **C = Ca + mpc Q**: Consumption (C) is composed of autonomous consumption (Ca) and a fraction of the income (Q), which is the marginal propensity to consume (mpc).
#### Equations:
1. **Equilibrium Output Equation**:
\[
Q = \frac{1}{1 - mpc} \left( C_a + I + G + X_n \right)
\]
This equation calculates the equilibrium output, accounting for autonomous consumption and the marginal propensity to consume.
2. **Change in Equilibrium Output**:
\[
\Delta Q = \frac{1}{1 - mpc} \Delta \left( C_a + I + G + X_n \right)
\]
This equation assesses how the equilibrium output changes with variations in the components of aggregate expenditure.
#### Parameter Values:
- **I = 100**: Investment is 100.
- **G = 200**: Government spending is 200.
- **Ca = 100**: Autonomous consumption is 100.
- **Xn = −100**: Net exports are -100.
- **mpc = 3/4**: The marginal propensity to consume is 0.75.
These components and equations are essential in understanding how different factors influence the overall economic output and how changes in spending can affect the economy's equilibrium.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fd71a05-cce6-42ce-8872-636d0d92cbc9%2F7dfb788f-e6d3-4a68-85c9-bc313fa77f3e%2F4tc7uj7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Aggregate Expenditure and Equilibrium Output
This image contains mathematical representations and definitions related to Aggregate Expenditure (AE) and equilibrium output (Q) in an economy. Here's a breakdown of the components:
#### Definitions:
- **Q = AE**: This states that the equilibrium output (Q) is equal to aggregate expenditure (AE).
- **AE ≡ C + I + G + Xn**: Aggregate Expenditure (AE) is the sum of Consumption (C), Investment (I), Government Spending (G), and Net Exports (Xn).
- **C = Ca + mpc Q**: Consumption (C) is composed of autonomous consumption (Ca) and a fraction of the income (Q), which is the marginal propensity to consume (mpc).
#### Equations:
1. **Equilibrium Output Equation**:
\[
Q = \frac{1}{1 - mpc} \left( C_a + I + G + X_n \right)
\]
This equation calculates the equilibrium output, accounting for autonomous consumption and the marginal propensity to consume.
2. **Change in Equilibrium Output**:
\[
\Delta Q = \frac{1}{1 - mpc} \Delta \left( C_a + I + G + X_n \right)
\]
This equation assesses how the equilibrium output changes with variations in the components of aggregate expenditure.
#### Parameter Values:
- **I = 100**: Investment is 100.
- **G = 200**: Government spending is 200.
- **Ca = 100**: Autonomous consumption is 100.
- **Xn = −100**: Net exports are -100.
- **mpc = 3/4**: The marginal propensity to consume is 0.75.
These components and equations are essential in understanding how different factors influence the overall economic output and how changes in spending can affect the economy's equilibrium.
Expert Solution
Step 1: State the given information:
AE is the sum of C, I, G and Xn.
i.e., AE = C + I + G + Xn
_____________________________
Consumption function:
C = Ca + mpc Q
where Q is income.
_____________________________
At equilibrium, Q = AE
_____________________________
I = 100, G = 200, Ca = 100, Xn = -100 and mpc = 3/4
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