Question:
Consider the following information:
Consumption (πΆ) = 250 + 0.25$π_π$, where $π_π$ is disposable income Autonomous Investment ($πΌ_0$) = 100
Government Expenditure ($πΊ_0$) = 50
Income tax rate (π‘) = 20 percent
The equilibrium level of consumption in the economy is ____ (in integer).
Consider the following information:
Consumption (πΆ) = 250 + 0.25$π_π$, where $π_π$ is disposable income Autonomous Investment ($πΌ_0$) = 100
Government Expenditure ($πΊ_0$) = 50
Income tax rate (π‘) = 20 percent
The equilibrium level of consumption in the economy is ____ (in integer).
Consumption (πΆ) = 250 + 0.25$π_π$, where $π_π$ is disposable income Autonomous Investment ($πΌ_0$) = 100
Government Expenditure ($πΊ_0$) = 50
Income tax rate (π‘) = 20 percent
The equilibrium level of consumption in the economy is ____ (in integer).
Updated On: Feb 10, 2025
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Correct Answer: 350
Solution and Explanation
Finding the Equilibrium Level of Consumption
Step 1: Given Information
- Consumption function: \( C = 250 + 0.25 Y_d \)
- Autonomous investment: \( I_0 = 100 \)
- Government expenditure: \( G_0 = 50 \)
- Income tax rate: \( t = 20\% \) or \( 0.2 \)
Step 2: Equilibrium Condition
At equilibrium, total output (income) is equal to total expenditure:
\[ Y = C + I_0 + G_0 \]
Step 3: Expressing Disposable Income
Disposable income is given by:
\[ Y_d = Y - \text{Taxes} = Y - (t Y) = Y(1 - 0.2) = 0.8Y \]
Step 4: Substituting \( Y_d \) into Consumption Function
\[ C = 250 + 0.25 (0.8Y) \]
\[ C = 250 + 0.2Y \]
Step 5: Substituting into Equilibrium Condition
\[ Y = (250 + 0.2Y) + 100 + 50 \]
\[ Y - 0.2Y = 250 + 100 + 50 \]
\[ 0.8Y = 400 \]
\[ Y = \frac{400}{0.8} = 500 \]
Step 6: Finding Equilibrium Consumption
Substituting \( Y = 500 \) into the consumption function:
\[ C = 250 + 0.2(500) \]
\[ C = 250 + 100 = 350 \]
Final Answer:
The equilibrium level of consumption is 350.
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