Solve the following national Income model by using Creameré's Role.

Y=C+I_{0}+G_{0} c=200+0.6(y-7) T=0.2~Y Where, I_{0}=100 Gr_{0}=100

To solve the national income model using Creamer's role (which I assume refers to solving for equilibrium in an income-expenditure model), we will follow these steps:

Given:
- \( Y = C + I_0 + G_0 \)
- \( C = 200 + 0.6(Y - T) \)
- \( T = 0.2Y \)
- \( I_0 = 100 \)
- \( G_0 = 100 \)

### Step 1: Substitute \( T \) into the Consumption Function \( C \).
The consumption function is given as:
\[ C = 200 + 0.6(Y - T) \]
Substituting \( T = 0.2Y \) into the equation:
\[ C = 200 + 0.6(Y - 0.2Y) \]
\[ C = 200 + 0.6(0.8Y) \]
\[ C = 200 + 0.48Y \]

### Step 2: Set up the National Income Equation
Now, substitute \( C = 200 + 0.48Y \), \( I_0 = 100 \), and \( G_0 = 100 \) into the national income equation:
\[ Y = C + I_0 + G_0 \]
\[ Y = (200 + 0.48Y) + 100 + 100 \]

### Step 3: Solve for Equilibrium Income \( Y \)
Now, solve for \( Y \):
\[ Y = 200 + 0.48Y + 100 + 100 \]
\[ Y = 400 + 0.48Y \]
Rearrange to isolate \( Y \):
\[ Y - 0.48Y = 400 \]
\[ 0.52Y = 400 \]
\[ Y = \frac{400}{0.52} \]

Let me calculate this for you.The equilibrium national income \( Y \) is approximately 769.23.

Would you like further details on this solution or any specific part of the process?

Here are 5 related questions to deepen your understanding:
1. How would changes in government spending \( G_0 \) affect the national income \( Y \)?
2. What happens to the equilibrium income if the tax rate \( T \) changes?
3. How does the marginal propensity to consume (0.48) influence the multiplier effect in this model?
4. Can you derive the multiplier formula from the given model?
5. What if the investment \( I_0 \) increases by 50%? How would that impact \( Y \)?

**Tip:** When solving equilibrium models, isolating the variable you're solving for and balancing the equation step by step can simplify complex relationships.

Learn how to solve the national income model using Creameré's Role with a detailed step-by-step solution. This problem involves calculating equilibrium national income by integrating consumption, investment, and government spending functions. Suitable for advanced economics students and researchers.

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