https://r2.erweima.ai/mathbot/image/1724504032359zc0qy22k.jpg

Let's break down the problem by translating and interpreting the mathematical relationships and questions presented in the image:

### Given:
1. **C = 800 + 0.8YD**
2. **I = 1,400 + 0.16Y**
3. **X = 600**
4. **M = 70 + 0.2Y**
5. **G = 750**
6. **T = 150 + 0.3Y**
7. **Y* = 8,500**

### Requirements:
1. **Calculate the equilibrium national income** and discuss the current budget balance.
2. **Calculate the budget balance** if government spending increases by 60. Evaluate the new budget balance.
3. **If the government wants to maintain the equilibrium income** (Y*), by how much should government spending be adjusted?
4. **Analyze the effect on savings (S)** given the changes.
5. **Calculate the total tax revenue** and the **marginal tax rate**.
6. **Determine the multiplier effect** on the economy.
7. **Determine the equilibrium national income** if investment increases by 20%.
8. **Calculate the balance of payments** and assess if there is a surplus or deficit.

### Approach:
1. **Equilibrium Condition:**  
   The national income equilibrium is determined where aggregate demand (AD) equals aggregate output (Y), i.e., \( AD = C + I + G + (X - M) \).

   Let's first calculate the equilibrium income using the equation \( AD = Y \) and then move on to the other questions.

2. **Budget Balance:**  
   Calculate the difference between government revenue (T) and spending (G).

3. **Policy Adjustments:**  
   Evaluate the necessary adjustments to G or T to achieve certain targets.

Let me calculate the equilibrium national income \( Y \) first and move step by step.

### Step 1: Equilibrium National Income
\[ Y = C + I + G + (X - M) \]

Substituting the given values:
\[
Y = \left(800 + 0.8YD\right) + \left(1,400 + 0.16Y\right) + 750 + \left(600 - \left(70 + 0.2Y\right)\right)
\]

Since \( YD = Y - T \), and \( T = 150 + 0.3Y \):

\[
YD = Y - (150 + 0.3Y) = 0.7Y - 150
\]

Now substitute \( YD \):

\[
Y = \left(800 + 0.8(0.7Y - 150)\right) + 1,400 + 0.16Y + 750 + 600 - (70 + 0.2Y)
\]

Expanding this equation:

\[
Y = 800 + 0.56Y - 120 + 1,400 + 0.16Y + 750 + 600 - 70 - 0.2Y
\]

Simplifying the terms:

\[
Y = (800 - 120 + 1,400 + 750 + 600 - 70) + (0.56Y + 0.16Y - 0.2Y)
\]
\[
Y = 3,360 + 0.52Y
\]
\[
0.48Y = 3,360
\]
\[
Y = \frac{3,360}{0.48} = 7,000
\]

So, the equilibrium national income \( Y \) is **7,000**.

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Would you like to continue with the remaining parts of the problem, such as calculating the budget balance or adjusting government spending?

Learn how to calculate equilibrium national income and budget balance using macroeconomic models. This problem involves understanding aggregate demand, government spending, taxes, and savings. Suitable for advanced college-level students and economics enthusiasts.

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