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The image contains an economics-related mathematical problem involving supply and demand functions with taxation. Here is the transcription of the problem:

1. **Demand and Supply Functions:**
   - Demand Function: \( 29 - 3p = 3q \)
   - Supply Function: \( q = 4p - 1.5 \)
   - If the government imposes a tax \( t = 4.125 \).

Questions:
   a. Calculate the equilibrium price and quantity before the tax.
   b. Calculate the equilibrium price and quantity after the tax is imposed.
   c. Determine the tax burden on consumers and producers.
   d. Draw a graph to represent this situation.

### Step-by-Step Solution

**1. Find the equilibrium price and quantity before the tax:**

The equilibrium occurs when demand equals supply:
\[ 29 - 3p = 4p - 1.5 \]

Solve for \( p \) (price).

**2. Find the equilibrium price and quantity after the tax:**

With the tax, the supply function is adjusted. The new supply function would be:
\[ q = 4(p - t) - 1.5 = 4(p - 4.125) - 1.5 \]

Set the new supply equal to the demand and solve for the new price and quantity.

**3. Calculate the tax burden on consumers and producers:**

This can be found by comparing the difference between the new price consumers pay and the old equilibrium price for consumers, and similarly for producers (how much less they receive).

**4. Graph the supply and demand curves:**

The graph will show both the original and the shifted supply curve due to the tax, along with the changes in equilibrium.

Would you like me to work through the calculations in detail for any of these parts? Let me know if you'd like further clarification or additional steps. 

### 5 Related Questions:
1. How do you find the equilibrium price and quantity using algebra?
2. What is the economic effect of a tax on the supply function?
3. How can we calculate the consumer's share of the tax burden?
4. How does taxation affect both the equilibrium price and quantity?
5. Why do governments impose taxes, and what are its effects on supply and demand?

### Tip:
When solving supply and demand problems with taxes, always adjust the supply function first before recalculating the new equilibrium price.

Given the demand function 29 - 3p = 3q and the supply function q = 4p - 1.5, calculate the equilibrium price and quantity before and after a tax t = 4.125 is imposed. Additionally, determine the tax burden on consumers and producers, and draw a graph representing the situation.

Understand how to calculate equilibrium price and quantity before and after a tax in a supply-demand model. Learn the impact of a tax t = 4.125 on the supply function and determine the tax burden on consumers and producers. Ideal for high school students studying economics.

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