https://file.aiquickdraw.com/mathbot/file/1729201556214ec01b3t4.jpg

The image you uploaded seems to explain a graphical and mathematical analysis related to consumer surplus and the impact of a tax on the market for a good. I'll break it down based on the contents of the image:

### Key Components:
1. **Initial Demand Equation:**
   \[
   Q_v = -2.5 \cdot P + 140
   \]
   Where:
   - \( Q_v \) is the quantity demanded in hectoliters.
   - \( P \) is the price per liter.
   This equation represents the initial demand curve.

2. **Tax Impact on Demand:**
   If the government imposes a tax of 10 euros per liter, the demand curve shifts downward. The new demand curve is given by:
   \[
   Q_v = -2.5 \cdot P + 115
   \]
   This equation shows a parallel shift of the demand curve due to the tax.

3. **New Intersection with Price Axis:**
   To find where the new demand curve intersects the price axis (when \( Q_v = 0 \)):
   \[
   0 = -2.5 \cdot P + 115
   \]
   Solving this gives \( P = 46 \) euros. This is the price at which demand drops to zero after the tax.

4. **Quantity Demanded at Price \( P = 30 \):**
   For the price \( P = 30 \), the quantity demanded can be calculated using the original demand equation:
   \[
   Q_v = -2.5 \cdot 30 + 140 = 40 \text{ hectoliters.}
   \]

5. **Consumer Surplus Shrinkage:**
   The consumer surplus shrinks due to the tax. The calculation of the consumer surplus is shown as:
   \[
   \left(\frac{(46 - 30) \cdot 40 \cdot 100}{2}\right) = 32,000 \text{ euros.}
   \]
   This represents the loss in consumer surplus due to the tax. The area lost is depicted in the green triangle in the graph.

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### Related Questions:
1. What is the significance of consumer surplus in economics?
2. How does a tax impact both consumer surplus and producer surplus?
3. Can you explain how the quantity demanded changes in response to price changes?
4. How would the calculation of consumer surplus differ if the tax were higher or lower?
5. What are the implications of such a tax on market equilibrium?

**Tip:** Remember, a tax usually causes the demand curve to shift downwards or the supply curve to shift upwards, depending on who bears the tax (consumer or producer).

How does a government tax impact consumer surplus and demand curve for a good?

This problem examines how a government-imposed tax affects the demand curve and reduces consumer surplus. The solution covers key algebraic concepts, including the shifts in the demand curve, new equilibrium price, and the decrease in consumer surplus. Suitable for advanced economics and algebra students.

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