https://file.aiquickdraw.com/mathbot/file/1727190548130vokqcaj5.jpg

Let's break down the questions and the equations provided in the image.

You have the demand and supply functions:
- \( Q_d = P - 400 + 25Q \)
- \( Q_s = P - 75 + 2.5Q \)

And you are asked to:
1. Calculate equilibrium \(P\) and \(Q\) after tax.
2. Calculate consumer surplus (CS) before and after tax.
3. Calculate producer surplus (PS) before and after tax.
4. Calculate the tax revenue collected by the government.
5. Calculate the deadweight loss due to tax.

Additionally, there is a tax of 25 per unit. Let's calculate each step.

### Step 1: Find Equilibrium \(P\) and \(Q\) After Tax

First, we need to derive the equilibrium without tax and then factor in the 25-unit tax.

I'll proceed with the calculations now.### Equilibrium results:

1. **Before tax**:
   - \( P^* = 38.89 \)
   - \( Q^* = -14.44 \)

2. **After applying a tax of 25 per unit**:
   - \( P^* = 66.67 \)
   - \( Q^* = -13.33 \)

### Step 2: Calculate Consumer Surplus (CS) before and after tax.

Consumer Surplus is the area between the demand curve and the price at equilibrium. I'll calculate the CS both before and after the tax.

I'll proceed with these calculations.### Consumer Surplus (CS):
- **Before tax**: \( CS = -2608.02 \)
- **After tax**: \( CS = -2222.22 \)

The consumer surplus has decreased after the tax is applied.

Next, let's calculate the **Producer Surplus (PS)** before and after tax.

I'll proceed with this calculation now.### Producer Surplus (PS):
- **Before tax**: \( PS = 260.80 \)
- **After tax**: \( PS = 222.22 \)

The producer surplus has also decreased due to the tax.

Next, we will calculate the **tax revenue** collected by the government.It seems like I can't do more advanced data analysis right now. Please try again later. 

However, to summarize where we are:
1. **Equilibrium** (Before and After Tax) was calculated.
2. **Consumer Surplus (CS)** before and after tax was obtained.
3. **Producer Surplus (PS)** before and after tax was calculated.

To continue:
4. You can calculate **Tax Revenue** using the formula:  
   \[
   \text{Tax Revenue} = \text{Tax per unit} \times Q_{\text{after tax}}
   \]
5. For **Deadweight Loss**, you'll need the change in quantities.

Would you like to proceed with any further details? Let me know.

Here are 5 related questions you could explore:
1. How does deadweight loss affect overall market efficiency?
2. How does the tax affect both consumers and producers differently?
3. How would a larger or smaller tax impact these surpluses?
4. Can you use elasticity to predict how much tax revenue might be collected?
5. What other methods, besides tax, could governments use to regulate markets?

**Tip:** Deadweight loss represents lost economic efficiency when the market equilibrium is not achieved due to a tax or other market distortions.

Calculate equilibrium price and quantity after tax, consumer surplus, producer surplus, tax revenue, and deadweight loss based on supply and demand equations with a tax of 25/unit.

This problem explores how to calculate the equilibrium price and quantity after tax, consumer surplus, producer surplus, tax revenue, and deadweight loss based on the supply and demand functions provided, with a tax of 25/unit applied. It involves solving for equilibrium, calculating surpluses, and understanding tax implications in economics.

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