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The image discusses a situation involving **market equilibrium** and **social economic surplus** in a supply and demand framework. The two curves presented are the **demand function** and **supply function**. The goal is to analyze the effect of a government intervention that imposes a cost of 5 units per item on the supply side due to health concerns.

The key functions provided are:

- **Demand curve**: \( p = 30 - x \)
- **Supply curve**: \( p = 5 + 0.25x \)

Where:
- \( p \) is the price of the product.
- \( x \) is the quantity of the product.

### To find the equilibrium:
1. **Set the demand equal to the supply** to find the equilibrium price and quantity.

\[
30 - x = 5 + 0.25x
\]

Now, solving for \( x \):

\[
30 - 5 = 0.25x + x
\]
\[
25 = 1.25x
\]
\[
x = \frac{25}{1.25} = 20
\]

Thus, the equilibrium quantity \( x_e \) is **20 units**.

2. **Substitute \( x = 20 \) into either the demand or supply function** to find the equilibrium price:

\[
p = 30 - 20 = 10
\]

Thus, the equilibrium price \( p_e \) is **10**.

### Impact of the 5-Unit Tax on the Supply Side:
The new supply curve shifts upwards by 5 units due to the tax, so the **new supply function** becomes:

\[
p = 5 + 0.25x + 5 = 10 + 0.25x
\]

Now, to find the new equilibrium after the tax:

\[
30 - x = 10 + 0.25x
\]
Solving for \( x \):

\[
30 - 10 = 0.25x + x
\]
\[
20 = 1.25x
\]
\[
x = \frac{20}{1.25} = 16
\]

Thus, the new equilibrium quantity \( x' = 16 \).

Substitute \( x = 16 \) into the new supply curve to find the new price:

\[
p = 10 + 0.25(16) = 10 + 4 = 14
\]

So, after the tax, the **new equilibrium price** \( p' = 14 \), and the **new equilibrium quantity** \( x' = 16 \).

This shows that the quantity sold in the market decreases due to the tax, while the price increases.

---

Would you like further details or explanations?

### Relative Questions:
1. What does market equilibrium represent in this scenario?
2. How does the tax affect both the demand and supply curves?
3. What would happen if the tax was placed on consumers instead of producers?
4. How can you calculate the consumer surplus before and after the tax?
5. What would be the deadweight loss due to this taxation?

**Tip**: When analyzing supply and demand shifts, always remember that taxes generally reduce the equilibrium quantity and affect prices depending on whether the tax is imposed on the supply or demand side.

Analyze the impact of a 5-unit tax on the supply side of a market with the demand curve p = 30 - x and supply curve p = 5 + 0.25x.

Explore the effects of a 5-unit tax on the supply side of a market with demand p = 30 - x and supply p = 5 + 0.25x. Learn how taxes influence equilibrium quantity and price with step-by-step solutions for finding the new equilibrium post-tax.

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