The demand function is P = 15-Q and the supply function is P = 3 + 1/2Q. Then the government sets a subsidy of Rp1.5 per unit, then determine and describe the equilibrium before and after the subsidy!

### 1. **Equilibrium Before the Subsidy**

The **equilibrium price and quantity** occur when the quantity demanded equals the quantity supplied. This is determined by setting the **demand function** equal to the **supply function**:

\[
P_{\text{demand}} = P_{\text{supply}}
\]

Given:

- **Demand function:** \( P = 15 - Q \)
- **Supply function:** \( P = 3 + \frac{1}{2}Q \)

Set the two functions equal:

\[
15 - Q = 3 + \frac{1}{2}Q
\]

Now solve for \( Q \):

\[
15 - 3 = Q + \frac{1}{2}Q
\]
\[
12 = \frac{3}{2}Q
\]
\[
Q = \frac{12 \times 2}{3} = 8
\]

Substitute \( Q = 8 \) into either the demand or supply function to find \( P \):

\[
P = 15 - 8 = 7
\]

So, the **equilibrium price before the subsidy** is \( P = 7 \) and the **equilibrium quantity** is \( Q = 8 \).

### 2. **Equilibrium After the Subsidy**

When a subsidy is given, the effective price received by the suppliers increases by the amount of the subsidy. In this case, the subsidy is **Rp1.5 per unit**. 

The new **effective supply function** becomes:

\[
P + 1.5 = 3 + \frac{1}{2}Q
\]

Now set this new supply function equal to the demand function:

\[
15 - Q = (3 + \frac{1}{2}Q) - 1.5
\]
\[
15 - Q = 1.5 + \frac{1}{2}Q
\]

Solve for \( Q \):

\[
15 - 1.5 = Q + \frac{1}{2}Q
\]
\[
13.5 = \frac{3}{2}Q
\]
\[
Q = \frac{13.5 \times 2}{3} = 9
\]

Substitute \( Q = 9 \) into the demand function to find the new equilibrium price \( P \):

\[
P = 15 - 9 = 6
\]

### 3. **Summary of Equilibrium Before and After the Subsidy**

- **Before the subsidy:**
  - Equilibrium quantity \( Q = 8 \)
  - Equilibrium price \( P = 7 \)

- **After the subsidy:**
  - Equilibrium quantity \( Q = 9 \)
  - Equilibrium price \( P = 6 \)

The subsidy causes the equilibrium quantity to increase from 8 to 9 units, and the equilibrium price (the price consumers pay) to decrease from 7 to 6.

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Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What happens to consumer surplus after the subsidy is introduced?
2. How would the subsidy affect the government's budget?
3. How do you calculate producer surplus before and after the subsidy?
4. What happens if the subsidy increases to Rp3 per unit instead of Rp1.5?
5. How would a tax instead of a subsidy affect the market equilibrium?

**Tip:** Subsidies can shift the supply curve downward or to the right, lowering prices for consumers while increasing the quantity supplied.

Determine and describe the market equilibrium before and after a subsidy is introduced with demand function P = 15 - Q and supply function P = 3 + 1/2Q. This solution covers key concepts in equilibrium, subsidy impact, and linear equations, suitable for students in Grades 10-12.

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