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The problem provides the following equations for demand and supply:

1. **Demand Function (Permintaan):**
   \[
   P = 15 - Q
   \]

2. **Supply Function (Penawaran):**
   \[
   P = 3 + 0.5Q
   \]

It also mentions that the government gives a subsidy of 1.5 per unit of the good produced. The subsidy reduces the price that suppliers receive, so we adjust the supply equation accordingly.

### Step 1: Adjust the supply equation
With a subsidy, the price the suppliers effectively receive is reduced by the subsidy amount. This means the new supply equation becomes:
\[
P = 3 + 0.5Q - 1.5
\]
Simplifying this:
\[
P = 1.5 + 0.5Q
\]

### Step 2: Set the demand equal to the new supply equation
To find the equilibrium price and quantity, set the demand equal to the new supply equation:
\[
15 - Q = 1.5 + 0.5Q
\]

### Step 3: Solve for Q (quantity)
First, bring all the terms involving \(Q\) on one side:
\[
15 - 1.5 = 0.5Q + Q
\]
\[
13.5 = 1.5Q
\]

Now, solve for \(Q\):
\[
Q = \frac{13.5}{1.5} = 9
\]

### Step 4: Solve for P (price)
Substitute \(Q = 9\) into either the demand or the supply equation to find \(P\). Using the demand equation:
\[
P = 15 - 9 = 6
\]

### Final Answer:
The equilibrium price after the subsidy is **6**, and the equilibrium quantity is **9**.

Would you like more details or have any further questions?

Here are 5 related questions for further practice:
1. What would the equilibrium price be without the subsidy?
2. How does a subsidy impact consumer and producer surplus?
3. What happens to the equilibrium quantity if the subsidy is increased to 2?
4. Can you calculate the total government expenditure on subsidies in this case?
5. How would the equilibrium change if the demand function became \( P = 14 - Q \)?

**Tip:** Subsidies often lower the equilibrium price and increase the quantity traded in the market, benefiting consumers but costing the government.

Fungsi permintaan suatu barang ditunjukkan oleh persamaan P = 15 - Q, sedangkan penawarannya P = 3 + 0.5Q. Jika pemerintah memberikan subsidi sebesar 1.5 terhadap barang yang diproduksi, tentukan harga keseimbangan setelah subsidi yang tercipta di pasar.

Learn how to calculate the equilibrium price and quantity after a subsidy in a market where demand is P = 15 - Q and supply is P = 3 + 0.5Q. This problem covers supply and demand curves and the impact of subsidies, ideal for university economics students.

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