https://file.aiquickdraw.com/mathbot/file/172723235561338uzpg6o.jpg

The problem in the image is an economic supply and demand question, where the functions for demand and supply are given:

1. **Demand function:**
   \[
   P = 17 - Q_d
   \]
   Where \(P\) is the price, and \(Q_d\) is the quantity demanded.

2. **Supply function:**
   \[
   P = \frac{1}{4} Q_s + \frac{3}{4}
   \]
   Where \(P\) is the price, and \(Q_s\) is the quantity supplied.

### The questions are:

a. **Berapa harga keseimbangan dan jumlah keseimbangannya?**  
(What is the equilibrium price and quantity?)

b. **Berapa subsidi harus diberikan agar komoditas tersebut menjadi gratis?**  
(How much subsidy should be provided to make the commodity free?)

### Solution for part (a):
The equilibrium price and quantity occur when the quantity demanded equals the quantity supplied (\(Q_d = Q_s\)). Thus, we need to solve the system of equations:

\[
17 - Q_d = \frac{1}{4} Q_s + \frac{3}{4}
\]

Since \(Q_d = Q_s = Q\), we can substitute and solve for the equilibrium:

\[
17 - Q = \frac{1}{4} Q + \frac{3}{4}
\]

Now, let's solve this step by step.

The equilibrium quantity is \( Q = 13 \).

Now, to find the equilibrium price, we substitute \( Q = 13 \) into either the demand or supply function. I'll use the demand function:

\[
P = 17 - Q_d
\]

Let's calculate the equilibrium price.

The equilibrium price is \( P = 4 \).

### Summary for part (a):
- The **equilibrium quantity** is \( Q = 13 \).
- The **equilibrium price** is \( P = 4 \).

### Now, moving to part (b):
We need to determine the subsidy required to make the commodity free. This means we want the price \( P = 0 \). We will use the supply function for this:

\[
P = \frac{1}{4} Q_s + \frac{3}{4}
\]

Setting \( P = 0 \), we solve for the subsidy needed. Let's calculate that next.

To make the commodity free (i.e., \(P = 0\)), the quantity would need to be \( Q = -3 \), which doesn't make practical sense in economic terms. This indicates that simply lowering the price via the supply function wouldn't work without additional intervention, such as a subsidy.

The subsidy required would essentially need to cover the price difference to reduce the cost to zero. Since the equilibrium price is \( P = 4 \), the subsidy per unit would need to be 4 units of currency.

### Summary for part (b):
- A subsidy of **4 units per item** is required to make the commodity free.

Would you like further details or have any additional questions?

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Here are 5 related questions to expand on this topic:

1. How would the equilibrium change if the demand function shifted?
2. What would happen if the supply function included a tax instead of a subsidy?
3. How do you calculate consumer and producer surplus in this scenario?
4. How does the elasticity of demand affect the amount of subsidy needed?
5. How would the market adjust if both demand and supply functions changed simultaneously?

**Tip:** In economics, equilibrium is not always stable; it's important to analyze factors such as elasticity and external influences to predict long-term effects.

Permintaan akan suatu komoditas diketahui fungsinya P = 17 - Q_d, sedangkan penawaran P = 1/4 Q_s + 3/4. a) Berapa harga keseimbangan dan jumlah keseimbangannya? b) Berapa subsidi harus diberikan agar komoditas tersebut menjadi gratis?

This problem involves calculating the equilibrium price and quantity for a commodity given the supply and demand functions, as well as determining the necessary subsidy to make the commodity free. The solution uses core concepts of economics, such as market equilibrium and government intervention through subsidies.

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