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The problem you provided involves supply and demand functions, which are given as:

- **Demand function**: \( Q_d = 230 - 4P \)
- **Supply function**: \( Q_s = -50 + 3P \)

The task is to:

1. **Calculate the equilibrium price (P) and quantity (Q).**
2. **Plot the graphs of both functions in one diagram.**
3. **Explain the meaning of the gradient for each function.**

### Step 1: Calculate the Equilibrium Price and Quantity
At equilibrium, the quantity demanded \( Q_d \) equals the quantity supplied \( Q_s \).

Thus, we set:
\[
230 - 4P = -50 + 3P
\]

Now, solve for \( P \):
\[
230 + 50 = 3P + 4P
\]
\[
280 = 7P
\]
\[
P = \frac{280}{7} = 40
\]

Now, substitute \( P = 40 \) into either the demand or supply function to find the equilibrium quantity:

For the demand function:
\[
Q_d = 230 - 4(40) = 230 - 160 = 70
\]

Thus, the **equilibrium price** is \( P = 40 \) and the **equilibrium quantity** is \( Q = 70 \).

### Step 2: Plotting the Graph
To plot the graph of both functions:
- The **demand function** is \( Q_d = 230 - 4P \), which has a y-intercept at 230 (when \( P = 0 \)) and a slope of -4.
- The **supply function** is \( Q_s = -50 + 3P \), which has a y-intercept at -50 (when \( P = 0 \)) and a slope of 3.

Both lines intersect at the equilibrium point \( (P = 40, Q = 70) \).

### Step 3: Explanation of the Gradients
- The **gradient of the demand function** \( Q_d = 230 - 4P \) is -4. This means that for every 1 unit increase in price, the quantity demanded decreases by 4 units. It reflects the law of demand, where higher prices result in lower quantity demanded.
  
- The **gradient of the supply function** \( Q_s = -50 + 3P \) is 3. This means that for every 1 unit increase in price, the quantity supplied increases by 3 units. This reflects the law of supply, where higher prices encourage producers to supply more of the good.

Would you like me to provide a detailed graph or further clarify any steps? Here are some related questions:

1. How do shifts in demand or supply affect the equilibrium price and quantity?
2. What would happen to the equilibrium if the demand function changed?
3. Can you explain the economic interpretation of a positive supply curve slope?
4. What is the role of price elasticity in these supply and demand functions?
5. How can changes in production costs influence the supply curve?

**Tip:** Always check that supply equals demand at the calculated equilibrium to verify your solution.

Diketahui fungsi permintaan suatu barang adalah Qd = 230 - 4P dan fungsi penawarannya adalah Qs = -50 + 3P. Hitunglah harga dan jumlah keseimbangan. a) Buatlah gambar grafik kedua fungsi tersebut dalam satu diagram. b) Jelaskan arti dari gradien pada masing-masing fungsi.

Learn how to calculate the equilibrium price and quantity from the demand function Qd = 230 - 4P and supply function Qs = -50 + 3P. This problem involves plotting both functions on a graph and explaining the meaning of the gradients for each function. Suitable for high school students studying economics.

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